| source University of Auckland (X) |
level |
department Engineering Science (X) |
Introduction to mathematical modelling. Differentiation and integration (polynomials, trigonometric, exponential, logarithmic, hyperbolic and rational functions). Integration by parts, substitution and numerical integration. Differential equations and their solutions (including Euler's method). Complex numbers and roots of functions. Vector and matrix algebra, transformations, solving systems of linear equations. Modelling using probability.
Score: 10.682133 Details | Listing | Web page
Introduction to mathematical modelling. Differentiation and integration (polynomials, trigonometric, exponential, logarithmic, hyperbolic and rational functions). Integration by parts, substitution and numerical integration. Differential equations and their solutions (including Euler's method). Complex numbers and roots of functions. Vector and matrix algebra, transformations, solving systems of linear equations. Modelling using probability. First and second order ordinary differential equations and solutions. Laplace transforms. Taylor series and series in general. Multivariate and vector calculus including divergence, gradient and curl. Further linear algebra. Eigenvalues and eigenvectors. Fourier series and transforms. Application of the techniques through appropriate modelling examples. Introductory data analysis and statistics.
Score: 10.682133 Details | Listing | Web page
Introduction to mathematical modelling. Differentiation and integration (polynomials, trigonometric, exponential, logarithmic, hyperbolic and rational functions). Integration by parts, substitution and numerical integration. Differential equations and their solutions (including Euler's method). Complex numbers and roots of functions. Vector and matrix algebra, transformations, solving systems of linear equations. Modelling using probability. First and second order ordinary differential equations and solutions. Laplace transforms. Taylor series and series in general. Multivariate and vector calculus including divergence, gradient and curl. Further linear algebra. Eigenvalues and eigenvectors. Fourier series and transforms. Application of the techniques through appropriate modelling examples. Introductory data analysis and statistics. Probability theory, random variables and distributions, statistics, linear algebra, discrete mathematics possibly including graph theory, trees and networks, optimisation.
Score: 10.682133 Details | Listing | Web page
Introduction to mathematical modelling. Differentiation and integration (polynomials, trigonometric, exponential, logarithmic, hyperbolic and rational functions). Integration by parts, substitution and numerical integration. Differential equations and their solutions (including Euler's method). Complex numbers and roots of functions. Vector and matrix algebra, transformations, solving systems of linear equations. Modelling using probability. First and second order ordinary differential equations and solutions. Laplace transforms. Taylor series and series in general. Multivariate and vector calculus including divergence, gradient and curl. Further linear algebra. Eigenvalues and eigenvectors. Fourier series and transforms. Application of the techniques through appropriate modelling examples. Introductory data analysis and statistics. Probability theory, random variables and distributions, statistics, linear algebra, discrete mathematics possibly including graph theory, trees and networks, optimisation. Introduction to digital electronics, computer organisation and computational techniques. Digital gates, combinatorial and synchronous circuits, data representation, instruction sets, memory, hardware, interfacing. Numerical computation, numerical algorithms.
Score: 10.682133 Details | Listing | Web page
Introduction to mathematical modelling. Differentiation and integration (polynomials, trigonometric, exponential, logarithmic, hyperbolic and rational functions). Integration by parts, substitution and numerical integration. Differential equations and their solutions (including Euler's method). Complex numbers and roots of functions. Vector and matrix algebra, transformations, solving systems of linear equations. Modelling using probability. First and second order ordinary differential equations and solutions. Laplace transforms. Taylor series and series in general. Multivariate and vector calculus including divergence, gradient and curl. Further linear algebra. Eigenvalues and eigenvectors. Fourier series and transforms. Application of the techniques through appropriate modelling examples. Introductory data analysis and statistics. Probability theory, random variables and distributions, statistics, linear algebra, discrete mathematics possibly including graph theory, trees and networks, optimisation. Introduction to digital electronics, computer organisation and computational techniques. Digital gates, combinatorial and synchronous circuits, data representation, instruction sets, memory, hardware, interfacing. Numerical computation, numerical algorithms. Emphasises the relationship between business and industrial applications and their associated operations research models. Software packages will be used to solve practical problems. Topics such as: linear programming, transportation and assignment models, network algorithms, queues, inventory models and simulation will be considered.
Score: 10.682133 Details | Listing | Web page
Introduction to mathematical modelling. Differentiation and integration (polynomials, trigonometric, exponential, logarithmic, hyperbolic and rational functions). Integration by parts, substitution and numerical integration. Differential equations and their solutions (including Euler's method). Complex numbers and roots of functions. Vector and matrix algebra, transformations, solving systems of linear equations. Modelling using probability. First and second order ordinary differential equations and solutions. Laplace transforms. Taylor series and series in general. Multivariate and vector calculus including divergence, gradient and curl. Further linear algebra. Eigenvalues and eigenvectors. Fourier series and transforms. Application of the techniques through appropriate modelling examples. Introductory data analysis and statistics. Probability theory, random variables and distributions, statistics, linear algebra, discrete mathematics possibly including graph theory, trees and networks, optimisation. Introduction to digital electronics, computer organisation and computational techniques. Digital gates, combinatorial and synchronous circuits, data representation, instruction sets, memory, hardware, interfacing. Numerical computation, numerical algorithms. Emphasises the relationship between business and industrial applications and their associated operations research models. Software packages will be used to solve practical problems. Topics such as: linear programming, transportation and assignment models, network algorithms, queues, inventory models and simulation will be considered. Introduction to concepts of modelling of engineering problems, including model formulation, dimensional analysis, solution procedures, comparisons with reality, and shortcomings, with examples from elementary mechanics, structures, hydrostatics, one-dimensional heat, diffusion and fluid motion. Further development of problem-solving skills and group project work. The use of computer tools in engineering design, including advanced spreadsheeting integrated with solid modelling.
Score: 10.682133 Details | Listing | Web page
Introduction to mathematical modelling. Differentiation and integration (polynomials, trigonometric, exponential, logarithmic, hyperbolic and rational functions). Integration by parts, substitution and numerical integration. Differential equations and their solutions (including Euler's method). Complex numbers and roots of functions. Vector and matrix algebra, transformations, solving systems of linear equations. Modelling using probability. First and second order ordinary differential equations and solutions. Laplace transforms. Taylor series and series in general. Multivariate and vector calculus including divergence, gradient and curl. Further linear algebra. Eigenvalues and eigenvectors. Fourier series and transforms. Application of the techniques through appropriate modelling examples. Introductory data analysis and statistics. Probability theory, random variables and distributions, statistics, linear algebra, discrete mathematics possibly including graph theory, trees and networks, optimisation. Introduction to digital electronics, computer organisation and computational techniques. Digital gates, combinatorial and synchronous circuits, data representation, instruction sets, memory, hardware, interfacing. Numerical computation, numerical algorithms. Emphasises the relationship between business and industrial applications and their associated operations research models. Software packages will be used to solve practical problems. Topics such as: linear programming, transportation and assignment models, network algorithms, queues, inventory models and simulation will be considered. Introduction to concepts of modelling of engineering problems, including model formulation, dimensional analysis, solution procedures, comparisons with reality, and shortcomings, with examples from elementary mechanics, structures, hydrostatics, one-dimensional heat, diffusion and fluid motion. Further development of problem-solving skills and group project work. The use of computer tools in engineering design, including advanced spreadsheeting integrated with solid modelling. A selection from: ordinary differential equations, systems of equations, analytical and numerical methods, non-linear ODEs, partial differential equations, separation of variables, numerical methods for solving PDEs, models for optimisation, industrial statistics, data analysis, regression, experimental design reliability methods, regression.
Score: 10.682133 Details | Listing | Web page
Introduction to mathematical modelling. Differentiation and integration (polynomials, trigonometric, exponential, logarithmic, hyperbolic and rational functions). Integration by parts, substitution and numerical integration. Differential equations and their solutions (including Euler's method). Complex numbers and roots of functions. Vector and matrix algebra, transformations, solving systems of linear equations. Modelling using probability. First and second order ordinary differential equations and solutions. Laplace transforms. Taylor series and series in general. Multivariate and vector calculus including divergence, gradient and curl. Further linear algebra. Eigenvalues and eigenvectors. Fourier series and transforms. Application of the techniques through appropriate modelling examples. Introductory data analysis and statistics. Probability theory, random variables and distributions, statistics, linear algebra, discrete mathematics possibly including graph theory, trees and networks, optimisation. Introduction to digital electronics, computer organisation and computational techniques. Digital gates, combinatorial and synchronous circuits, data representation, instruction sets, memory, hardware, interfacing. Numerical computation, numerical algorithms. Emphasises the relationship between business and industrial applications and their associated operations research models. Software packages will be used to solve practical problems. Topics such as: linear programming, transportation and assignment models, network algorithms, queues, inventory models and simulation will be considered. Introduction to concepts of modelling of engineering problems, including model formulation, dimensional analysis, solution procedures, comparisons with reality, and shortcomings, with examples from elementary mechanics, structures, hydrostatics, one-dimensional heat, diffusion and fluid motion. Further development of problem-solving skills and group project work. The use of computer tools in engineering design, including advanced spreadsheeting integrated with solid modelling. A selection from: ordinary differential equations, systems of equations, analytical and numerical methods, non-linear ODEs, partial differential equations, separation of variables, numerical methods for solving PDEs, models for optimisation, industrial statistics, data analysis, regression, experimental design reliability methods, regression. Complex Analysis, including complex numbers, analytic functions, complex integration, Cauchy's theorem, Laurent series, residue theory; Laplace transforms; Modelling with partial differential equations, including electronic and electrical applications; Fourier Analysis, Fourier transform, Fast Fourier transform; Optimisation, including unconstrained and constrained models, linear programming and nonlinear optimisation.
Score: 10.682133 Details | Listing | Web page
Introduction to mathematical modelling. Differentiation and integration (polynomials, trigonometric, exponential, logarithmic, hyperbolic and rational functions). Integration by parts, substitution and numerical integration. Differential equations and their solutions (including Euler's method). Complex numbers and roots of functions. Vector and matrix algebra, transformations, solving systems of linear equations. Modelling using probability. First and second order ordinary differential equations and solutions. Laplace transforms. Taylor series and series in general. Multivariate and vector calculus including divergence, gradient and curl. Further linear algebra. Eigenvalues and eigenvectors. Fourier series and transforms. Application of the techniques through appropriate modelling examples. Introductory data analysis and statistics. Probability theory, random variables and distributions, statistics, linear algebra, discrete mathematics possibly including graph theory, trees and networks, optimisation. Introduction to digital electronics, computer organisation and computational techniques. Digital gates, combinatorial and synchronous circuits, data representation, instruction sets, memory, hardware, interfacing. Numerical computation, numerical algorithms. Emphasises the relationship between business and industrial applications and their associated operations research models. Software packages will be used to solve practical problems. Topics such as: linear programming, transportation and assignment models, network algorithms, queues, inventory models and simulation will be considered. Introduction to concepts of modelling of engineering problems, including model formulation, dimensional analysis, solution procedures, comparisons with reality, and shortcomings, with examples from elementary mechanics, structures, hydrostatics, one-dimensional heat, diffusion and fluid motion. Further development of problem-solving skills and group project work. The use of computer tools in engineering design, including advanced spreadsheeting integrated with solid modelling. A selection from: ordinary differential equations, systems of equations, analytical and numerical methods, non-linear ODEs, partial differential equations, separation of variables, numerical methods for solving PDEs, models for optimisation, industrial statistics, data analysis, regression, experimental design reliability methods, regression. Complex Analysis, including complex numbers, analytic functions, complex integration, Cauchy's theorem, Laurent series, residue theory; Laplace transforms; Modelling with partial differential equations, including electronic and electrical applications; Fourier Analysis, Fourier transform, Fast Fourier transform; Optimisation, including unconstrained and constrained models, linear programming and nonlinear optimisation. Mathematical modelling using ordinary and partial differential equations. Probability. Conditional probability, random variables as models of a population, common distribution models, the Poisson process, applications to reliability. Exploratory data analysis, confidence intervals, tests of hypothesis, t-tests, sample tests and intervals, paired comparisons. Introduction to one-way ANOVA. Linear and polynomial regression, regression diagnostics.
Score: 10.682133 Details | Listing | Web page
Introduction to mathematical modelling. Differentiation and integration (polynomials, trigonometric, exponential, logarithmic, hyperbolic and rational functions). Integration by parts, substitution and numerical integration. Differential equations and their solutions (including Euler's method). Complex numbers and roots of functions. Vector and matrix algebra, transformations, solving systems of linear equations. Modelling using probability. First and second order ordinary differential equations and solutions. Laplace transforms. Taylor series and series in general. Multivariate and vector calculus including divergence, gradient and curl. Further linear algebra. Eigenvalues and eigenvectors. Fourier series and transforms. Application of the techniques through appropriate modelling examples. Introductory data analysis and statistics. Probability theory, random variables and distributions, statistics, linear algebra, discrete mathematics possibly including graph theory, trees and networks, optimisation. Introduction to digital electronics, computer organisation and computational techniques. Digital gates, combinatorial and synchronous circuits, data representation, instruction sets, memory, hardware, interfacing. Numerical computation, numerical algorithms. Emphasises the relationship between business and industrial applications and their associated operations research models. Software packages will be used to solve practical problems. Topics such as: linear programming, transportation and assignment models, network algorithms, queues, inventory models and simulation will be considered. Introduction to concepts of modelling of engineering problems, including model formulation, dimensional analysis, solution procedures, comparisons with reality, and shortcomings, with examples from elementary mechanics, structures, hydrostatics, one-dimensional heat, diffusion and fluid motion. Further development of problem-solving skills and group project work. The use of computer tools in engineering design, including advanced spreadsheeting integrated with solid modelling. A selection from: ordinary differential equations, systems of equations, analytical and numerical methods, non-linear ODEs, partial differential equations, separation of variables, numerical methods for solving PDEs, models for optimisation, industrial statistics, data analysis, regression, experimental design reliability methods, regression. Complex Analysis, including complex numbers, analytic functions, complex integration, Cauchy's theorem, Laurent series, residue theory; Laplace transforms; Modelling with partial differential equations, including electronic and electrical applications; Fourier Analysis, Fourier transform, Fast Fourier transform; Optimisation, including unconstrained and constrained models, linear programming and nonlinear optimisation. Mathematical modelling using ordinary and partial differential equations. Probability. Conditional probability, random variables as models of a population, common distribution models, the Poisson process, applications to reliability. Exploratory data analysis, confidence intervals, tests of hypothesis, t-tests, sample tests and intervals, paired comparisons. Introduction to one-way ANOVA. Linear and polynomial regression, regression diagnostics. Numerical algorithms and their translation to computer code. A selection of topics from numerical solution of linear equations, eigen problems, ordinary differential equations, numerical integration, nonlinear equations, finite differences and partial differential equations.
Score: 10.682133 Details | Listing | Web page
Introduction to mathematical modelling. Differentiation and integration (polynomials, trigonometric, exponential, logarithmic, hyperbolic and rational functions). Integration by parts, substitution and numerical integration. Differential equations and their solutions (including Euler's method). Complex numbers and roots of functions. Vector and matrix algebra, transformations, solving systems of linear equations. Modelling using probability. First and second order ordinary differential equations and solutions. Laplace transforms. Taylor series and series in general. Multivariate and vector calculus including divergence, gradient and curl. Further linear algebra. Eigenvalues and eigenvectors. Fourier series and transforms. Application of the techniques through appropriate modelling examples. Introductory data analysis and statistics. Probability theory, random variables and distributions, statistics, linear algebra, discrete mathematics possibly including graph theory, trees and networks, optimisation. Introduction to digital electronics, computer organisation and computational techniques. Digital gates, combinatorial and synchronous circuits, data representation, instruction sets, memory, hardware, interfacing. Numerical computation, numerical algorithms. Emphasises the relationship between business and industrial applications and their associated operations research models. Software packages will be used to solve practical problems. Topics such as: linear programming, transportation and assignment models, network algorithms, queues, inventory models and simulation will be considered. Introduction to concepts of modelling of engineering problems, including model formulation, dimensional analysis, solution procedures, comparisons with reality, and shortcomings, with examples from elementary mechanics, structures, hydrostatics, one-dimensional heat, diffusion and fluid motion. Further development of problem-solving skills and group project work. The use of computer tools in engineering design, including advanced spreadsheeting integrated with solid modelling. A selection from: ordinary differential equations, systems of equations, analytical and numerical methods, non-linear ODEs, partial differential equations, separation of variables, numerical methods for solving PDEs, models for optimisation, industrial statistics, data analysis, regression, experimental design reliability methods, regression. Complex Analysis, including complex numbers, analytic functions, complex integration, Cauchy's theorem, Laurent series, residue theory; Laplace transforms; Modelling with partial differential equations, including electronic and electrical applications; Fourier Analysis, Fourier transform, Fast Fourier transform; Optimisation, including unconstrained and constrained models, linear programming and nonlinear optimisation. Mathematical modelling using ordinary and partial differential equations. Probability. Conditional probability, random variables as models of a population, common distribution models, the Poisson process, applications to reliability. Exploratory data analysis, confidence intervals, tests of hypothesis, t-tests, sample tests and intervals, paired comparisons. Introduction to one-way ANOVA. Linear and polynomial regression, regression diagnostics. Numerical algorithms and their translation to computer code. A selection of topics from numerical solution of linear equations, eigen problems, ordinary differential equations, numerical integration, nonlinear equations, finite differences and partial differential equations. Vector calculus and integral theorems. Continuum hypothesis, indicial notation, deformation, strain, traction, stress, principal directions, tensors, invariants, constitutive laws, isotropy, homogeneity. Navier-Stokes and Navier's equations. Isotropic elasticity, elastic moduli, plane stress and plane strain. Airy stress function, Viscous flow, simple solutions of the Navier-Stokes equations. Flow over flat plates, boundary layers. Ideal flow, velocity potential, stream function, 2-D flows.
Score: 10.682133 Details | Listing | Web page
Introduction to mathematical modelling. Differentiation and integration (polynomials, trigonometric, exponential, logarithmic, hyperbolic and rational functions). Integration by parts, substitution and numerical integration. Differential equations and their solutions (including Euler's method). Complex numbers and roots of functions. Vector and matrix algebra, transformations, solving systems of linear equations. Modelling using probability. First and second order ordinary differential equations and solutions. Laplace transforms. Taylor series and series in general. Multivariate and vector calculus including divergence, gradient and curl. Further linear algebra. Eigenvalues and eigenvectors. Fourier series and transforms. Application of the techniques through appropriate modelling examples. Introductory data analysis and statistics. Probability theory, random variables and distributions, statistics, linear algebra, discrete mathematics possibly including graph theory, trees and networks, optimisation. Introduction to digital electronics, computer organisation and computational techniques. Digital gates, combinatorial and synchronous circuits, data representation, instruction sets, memory, hardware, interfacing. Numerical computation, numerical algorithms. Emphasises the relationship between business and industrial applications and their associated operations research models. Software packages will be used to solve practical problems. Topics such as: linear programming, transportation and assignment models, network algorithms, queues, inventory models and simulation will be considered. Introduction to concepts of modelling of engineering problems, including model formulation, dimensional analysis, solution procedures, comparisons with reality, and shortcomings, with examples from elementary mechanics, structures, hydrostatics, one-dimensional heat, diffusion and fluid motion. Further development of problem-solving skills and group project work. The use of computer tools in engineering design, including advanced spreadsheeting integrated with solid modelling. A selection from: ordinary differential equations, systems of equations, analytical and numerical methods, non-linear ODEs, partial differential equations, separation of variables, numerical methods for solving PDEs, models for optimisation, industrial statistics, data analysis, regression, experimental design reliability methods, regression. Complex Analysis, including complex numbers, analytic functions, complex integration, Cauchy's theorem, Laurent series, residue theory; Laplace transforms; Modelling with partial differential equations, including electronic and electrical applications; Fourier Analysis, Fourier transform, Fast Fourier transform; Optimisation, including unconstrained and constrained models, linear programming and nonlinear optimisation. Mathematical modelling using ordinary and partial differential equations. Probability. Conditional probability, random variables as models of a population, common distribution models, the Poisson process, applications to reliability. Exploratory data analysis, confidence intervals, tests of hypothesis, t-tests, sample tests and intervals, paired comparisons. Introduction to one-way ANOVA. Linear and polynomial regression, regression diagnostics. Numerical algorithms and their translation to computer code. A selection of topics from numerical solution of linear equations, eigen problems, ordinary differential equations, numerical integration, nonlinear equations, finite differences and partial differential equations. Vector calculus and integral theorems. Continuum hypothesis, indicial notation, deformation, strain, traction, stress, principal directions, tensors, invariants, constitutive laws, isotropy, homogeneity. Navier-Stokes and Navier's equations. Isotropic elasticity, elastic moduli, plane stress and plane strain. Airy stress function, Viscous flow, simple solutions of the Navier-Stokes equations. Flow over flat plates, boundary layers. Ideal flow, velocity potential, stream function, 2-D flows. Use of optimisation modelling languages, simulation software and databases, with an emphasis on practical problem solving and laboratory-based learning.
Score: 10.682133 Details | Listing | Web page
Introduction to mathematical modelling. Differentiation and integration (polynomials, trigonometric, exponential, logarithmic, hyperbolic and rational functions). Integration by parts, substitution and numerical integration. Differential equations and their solutions (including Euler's method). Complex numbers and roots of functions. Vector and matrix algebra, transformations, solving systems of linear equations. Modelling using probability. First and second order ordinary differential equations and solutions. Laplace transforms. Taylor series and series in general. Multivariate and vector calculus including divergence, gradient and curl. Further linear algebra. Eigenvalues and eigenvectors. Fourier series and transforms. Application of the techniques through appropriate modelling examples. Introductory data analysis and statistics. Probability theory, random variables and distributions, statistics, linear algebra, discrete mathematics possibly including graph theory, trees and networks, optimisation. Introduction to digital electronics, computer organisation and computational techniques. Digital gates, combinatorial and synchronous circuits, data representation, instruction sets, memory, hardware, interfacing. Numerical computation, numerical algorithms. Emphasises the relationship between business and industrial applications and their associated operations research models. Software packages will be used to solve practical problems. Topics such as: linear programming, transportation and assignment models, network algorithms, queues, inventory models and simulation will be considered. Introduction to concepts of modelling of engineering problems, including model formulation, dimensional analysis, solution procedures, comparisons with reality, and shortcomings, with examples from elementary mechanics, structures, hydrostatics, one-dimensional heat, diffusion and fluid motion. Further development of problem-solving skills and group project work. The use of computer tools in engineering design, including advanced spreadsheeting integrated with solid modelling. A selection from: ordinary differential equations, systems of equations, analytical and numerical methods, non-linear ODEs, partial differential equations, separation of variables, numerical methods for solving PDEs, models for optimisation, industrial statistics, data analysis, regression, experimental design reliability methods, regression. Complex Analysis, including complex numbers, analytic functions, complex integration, Cauchy's theorem, Laurent series, residue theory; Laplace transforms; Modelling with partial differential equations, including electronic and electrical applications; Fourier Analysis, Fourier transform, Fast Fourier transform; Optimisation, including unconstrained and constrained models, linear programming and nonlinear optimisation. Mathematical modelling using ordinary and partial differential equations. Probability. Conditional probability, random variables as models of a population, common distribution models, the Poisson process, applications to reliability. Exploratory data analysis, confidence intervals, tests of hypothesis, t-tests, sample tests and intervals, paired comparisons. Introduction to one-way ANOVA. Linear and polynomial regression, regression diagnostics. Numerical algorithms and their translation to computer code. A selection of topics from numerical solution of linear equations, eigen problems, ordinary differential equations, numerical integration, nonlinear equations, finite differences and partial differential equations. Vector calculus and integral theorems. Continuum hypothesis, indicial notation, deformation, strain, traction, stress, principal directions, tensors, invariants, constitutive laws, isotropy, homogeneity. Navier-Stokes and Navier's equations. Isotropic elasticity, elastic moduli, plane stress and plane strain. Airy stress function, Viscous flow, simple solutions of the Navier-Stokes equations. Flow over flat plates, boundary layers. Ideal flow, velocity potential, stream function, 2-D flows. Use of optimisation modelling languages, simulation software and databases, with an emphasis on practical problem solving and laboratory-based learning. Applications of elasticity and fluid dynamics theory to engineering problems including design and analysis of mechanical assemblies. Group projects to formulate design proposals, including costings for development and manufacture. Underlying Finite Element Modelling (FEM) and Continuum Mechanics concepts. Utilisation of 3D CAD and FEM software during both design and analysis phases.
Score: 10.682133 Details | Listing | Web page
Introduction to mathematical modelling. Differentiation and integration (polynomials, trigonometric, exponential, logarithmic, hyperbolic and rational functions). Integration by parts, substitution and numerical integration. Differential equations and their solutions (including Euler's method). Complex numbers and roots of functions. Vector and matrix algebra, transformations, solving systems of linear equations. Modelling using probability. First and second order ordinary differential equations and solutions. Laplace transforms. Taylor series and series in general. Multivariate and vector calculus including divergence, gradient and curl. Further linear algebra. Eigenvalues and eigenvectors. Fourier series and transforms. Application of the techniques through appropriate modelling examples. Introductory data analysis and statistics. Probability theory, random variables and distributions, statistics, linear algebra, discrete mathematics possibly including graph theory, trees and networks, optimisation. Introduction to digital electronics, computer organisation and computational techniques. Digital gates, combinatorial and synchronous circuits, data representation, instruction sets, memory, hardware, interfacing. Numerical computation, numerical algorithms. Emphasises the relationship between business and industrial applications and their associated operations research models. Software packages will be used to solve practical problems. Topics such as: linear programming, transportation and assignment models, network algorithms, queues, inventory models and simulation will be considered. Introduction to concepts of modelling of engineering problems, including model formulation, dimensional analysis, solution procedures, comparisons with reality, and shortcomings, with examples from elementary mechanics, structures, hydrostatics, one-dimensional heat, diffusion and fluid motion. Further development of problem-solving skills and group project work. The use of computer tools in engineering design, including advanced spreadsheeting integrated with solid modelling. A selection from: ordinary differential equations, systems of equations, analytical and numerical methods, non-linear ODEs, partial differential equations, separation of variables, numerical methods for solving PDEs, models for optimisation, industrial statistics, data analysis, regression, experimental design reliability methods, regression. Complex Analysis, including complex numbers, analytic functions, complex integration, Cauchy's theorem, Laurent series, residue theory; Laplace transforms; Modelling with partial differential equations, including electronic and electrical applications; Fourier Analysis, Fourier transform, Fast Fourier transform; Optimisation, including unconstrained and constrained models, linear programming and nonlinear optimisation. Mathematical modelling using ordinary and partial differential equations. Probability. Conditional probability, random variables as models of a population, common distribution models, the Poisson process, applications to reliability. Exploratory data analysis, confidence intervals, tests of hypothesis, t-tests, sample tests and intervals, paired comparisons. Introduction to one-way ANOVA. Linear and polynomial regression, regression diagnostics. Numerical algorithms and their translation to computer code. A selection of topics from numerical solution of linear equations, eigen problems, ordinary differential equations, numerical integration, nonlinear equations, finite differences and partial differential equations. Vector calculus and integral theorems. Continuum hypothesis, indicial notation, deformation, strain, traction, stress, principal directions, tensors, invariants, constitutive laws, isotropy, homogeneity. Navier-Stokes and Navier's equations. Isotropic elasticity, elastic moduli, plane stress and plane strain. Airy stress function, Viscous flow, simple solutions of the Navier-Stokes equations. Flow over flat plates, boundary layers. Ideal flow, velocity potential, stream function, 2-D flows. Use of optimisation modelling languages, simulation software and databases, with an emphasis on practical problem solving and laboratory-based learning. Applications of elasticity and fluid dynamics theory to engineering problems including design and analysis of mechanical assemblies. Group projects to formulate design proposals, including costings for development and manufacture. Underlying Finite Element Modelling (FEM) and Continuum Mechanics concepts. Utilisation of 3D CAD and FEM software during both design and analysis phases. Linear programming, the revised simplex method and its computational aspects, duality and the dual simplex method, sensitivity and post-optimal analysis. Network optimisation models, maximum flow, shortest path and spanning tree algorithms. Transportation, assignment and transhipment models, and the network simplex method.
Score: 10.682133 Details | Listing | Web page
Introduction to mathematical modelling. Differentiation and integration (polynomials, trigonometric, exponential, logarithmic, hyperbolic and rational functions). Integration by parts, substitution and numerical integration. Differential equations and their solutions (including Euler's method). Complex numbers and roots of functions. Vector and matrix algebra, transformations, solving systems of linear equations. Modelling using probability. First and second order ordinary differential equations and solutions. Laplace transforms. Taylor series and series in general. Multivariate and vector calculus including divergence, gradient and curl. Further linear algebra. Eigenvalues and eigenvectors. Fourier series and transforms. Application of the techniques through appropriate modelling examples. Introductory data analysis and statistics. Probability theory, random variables and distributions, statistics, linear algebra, discrete mathematics possibly including graph theory, trees and networks, optimisation. Introduction to digital electronics, computer organisation and computational techniques. Digital gates, combinatorial and synchronous circuits, data representation, instruction sets, memory, hardware, interfacing. Numerical computation, numerical algorithms. Emphasises the relationship between business and industrial applications and their associated operations research models. Software packages will be used to solve practical problems. Topics such as: linear programming, transportation and assignment models, network algorithms, queues, inventory models and simulation will be considered. Introduction to concepts of modelling of engineering problems, including model formulation, dimensional analysis, solution procedures, comparisons with reality, and shortcomings, with examples from elementary mechanics, structures, hydrostatics, one-dimensional heat, diffusion and fluid motion. Further development of problem-solving skills and group project work. The use of computer tools in engineering design, including advanced spreadsheeting integrated with solid modelling. A selection from: ordinary differential equations, systems of equations, analytical and numerical methods, non-linear ODEs, partial differential equations, separation of variables, numerical methods for solving PDEs, models for optimisation, industrial statistics, data analysis, regression, experimental design reliability methods, regression. Complex Analysis, including complex numbers, analytic functions, complex integration, Cauchy's theorem, Laurent series, residue theory; Laplace transforms; Modelling with partial differential equations, including electronic and electrical applications; Fourier Analysis, Fourier transform, Fast Fourier transform; Optimisation, including unconstrained and constrained models, linear programming and nonlinear optimisation. Mathematical modelling using ordinary and partial differential equations. Probability. Conditional probability, random variables as models of a population, common distribution models, the Poisson process, applications to reliability. Exploratory data analysis, confidence intervals, tests of hypothesis, t-tests, sample tests and intervals, paired comparisons. Introduction to one-way ANOVA. Linear and polynomial regression, regression diagnostics. Numerical algorithms and their translation to computer code. A selection of topics from numerical solution of linear equations, eigen problems, ordinary differential equations, numerical integration, nonlinear equations, finite differences and partial differential equations. Vector calculus and integral theorems. Continuum hypothesis, indicial notation, deformation, strain, traction, stress, principal directions, tensors, invariants, constitutive laws, isotropy, homogeneity. Navier-Stokes and Navier's equations. Isotropic elasticity, elastic moduli, plane stress and plane strain. Airy stress function, Viscous flow, simple solutions of the Navier-Stokes equations. Flow over flat plates, boundary layers. Ideal flow, velocity potential, stream function, 2-D flows. Use of optimisation modelling languages, simulation software and databases, with an emphasis on practical problem solving and laboratory-based learning. Applications of elasticity and fluid dynamics theory to engineering problems including design and analysis of mechanical assemblies. Group projects to formulate design proposals, including costings for development and manufacture. Underlying Finite Element Modelling (FEM) and Continuum Mechanics concepts. Utilisation of 3D CAD and FEM software during both design and analysis phases. Linear programming, the revised simplex method and its computational aspects, duality and the dual simplex method, sensitivity and post-optimal analysis. Network optimisation models, maximum flow, shortest path and spanning tree algorithms. Transportation, assignment and transhipment models, and the network simplex method. An investigation carried out under the supervision of a member of staff on a topic assigned by the Head of Department of Engineering Science. A written report on the work must be submitted.
Score: 10.682133 Details | Listing | Web page
Introduction to mathematical modelling. Differentiation and integration (polynomials, trigonometric, exponential, logarithmic, hyperbolic and rational functions). Integration by parts, substitution and numerical integration. Differential equations and their solutions (including Euler's method). Complex numbers and roots of functions. Vector and matrix algebra, transformations, solving systems of linear equations. Modelling using probability. First and second order ordinary differential equations and solutions. Laplace transforms. Taylor series and series in general. Multivariate and vector calculus including divergence, gradient and curl. Further linear algebra. Eigenvalues and eigenvectors. Fourier series and transforms. Application of the techniques through appropriate modelling examples. Introductory data analysis and statistics. Probability theory, random variables and distributions, statistics, linear algebra, discrete mathematics possibly including graph theory, trees and networks, optimisation. Introduction to digital electronics, computer organisation and computational techniques. Digital gates, combinatorial and synchronous circuits, data representation, instruction sets, memory, hardware, interfacing. Numerical computation, numerical algorithms. Emphasises the relationship between business and industrial applications and their associated operations research models. Software packages will be used to solve practical problems. Topics such as: linear programming, transportation and assignment models, network algorithms, queues, inventory models and simulation will be considered. Introduction to concepts of modelling of engineering problems, including model formulation, dimensional analysis, solution procedures, comparisons with reality, and shortcomings, with examples from elementary mechanics, structures, hydrostatics, one-dimensional heat, diffusion and fluid motion. Further development of problem-solving skills and group project work. The use of computer tools in engineering design, including advanced spreadsheeting integrated with solid modelling. A selection from: ordinary differential equations, systems of equations, analytical and numerical methods, non-linear ODEs, partial differential equations, separation of variables, numerical methods for solving PDEs, models for optimisation, industrial statistics, data analysis, regression, experimental design reliability methods, regression. Complex Analysis, including complex numbers, analytic functions, complex integration, Cauchy's theorem, Laurent series, residue theory; Laplace transforms; Modelling with partial differential equations, including electronic and electrical applications; Fourier Analysis, Fourier transform, Fast Fourier transform; Optimisation, including unconstrained and constrained models, linear programming and nonlinear optimisation. Mathematical modelling using ordinary and partial differential equations. Probability. Conditional probability, random variables as models of a population, common distribution models, the Poisson process, applications to reliability. Exploratory data analysis, confidence intervals, tests of hypothesis, t-tests, sample tests and intervals, paired comparisons. Introduction to one-way ANOVA. Linear and polynomial regression, regression diagnostics. Numerical algorithms and their translation to computer code. A selection of topics from numerical solution of linear equations, eigen problems, ordinary differential equations, numerical integration, nonlinear equations, finite differences and partial differential equations. Vector calculus and integral theorems. Continuum hypothesis, indicial notation, deformation, strain, traction, stress, principal directions, tensors, invariants, constitutive laws, isotropy, homogeneity. Navier-Stokes and Navier's equations. Isotropic elasticity, elastic moduli, plane stress and plane strain. Airy stress function, Viscous flow, simple solutions of the Navier-Stokes equations. Flow over flat plates, boundary layers. Ideal flow, velocity potential, stream function, 2-D flows. Use of optimisation modelling languages, simulation software and databases, with an emphasis on practical problem solving and laboratory-based learning. Applications of elasticity and fluid dynamics theory to engineering problems including design and analysis of mechanical assemblies. Group projects to formulate design proposals, including costings for development and manufacture. Underlying Finite Element Modelling (FEM) and Continuum Mechanics concepts. Utilisation of 3D CAD and FEM software during both design and analysis phases. Linear programming, the revised simplex method and its computational aspects, duality and the dual simplex method, sensitivity and post-optimal analysis. Network optimisation models, maximum flow, shortest path and spanning tree algorithms. Transportation, assignment and transhipment models, and the network simplex method. An investigation carried out under the supervision of a member of staff on a topic assigned by the Head of Department of Engineering Science. A written report on the work must be submitted. An advanced course on topics to be determined each year by the Head of Department of Engineering Science.
Score: 10.682133 Details | Listing | Web page
Introduction to mathematical modelling. Differentiation and integration (polynomials, trigonometric, exponential, logarithmic, hyperbolic and rational functions). Integration by parts, substitution and numerical integration. Differential equations and their solutions (including Euler's method). Complex numbers and roots of functions. Vector and matrix algebra, transformations, solving systems of linear equations. Modelling using probability. First and second order ordinary differential equations and solutions. Laplace transforms. Taylor series and series in general. Multivariate and vector calculus including divergence, gradient and curl. Further linear algebra. Eigenvalues and eigenvectors. Fourier series and transforms. Application of the techniques through appropriate modelling examples. Introductory data analysis and statistics. Probability theory, random variables and distributions, statistics, linear algebra, discrete mathematics possibly including graph theory, trees and networks, optimisation. Introduction to digital electronics, computer organisation and computational techniques. Digital gates, combinatorial and synchronous circuits, data representation, instruction sets, memory, hardware, interfacing. Numerical computation, numerical algorithms. Emphasises the relationship between business and industrial applications and their associated operations research models. Software packages will be used to solve practical problems. Topics such as: linear programming, transportation and assignment models, network algorithms, queues, inventory models and simulation will be considered. Introduction to concepts of modelling of engineering problems, including model formulation, dimensional analysis, solution procedures, comparisons with reality, and shortcomings, with examples from elementary mechanics, structures, hydrostatics, one-dimensional heat, diffusion and fluid motion. Further development of problem-solving skills and group project work. The use of computer tools in engineering design, including advanced spreadsheeting integrated with solid modelling. A selection from: ordinary differential equations, systems of equations, analytical and numerical methods, non-linear ODEs, partial differential equations, separation of variables, numerical methods for solving PDEs, models for optimisation, industrial statistics, data analysis, regression, experimental design reliability methods, regression. Complex Analysis, including complex numbers, analytic functions, complex integration, Cauchy's theorem, Laurent series, residue theory; Laplace transforms; Modelling with partial differential equations, including electronic and electrical applications; Fourier Analysis, Fourier transform, Fast Fourier transform; Optimisation, including unconstrained and constrained models, linear programming and nonlinear optimisation. Mathematical modelling using ordinary and partial differential equations. Probability. Conditional probability, random variables as models of a population, common distribution models, the Poisson process, applications to reliability. Exploratory data analysis, confidence intervals, tests of hypothesis, t-tests, sample tests and intervals, paired comparisons. Introduction to one-way ANOVA. Linear and polynomial regression, regression diagnostics. Numerical algorithms and their translation to computer code. A selection of topics from numerical solution of linear equations, eigen problems, ordinary differential equations, numerical integration, nonlinear equations, finite differences and partial differential equations. Vector calculus and integral theorems. Continuum hypothesis, indicial notation, deformation, strain, traction, stress, principal directions, tensors, invariants, constitutive laws, isotropy, homogeneity. Navier-Stokes and Navier's equations. Isotropic elasticity, elastic moduli, plane stress and plane strain. Airy stress function, Viscous flow, simple solutions of the Navier-Stokes equations. Flow over flat plates, boundary layers. Ideal flow, velocity potential, stream function, 2-D flows. Use of optimisation modelling languages, simulation software and databases, with an emphasis on practical problem solving and laboratory-based learning. Applications of elasticity and fluid dynamics theory to engineering problems including design and analysis of mechanical assemblies. Group projects to formulate design proposals, including costings for development and manufacture. Underlying Finite Element Modelling (FEM) and Continuum Mechanics concepts. Utilisation of 3D CAD and FEM software during both design and analysis phases. Linear programming, the revised simplex method and its computational aspects, duality and the dual simplex method, sensitivity and post-optimal analysis. Network optimisation models, maximum flow, shortest path and spanning tree algorithms. Transportation, assignment and transhipment models, and the network simplex method. An investigation carried out under the supervision of a member of staff on a topic assigned by the Head of Department of Engineering Science. A written report on the work must be submitted. An advanced course on topics to be determined each year by the Head of Department of Engineering Science. A selection of modules on mathematical modelling methods in engineering, including theory of partial differential equations, integral transforms, methods of characteristics, similarity solutions, asymptotic expressions, theory of waves, special functions, non-linear ordinary differential equations, calculus of variations, tensor analysis, complex variables, wavelet theory and other modules offered from year to year.
Score: 10.682133 Details | Listing | Web page
Introduction to mathematical modelling. Differentiation and integration (polynomials, trigonometric, exponential, logarithmic, hyperbolic and rational functions). Integration by parts, substitution and numerical integration. Differential equations and their solutions (including Euler's method). Complex numbers and roots of functions. Vector and matrix algebra, transformations, solving systems of linear equations. Modelling using probability. First and second order ordinary differential equations and solutions. Laplace transforms. Taylor series and series in general. Multivariate and vector calculus including divergence, gradient and curl. Further linear algebra. Eigenvalues and eigenvectors. Fourier series and transforms. Application of the techniques through appropriate modelling examples. Introductory data analysis and statistics. Probability theory, random variables and distributions, statistics, linear algebra, discrete mathematics possibly including graph theory, trees and networks, optimisation. Introduction to digital electronics, computer organisation and computational techniques. Digital gates, combinatorial and synchronous circuits, data representation, instruction sets, memory, hardware, interfacing. Numerical computation, numerical algorithms. Emphasises the relationship between business and industrial applications and their associated operations research models. Software packages will be used to solve practical problems. Topics such as: linear programming, transportation and assignment models, network algorithms, queues, inventory models and simulation will be considered. Introduction to concepts of modelling of engineering problems, including model formulation, dimensional analysis, solution procedures, comparisons with reality, and shortcomings, with examples from elementary mechanics, structures, hydrostatics, one-dimensional heat, diffusion and fluid motion. Further development of problem-solving skills and group project work. The use of computer tools in engineering design, including advanced spreadsheeting integrated with solid modelling. A selection from: ordinary differential equations, systems of equations, analytical and numerical methods, non-linear ODEs, partial differential equations, separation of variables, numerical methods for solving PDEs, models for optimisation, industrial statistics, data analysis, regression, experimental design reliability methods, regression. Complex Analysis, including complex numbers, analytic functions, complex integration, Cauchy's theorem, Laurent series, residue theory; Laplace transforms; Modelling with partial differential equations, including electronic and electrical applications; Fourier Analysis, Fourier transform, Fast Fourier transform; Optimisation, including unconstrained and constrained models, linear programming and nonlinear optimisation. Mathematical modelling using ordinary and partial differential equations. Probability. Conditional probability, random variables as models of a population, common distribution models, the Poisson process, applications to reliability. Exploratory data analysis, confidence intervals, tests of hypothesis, t-tests, sample tests and intervals, paired comparisons. Introduction to one-way ANOVA. Linear and polynomial regression, regression diagnostics. Numerical algorithms and their translation to computer code. A selection of topics from numerical solution of linear equations, eigen problems, ordinary differential equations, numerical integration, nonlinear equations, finite differences and partial differential equations. Vector calculus and integral theorems. Continuum hypothesis, indicial notation, deformation, strain, traction, stress, principal directions, tensors, invariants, constitutive laws, isotropy, homogeneity. Navier-Stokes and Navier's equations. Isotropic elasticity, elastic moduli, plane stress and plane strain. Airy stress function, Viscous flow, simple solutions of the Navier-Stokes equations. Flow over flat plates, boundary layers. Ideal flow, velocity potential, stream function, 2-D flows. Use of optimisation modelling languages, simulation software and databases, with an emphasis on practical problem solving and laboratory-based learning. Applications of elasticity and fluid dynamics theory to engineering problems including design and analysis of mechanical assemblies. Group projects to formulate design proposals, including costings for development and manufacture. Underlying Finite Element Modelling (FEM) and Continuum Mechanics concepts. Utilisation of 3D CAD and FEM software during both design and analysis phases. Linear programming, the revised simplex method and its computational aspects, duality and the dual simplex method, sensitivity and post-optimal analysis. Network optimisation models, maximum flow, shortest path and spanning tree algorithms. Transportation, assignment and transhipment models, and the network simplex method. An investigation carried out under the supervision of a member of staff on a topic assigned by the Head of Department of Engineering Science. A written report on the work must be submitted. An advanced course on topics to be determined each year by the Head of Department of Engineering Science. A selection of modules on mathematical modelling methods in engineering, including theory of partial differential equations, integral transforms, methods of characteristics, similarity solutions, asymptotic expressions, theory of waves, special functions, non-linear ordinary differential equations, calculus of variations, tensor analysis, complex variables, wavelet theory and other modules offered from year to year. Advanced topics in mathematical modelling and computational techniques, including linear algebra and its applications (topics on singular value decomposition, ill-conditioning, orthogonal factorisation, least squares, eigen-problems and iterative methods), perturbation theory (topics on dimensional analysis, regular and singular perturbation analysis) and signal processing (topics on neural network models such as the multi-layer perception and self organising map).
Score: 10.682133 Details | Listing | Web page
Introduction to mathematical modelling. Differentiation and integration (polynomials, trigonometric, exponential, logarithmic, hyperbolic and rational functions). Integration by parts, substitution and numerical integration. Differential equations and their solutions (including Euler's method). Complex numbers and roots of functions. Vector and matrix algebra, transformations, solving systems of linear equations. Modelling using probability. First and second order ordinary differential equations and solutions. Laplace transforms. Taylor series and series in general. Multivariate and vector calculus including divergence, gradient and curl. Further linear algebra. Eigenvalues and eigenvectors. Fourier series and transforms. Application of the techniques through appropriate modelling examples. Introductory data analysis and statistics. Probability theory, random variables and distributions, statistics, linear algebra, discrete mathematics possibly including graph theory, trees and networks, optimisation. Introduction to digital electronics, computer organisation and computational techniques. Digital gates, combinatorial and synchronous circuits, data representation, instruction sets, memory, hardware, interfacing. Numerical computation, numerical algorithms. Emphasises the relationship between business and industrial applications and their associated operations research models. Software packages will be used to solve practical problems. Topics such as: linear programming, transportation and assignment models, network algorithms, queues, inventory models and simulation will be considered. Introduction to concepts of modelling of engineering problems, including model formulation, dimensional analysis, solution procedures, comparisons with reality, and shortcomings, with examples from elementary mechanics, structures, hydrostatics, one-dimensional heat, diffusion and fluid motion. Further development of problem-solving skills and group project work. The use of computer tools in engineering design, including advanced spreadsheeting integrated with solid modelling. A selection from: ordinary differential equations, systems of equations, analytical and numerical methods, non-linear ODEs, partial differential equations, separation of variables, numerical methods for solving PDEs, models for optimisation, industrial statistics, data analysis, regression, experimental design reliability methods, regression. Complex Analysis, including complex numbers, analytic functions, complex integration, Cauchy's theorem, Laurent series, residue theory; Laplace transforms; Modelling with partial differential equations, including electronic and electrical applications; Fourier Analysis, Fourier transform, Fast Fourier transform; Optimisation, including unconstrained and constrained models, linear programming and nonlinear optimisation. Mathematical modelling using ordinary and partial differential equations. Probability. Conditional probability, random variables as models of a population, common distribution models, the Poisson process, applications to reliability. Exploratory data analysis, confidence intervals, tests of hypothesis, t-tests, sample tests and intervals, paired comparisons. Introduction to one-way ANOVA. Linear and polynomial regression, regression diagnostics. Numerical algorithms and their translation to computer code. A selection of topics from numerical solution of linear equations, eigen problems, ordinary differential equations, numerical integration, nonlinear equations, finite differences and partial differential equations. Vector calculus and integral theorems. Continuum hypothesis, indicial notation, deformation, strain, traction, stress, principal directions, tensors, invariants, constitutive laws, isotropy, homogeneity. Navier-Stokes and Navier's equations. Isotropic elasticity, elastic moduli, plane stress and plane strain. Airy stress function, Viscous flow, simple solutions of the Navier-Stokes equations. Flow over flat plates, boundary layers. Ideal flow, velocity potential, stream function, 2-D flows. Use of optimisation modelling languages, simulation software and databases, with an emphasis on practical problem solving and laboratory-based learning. Applications of elasticity and fluid dynamics theory to engineering problems including design and analysis of mechanical assemblies. Group projects to formulate design proposals, including costings for development and manufacture. Underlying Finite Element Modelling (FEM) and Continuum Mechanics concepts. Utilisation of 3D CAD and FEM software during both design and analysis phases. Linear programming, the revised simplex method and its computational aspects, duality and the dual simplex method, sensitivity and post-optimal analysis. Network optimisation models, maximum flow, shortest path and spanning tree algorithms. Transportation, assignment and transhipment models, and the network simplex method. An investigation carried out under the supervision of a member of staff on a topic assigned by the Head of Department of Engineering Science. A written report on the work must be submitted. An advanced course on topics to be determined each year by the Head of Department of Engineering Science. A selection of modules on mathematical modelling methods in engineering, including theory of partial differential equations, integral transforms, methods of characteristics, similarity solutions, asymptotic expressions, theory of waves, special functions, non-linear ordinary differential equations, calculus of variations, tensor analysis, complex variables, wavelet theory and other modules offered from year to year. Advanced topics in mathematical modelling and computational techniques, including linear algebra and its applications (topics on singular value decomposition, ill-conditioning, orthogonal factorisation, least squares, eigen-problems and iterative methods), perturbation theory (topics on dimensional analysis, regular and singular perturbation analysis) and signal processing (topics on neural network models such as the multi-layer perception and self organising map). An advanced course on finite elements, boundary elements and finite differences.
Score: 10.682133 Details | Listing | Web page
Introduction to mathematical modelling. Differentiation and integration (polynomials, trigonometric, exponential, logarithmic, hyperbolic and rational functions). Integration by parts, substitution and numerical integration. Differential equations and their solutions (including Euler's method). Complex numbers and roots of functions. Vector and matrix algebra, transformations, solving systems of linear equations. Modelling using probability. First and second order ordinary differential equations and solutions. Laplace transforms. Taylor series and series in general. Multivariate and vector calculus including divergence, gradient and curl. Further linear algebra. Eigenvalues and eigenvectors. Fourier series and transforms. Application of the techniques through appropriate modelling examples. Introductory data analysis and statistics. Probability theory, random variables and distributions, statistics, linear algebra, discrete mathematics possibly including graph theory, trees and networks, optimisation. Introduction to digital electronics, computer organisation and computational techniques. Digital gates, combinatorial and synchronous circuits, data representation, instruction sets, memory, hardware, interfacing. Numerical computation, numerical algorithms. Emphasises the relationship between business and industrial applications and their associated operations research models. Software packages will be used to solve practical problems. Topics such as: linear programming, transportation and assignment models, network algorithms, queues, inventory models and simulation will be considered. Introduction to concepts of modelling of engineering problems, including model formulation, dimensional analysis, solution procedures, comparisons with reality, and shortcomings, with examples from elementary mechanics, structures, hydrostatics, one-dimensional heat, diffusion and fluid motion. Further development of problem-solving skills and group project work. The use of computer tools in engineering design, including advanced spreadsheeting integrated with solid modelling. A selection from: ordinary differential equations, systems of equations, analytical and numerical methods, non-linear ODEs, partial differential equations, separation of variables, numerical methods for solving PDEs, models for optimisation, industrial statistics, data analysis, regression, experimental design reliability methods, regression. Complex Analysis, including complex numbers, analytic functions, complex integration, Cauchy's theorem, Laurent series, residue theory; Laplace transforms; Modelling with partial differential equations, including electronic and electrical applications; Fourier Analysis, Fourier transform, Fast Fourier transform; Optimisation, including unconstrained and constrained models, linear programming and nonlinear optimisation. Mathematical modelling using ordinary and partial differential equations. Probability. Conditional probability, random variables as models of a population, common distribution models, the Poisson process, applications to reliability. Exploratory data analysis, confidence intervals, tests of hypothesis, t-tests, sample tests and intervals, paired comparisons. Introduction to one-way ANOVA. Linear and polynomial regression, regression diagnostics. Numerical algorithms and their translation to computer code. A selection of topics from numerical solution of linear equations, eigen problems, ordinary differential equations, numerical integration, nonlinear equations, finite differences and partial differential equations. Vector calculus and integral theorems. Continuum hypothesis, indicial notation, deformation, strain, traction, stress, principal directions, tensors, invariants, constitutive laws, isotropy, homogeneity. Navier-Stokes and Navier's equations. Isotropic elasticity, elastic moduli, plane stress and plane strain. Airy stress function, Viscous flow, simple solutions of the Navier-Stokes equations. Flow over flat plates, boundary layers. Ideal flow, velocity potential, stream function, 2-D flows. Use of optimisation modelling languages, simulation software and databases, with an emphasis on practical problem solving and laboratory-based learning. Applications of elasticity and fluid dynamics theory to engineering problems including design and analysis of mechanical assemblies. Group projects to formulate design proposals, including costings for development and manufacture. Underlying Finite Element Modelling (FEM) and Continuum Mechanics concepts. Utilisation of 3D CAD and FEM software during both design and analysis phases. Linear programming, the revised simplex method and its computational aspects, duality and the dual simplex method, sensitivity and post-optimal analysis. Network optimisation models, maximum flow, shortest path and spanning tree algorithms. Transportation, assignment and transhipment models, and the network simplex method. An investigation carried out under the supervision of a member of staff on a topic assigned by the Head of Department of Engineering Science. A written report on the work must be submitted. An advanced course on topics to be determined each year by the Head of Department of Engineering Science. A selection of modules on mathematical modelling methods in engineering, including theory of partial differential equations, integral transforms, methods of characteristics, similarity solutions, asymptotic expressions, theory of waves, special functions, non-linear ordinary differential equations, calculus of variations, tensor analysis, complex variables, wavelet theory and other modules offered from year to year. Advanced topics in mathematical modelling and computational techniques, including linear algebra and its applications (topics on singular value decomposition, ill-conditioning, orthogonal factorisation, least squares, eigen-problems and iterative methods), perturbation theory (topics on dimensional analysis, regular and singular perturbation analysis) and signal processing (topics on neural network models such as the multi-layer perception and self organising map). An advanced course on finite elements, boundary elements and finite differences. Applications of continuum mechanics to problems in biomechanics, fluid mechanics and solid mechanics. Including topics such as large deformation elasticity theory applied to soft tissues, inviscid flow theory, compressible flows, viscous flows, meteorology, oceanography, coastal ocean modelling, mixing in rivers and estuaries. Fracture, composite materials and geomechanics.
Score: 10.682133 Details | Listing | Web page
Introduction to mathematical modelling. Differentiation and integration (polynomials, trigonometric, exponential, logarithmic, hyperbolic and rational functions). Integration by parts, substitution and numerical integration. Differential equations and their solutions (including Euler's method). Complex numbers and roots of functions. Vector and matrix algebra, transformations, solving systems of linear equations. Modelling using probability. First and second order ordinary differential equations and solutions. Laplace transforms. Taylor series and series in general. Multivariate and vector calculus including divergence, gradient and curl. Further linear algebra. Eigenvalues and eigenvectors. Fourier series and transforms. Application of the techniques through appropriate modelling examples. Introductory data analysis and statistics. Probability theory, random variables and distributions, statistics, linear algebra, discrete mathematics possibly including graph theory, trees and networks, optimisation. Introduction to digital electronics, computer organisation and computational techniques. Digital gates, combinatorial and synchronous circuits, data representation, instruction sets, memory, hardware, interfacing. Numerical computation, numerical algorithms. Emphasises the relationship between business and industrial applications and their associated operations research models. Software packages will be used to solve practical problems. Topics such as: linear programming, transportation and assignment models, network algorithms, queues, inventory models and simulation will be considered. Introduction to concepts of modelling of engineering problems, including model formulation, dimensional analysis, solution procedures, comparisons with reality, and shortcomings, with examples from elementary mechanics, structures, hydrostatics, one-dimensional heat, diffusion and fluid motion. Further development of problem-solving skills and group project work. The use of computer tools in engineering design, including advanced spreadsheeting integrated with solid modelling. A selection from: ordinary differential equations, systems of equations, analytical and numerical methods, non-linear ODEs, partial differential equations, separation of variables, numerical methods for solving PDEs, models for optimisation, industrial statistics, data analysis, regression, experimental design reliability methods, regression. Complex Analysis, including complex numbers, analytic functions, complex integration, Cauchy's theorem, Laurent series, residue theory; Laplace transforms; Modelling with partial differential equations, including electronic and electrical applications; Fourier Analysis, Fourier transform, Fast Fourier transform; Optimisation, including unconstrained and constrained models, linear programming and nonlinear optimisation. Mathematical modelling using ordinary and partial differential equations. Probability. Conditional probability, random variables as models of a population, common distribution models, the Poisson process, applications to reliability. Exploratory data analysis, confidence intervals, tests of hypothesis, t-tests, sample tests and intervals, paired comparisons. Introduction to one-way ANOVA. Linear and polynomial regression, regression diagnostics. Numerical algorithms and their translation to computer code. A selection of topics from numerical solution of linear equations, eigen problems, ordinary differential equations, numerical integration, nonlinear equations, finite differences and partial differential equations. Vector calculus and integral theorems. Continuum hypothesis, indicial notation, deformation, strain, traction, stress, principal directions, tensors, invariants, constitutive laws, isotropy, homogeneity. Navier-Stokes and Navier's equations. Isotropic elasticity, elastic moduli, plane stress and plane strain. Airy stress function, Viscous flow, simple solutions of the Navier-Stokes equations. Flow over flat plates, boundary layers. Ideal flow, velocity potential, stream function, 2-D flows. Use of optimisation modelling languages, simulation software and databases, with an emphasis on practical problem solving and laboratory-based learning. Applications of elasticity and fluid dynamics theory to engineering problems including design and analysis of mechanical assemblies. Group projects to formulate design proposals, including costings for development and manufacture. Underlying Finite Element Modelling (FEM) and Continuum Mechanics concepts. Utilisation of 3D CAD and FEM software during both design and analysis phases. Linear programming, the revised simplex method and its computational aspects, duality and the dual simplex method, sensitivity and post-optimal analysis. Network optimisation models, maximum flow, shortest path and spanning tree algorithms. Transportation, assignment and transhipment models, and the network simplex method. An investigation carried out under the supervision of a member of staff on a topic assigned by the Head of Department of Engineering Science. A written report on the work must be submitted. An advanced course on topics to be determined each year by the Head of Department of Engineering Science. A selection of modules on mathematical modelling methods in engineering, including theory of partial differential equations, integral transforms, methods of characteristics, similarity solutions, asymptotic expressions, theory of waves, special functions, non-linear ordinary differential equations, calculus of variations, tensor analysis, complex variables, wavelet theory and other modules offered from year to year. Advanced topics in mathematical modelling and computational techniques, including linear algebra and its applications (topics on singular value decomposition, ill-conditioning, orthogonal factorisation, least squares, eigen-problems and iterative methods), perturbation theory (topics on dimensional analysis, regular and singular perturbation analysis) and signal processing (topics on neural network models such as the multi-layer perception and self organising map). An advanced course on finite elements, boundary elements and finite differences. Applications of continuum mechanics to problems in biomechanics, fluid mechanics and solid mechanics. Including topics such as large deformation elasticity theory applied to soft tissues, inviscid flow theory, compressible flows, viscous flows, meteorology, oceanography, coastal ocean modelling, mixing in rivers and estuaries. Fracture, composite materials and geomechanics. Turbulence and turbulence modelling. Advanced numerical techniques in computational fluid dynamics (CFD). Application of CFD to environmental flows and aerodynamics. A variety of topics in engineering solid mechanics which could include composite materials, geomechanics, contact mechanics, fracture mechanics, rheology, thermomechanics, constitutive theory and computational methods.
Score: 10.682133 Details | Listing | Web page
Introduction to mathematical modelling. Differentiation and integration (polynomials, trigonometric, exponential, logarithmic, hyperbolic and rational functions). Integration by parts, substitution and numerical integration. Differential equations and their solutions (including Euler's method). Complex numbers and roots of functions. Vector and matrix algebra, transformations, solving systems of linear equations. Modelling using probability. First and second order ordinary differential equations and solutions. Laplace transforms. Taylor series and series in general. Multivariate and vector calculus including divergence, gradient and curl. Further linear algebra. Eigenvalues and eigenvectors. Fourier series and transforms. Application of the techniques through appropriate modelling examples. Introductory data analysis and statistics. Probability theory, random variables and distributions, statistics, linear algebra, discrete mathematics possibly including graph theory, trees and networks, optimisation. Introduction to digital electronics, computer organisation and computational techniques. Digital gates, combinatorial and synchronous circuits, data representation, instruction sets, memory, hardware, interfacing. Numerical computation, numerical algorithms. Emphasises the relationship between business and industrial applications and their associated operations research models. Software packages will be used to solve practical problems. Topics such as: linear programming, transportation and assignment models, network algorithms, queues, inventory models and simulation will be considered. Introduction to concepts of modelling of engineering problems, including model formulation, dimensional analysis, solution procedures, comparisons with reality, and shortcomings, with examples from elementary mechanics, structures, hydrostatics, one-dimensional heat, diffusion and fluid motion. Further development of problem-solving skills and group project work. The use of computer tools in engineering design, including advanced spreadsheeting integrated with solid modelling. A selection from: ordinary differential equations, systems of equations, analytical and numerical methods, non-linear ODEs, partial differential equations, separation of variables, numerical methods for solving PDEs, models for optimisation, industrial statistics, data analysis, regression, experimental design reliability methods, regression. Complex Analysis, including complex numbers, analytic functions, complex integration, Cauchy's theorem, Laurent series, residue theory; Laplace transforms; Modelling with partial differential equations, including electronic and electrical applications; Fourier Analysis, Fourier transform, Fast Fourier transform; Optimisation, including unconstrained and constrained models, linear programming and nonlinear optimisation. Mathematical modelling using ordinary and partial differential equations. Probability. Conditional probability, random variables as models of a population, common distribution models, the Poisson process, applications to reliability. Exploratory data analysis, confidence intervals, tests of hypothesis, t-tests, sample tests and intervals, paired comparisons. Introduction to one-way ANOVA. Linear and polynomial regression, regression diagnostics. Numerical algorithms and their translation to computer code. A selection of topics from numerical solution of linear equations, eigen problems, ordinary differential equations, numerical integration, nonlinear equations, finite differences and partial differential equations. Vector calculus and integral theorems. Continuum hypothesis, indicial notation, deformation, strain, traction, stress, principal directions, tensors, invariants, constitutive laws, isotropy, homogeneity. Navier-Stokes and Navier's equations. Isotropic elasticity, elastic moduli, plane stress and plane strain. Airy stress function, Viscous flow, simple solutions of the Navier-Stokes equations. Flow over flat plates, boundary layers. Ideal flow, velocity potential, stream function, 2-D flows. Use of optimisation modelling languages, simulation software and databases, with an emphasis on practical problem solving and laboratory-based learning. Applications of elasticity and fluid dynamics theory to engineering problems including design and analysis of mechanical assemblies. Group projects to formulate design proposals, including costings for development and manufacture. Underlying Finite Element Modelling (FEM) and Continuum Mechanics concepts. Utilisation of 3D CAD and FEM software during both design and analysis phases. Linear programming, the revised simplex method and its computational aspects, duality and the dual simplex method, sensitivity and post-optimal analysis. Network optimisation models, maximum flow, shortest path and spanning tree algorithms. Transportation, assignment and transhipment models, and the network simplex method. An investigation carried out under the supervision of a member of staff on a topic assigned by the Head of Department of Engineering Science. A written report on the work must be submitted. An advanced course on topics to be determined each year by the Head of Department of Engineering Science. A selection of modules on mathematical modelling methods in engineering, including theory of partial differential equations, integral transforms, methods of characteristics, similarity solutions, asymptotic expressions, theory of waves, special functions, non-linear ordinary differential equations, calculus of variations, tensor analysis, complex variables, wavelet theory and other modules offered from year to year. Advanced topics in mathematical modelling and computational techniques, including linear algebra and its applications (topics on singular value decomposition, ill-conditioning, orthogonal factorisation, least squares, eigen-problems and iterative methods), perturbation theory (topics on dimensional analysis, regular and singular perturbation analysis) and signal processing (topics on neural network models such as the multi-layer perception and self organising map). An advanced course on finite elements, boundary elements and finite differences. Applications of continuum mechanics to problems in biomechanics, fluid mechanics and solid mechanics. Including topics such as large deformation elasticity theory applied to soft tissues, inviscid flow theory, compressible flows, viscous flows, meteorology, oceanography, coastal ocean modelling, mixing in rivers and estuaries. Fracture, composite materials and geomechanics. Turbulence and turbulence modelling. Advanced numerical techniques in computational fluid dynamics (CFD). Application of CFD to environmental flows and aerodynamics. A variety of topics in engineering solid mechanics which could include composite materials, geomechanics, contact mechanics, fracture mechanics, rheology, thermomechanics, constitutive theory and computational methods. An advanced course in continuum mechanics covering topics in the mechanics of solids and fluids and other continua.
Score: 10.682133 Details | Listing | Web page
Introduction to mathematical modelling. Differentiation and integration (polynomials, trigonometric, exponential, logarithmic, hyperbolic and rational functions). Integration by parts, substitution and numerical integration. Differential equations and their solutions (including Euler's method). Complex numbers and roots of functions. Vector and matrix algebra, transformations, solving systems of linear equations. Modelling using probability. First and second order ordinary differential equations and solutions. Laplace transforms. Taylor series and series in general. Multivariate and vector calculus including divergence, gradient and curl. Further linear algebra. Eigenvalues and eigenvectors. Fourier series and transforms. Application of the techniques through appropriate modelling examples. Introductory data analysis and statistics. Probability theory, random variables and distributions, statistics, linear algebra, discrete mathematics possibly including graph theory, trees and networks, optimisation. Introduction to digital electronics, computer organisation and computational techniques. Digital gates, combinatorial and synchronous circuits, data representation, instruction sets, memory, hardware, interfacing. Numerical computation, numerical algorithms. Emphasises the relationship between business and industrial applications and their associated operations research models. Software packages will be used to solve practical problems. Topics such as: linear programming, transportation and assignment models, network algorithms, queues, inventory models and simulation will be considered. Introduction to concepts of modelling of engineering problems, including model formulation, dimensional analysis, solution procedures, comparisons with reality, and shortcomings, with examples from elementary mechanics, structures, hydrostatics, one-dimensional heat, diffusion and fluid motion. Further development of problem-solving skills and group project work. The use of computer tools in engineering design, including advanced spreadsheeting integrated with solid modelling. A selection from: ordinary differential equations, systems of equations, analytical and numerical methods, non-linear ODEs, partial differential equations, separation of variables, numerical methods for solving PDEs, models for optimisation, industrial statistics, data analysis, regression, experimental design reliability methods, regression. Complex Analysis, including complex numbers, analytic functions, complex integration, Cauchy's theorem, Laurent series, residue theory; Laplace transforms; Modelling with partial differential equations, including electronic and electrical applications; Fourier Analysis, Fourier transform, Fast Fourier transform; Optimisation, including unconstrained and constrained models, linear programming and nonlinear optimisation. Mathematical modelling using ordinary and partial differential equations. Probability. Conditional probability, random variables as models of a population, common distribution models, the Poisson process, applications to reliability. Exploratory data analysis, confidence intervals, tests of hypothesis, t-tests, sample tests and intervals, paired comparisons. Introduction to one-way ANOVA. Linear and polynomial regression, regression diagnostics. Numerical algorithms and their translation to computer code. A selection of topics from numerical solution of linear equations, eigen problems, ordinary differential equations, numerical integration, nonlinear equations, finite differences and partial differential equations. Vector calculus and integral theorems. Continuum hypothesis, indicial notation, deformation, strain, traction, stress, principal directions, tensors, invariants, constitutive laws, isotropy, homogeneity. Navier-Stokes and Navier's equations. Isotropic elasticity, elastic moduli, plane stress and plane strain. Airy stress function, Viscous flow, simple solutions of the Navier-Stokes equations. Flow over flat plates, boundary layers. Ideal flow, velocity potential, stream function, 2-D flows. Use of optimisation modelling languages, simulation software and databases, with an emphasis on practical problem solving and laboratory-based learning. Applications of elasticity and fluid dynamics theory to engineering problems including design and analysis of mechanical assemblies. Group projects to formulate design proposals, including costings for development and manufacture. Underlying Finite Element Modelling (FEM) and Continuum Mechanics concepts. Utilisation of 3D CAD and FEM software during both design and analysis phases. Linear programming, the revised simplex method and its computational aspects, duality and the dual simplex method, sensitivity and post-optimal analysis. Network optimisation models, maximum flow, shortest path and spanning tree algorithms. Transportation, assignment and transhipment models, and the network simplex method. An investigation carried out under the supervision of a member of staff on a topic assigned by the Head of Department of Engineering Science. A written report on the work must be submitted. An advanced course on topics to be determined each year by the Head of Department of Engineering Science. A selection of modules on mathematical modelling methods in engineering, including theory of partial differential equations, integral transforms, methods of characteristics, similarity solutions, asymptotic expressions, theory of waves, special functions, non-linear ordinary differential equations, calculus of variations, tensor analysis, complex variables, wavelet theory and other modules offered from year to year. Advanced topics in mathematical modelling and computational techniques, including linear algebra and its applications (topics on singular value decomposition, ill-conditioning, orthogonal factorisation, least squares, eigen-problems and iterative methods), perturbation theory (topics on dimensional analysis, regular and singular perturbation analysis) and signal processing (topics on neural network models such as the multi-layer perception and self organising map). An advanced course on finite elements, boundary elements and finite differences. Applications of continuum mechanics to problems in biomechanics, fluid mechanics and solid mechanics. Including topics such as large deformation elasticity theory applied to soft tissues, inviscid flow theory, compressible flows, viscous flows, meteorology, oceanography, coastal ocean modelling, mixing in rivers and estuaries. Fracture, composite materials and geomechanics. Turbulence and turbulence modelling. Advanced numerical techniques in computational fluid dynamics (CFD). Application of CFD to environmental flows and aerodynamics. A variety of topics in engineering solid mechanics which could include composite materials, geomechanics, contact mechanics, fracture mechanics, rheology, thermomechanics, constitutive theory and computational methods. An advanced course in continuum mechanics covering topics in the mechanics of solids and fluids and other continua. Theoretical and applied finite element and boundary element methods for static and time dependent problems of heat flow, bioelectricity and linear elasticity.
Score: 10.682133 Details | Listing | Web page
Introduction to mathematical modelling. Differentiation and integration (polynomials, trigonometric, exponential, logarithmic, hyperbolic and rational functions). Integration by parts, substitution and numerical integration. Differential equations and their solutions (including Euler's method). Complex numbers and roots of functions. Vector and matrix algebra, transformations, solving systems of linear equations. Modelling using probability. First and second order ordinary differential equations and solutions. Laplace transforms. Taylor series and series in general. Multivariate and vector calculus including divergence, gradient and curl. Further linear algebra. Eigenvalues and eigenvectors. Fourier series and transforms. Application of the techniques through appropriate modelling examples. Introductory data analysis and statistics. Probability theory, random variables and distributions, statistics, linear algebra, discrete mathematics possibly including graph theory, trees and networks, optimisation. Introduction to digital electronics, computer organisation and computational techniques. Digital gates, combinatorial and synchronous circuits, data representation, instruction sets, memory, hardware, interfacing. Numerical computation, numerical algorithms. Emphasises the relationship between business and industrial applications and their associated operations research models. Software packages will be used to solve practical problems. Topics such as: linear programming, transportation and assignment models, network algorithms, queues, inventory models and simulation will be considered. Introduction to concepts of modelling of engineering problems, including model formulation, dimensional analysis, solution procedures, comparisons with reality, and shortcomings, with examples from elementary mechanics, structures, hydrostatics, one-dimensional heat, diffusion and fluid motion. Further development of problem-solving skills and group project work. The use of computer tools in engineering design, including advanced spreadsheeting integrated with solid modelling. A selection from: ordinary differential equations, systems of equations, analytical and numerical methods, non-linear ODEs, partial differential equations, separation of variables, numerical methods for solving PDEs, models for optimisation, industrial statistics, data analysis, regression, experimental design reliability methods, regression. Complex Analysis, including complex numbers, analytic functions, complex integration, Cauchy's theorem, Laurent series, residue theory; Laplace transforms; Modelling with partial differential equations, including electronic and electrical applications; Fourier Analysis, Fourier transform, Fast Fourier transform; Optimisation, including unconstrained and constrained models, linear programming and nonlinear optimisation. Mathematical modelling using ordinary and partial differential equations. Probability. Conditional probability, random variables as models of a population, common distribution models, the Poisson process, applications to reliability. Exploratory data analysis, confidence intervals, tests of hypothesis, t-tests, sample tests and intervals, paired comparisons. Introduction to one-way ANOVA. Linear and polynomial regression, regression diagnostics. Numerical algorithms and their translation to computer code. A selection of topics from numerical solution of linear equations, eigen problems, ordinary differential equations, numerical integration, nonlinear equations, finite differences and partial differential equations. Vector calculus and integral theorems. Continuum hypothesis, indicial notation, deformation, strain, traction, stress, principal directions, tensors, invariants, constitutive laws, isotropy, homogeneity. Navier-Stokes and Navier's equations. Isotropic elasticity, elastic moduli, plane stress and plane strain. Airy stress function, Viscous flow, simple solutions of the Navier-Stokes equations. Flow over flat plates, boundary layers. Ideal flow, velocity potential, stream function, 2-D flows. Use of optimisation modelling languages, simulation software and databases, with an emphasis on practical problem solving and laboratory-based learning. Applications of elasticity and fluid dynamics theory to engineering problems including design and analysis of mechanical assemblies. Group projects to formulate design proposals, including costings for development and manufacture. Underlying Finite Element Modelling (FEM) and Continuum Mechanics concepts. Utilisation of 3D CAD and FEM software during both design and analysis phases. Linear programming, the revised simplex method and its computational aspects, duality and the dual simplex method, sensitivity and post-optimal analysis. Network optimisation models, maximum flow, shortest path and spanning tree algorithms. Transportation, assignment and transhipment models, and the network simplex method. An investigation carried out under the supervision of a member of staff on a topic assigned by the Head of Department of Engineering Science. A written report on the work must be submitted. An advanced course on topics to be determined each year by the Head of Department of Engineering Science. A selection of modules on mathematical modelling methods in engineering, including theory of partial differential equations, integral transforms, methods of characteristics, similarity solutions, asymptotic expressions, theory of waves, special functions, non-linear ordinary differential equations, calculus of variations, tensor analysis, complex variables, wavelet theory and other modules offered from year to year. Advanced topics in mathematical modelling and computational techniques, including linear algebra and its applications (topics on singular value decomposition, ill-conditioning, orthogonal factorisation, least squares, eigen-problems and iterative methods), perturbation theory (topics on dimensional analysis, regular and singular perturbation analysis) and signal processing (topics on neural network models such as the multi-layer perception and self organising map). An advanced course on finite elements, boundary elements and finite differences. Applications of continuum mechanics to problems in biomechanics, fluid mechanics and solid mechanics. Including topics such as large deformation elasticity theory applied to soft tissues, inviscid flow theory, compressible flows, viscous flows, meteorology, oceanography, coastal ocean modelling, mixing in rivers and estuaries. Fracture, composite materials and geomechanics. Turbulence and turbulence modelling. Advanced numerical techniques in computational fluid dynamics (CFD). Application of CFD to environmental flows and aerodynamics. A variety of topics in engineering solid mechanics which could include composite materials, geomechanics, contact mechanics, fracture mechanics, rheology, thermomechanics, constitutive theory and computational methods. An advanced course in continuum mechanics covering topics in the mechanics of solids and fluids and other continua. Theoretical and applied finite element and boundary element methods for static and time dependent problems of heat flow, bioelectricity and linear elasticity. Meta-heuristics and local search techniques such as Genetic Algorithms, Simulated Annealing, Tabu Search and Ant Colony Optimisation for practical optimisation. Introduction to optimisation under uncertainty, including discrete event simulation, decision analysis, Markov chains and Markov decision processes and dynamic programming.
Score: 10.682133 Details | Listing | Web page
Introduction to mathematical modelling. Differentiation and integration (polynomials, trigonometric, exponential, logarithmic, hyperbolic and rational functions). Integration by parts, substitution and numerical integration. Differential equations and their solutions (including Euler's method). Complex numbers and roots of functions. Vector and matrix algebra, transformations, solving systems of linear equations. Modelling using probability. First and second order ordinary differential equations and solutions. Laplace transforms. Taylor series and series in general. Multivariate and vector calculus including divergence, gradient and curl. Further linear algebra. Eigenvalues and eigenvectors. Fourier series and transforms. Application of the techniques through appropriate modelling examples. Introductory data analysis and statistics. Probability theory, random variables and distributions, statistics, linear algebra, discrete mathematics possibly including graph theory, trees and networks, optimisation. Introduction to digital electronics, computer organisation and computational techniques. Digital gates, combinatorial and synchronous circuits, data representation, instruction sets, memory, hardware, interfacing. Numerical computation, numerical algorithms. Emphasises the relationship between business and industrial applications and their associated operations research models. Software packages will be used to solve practical problems. Topics such as: linear programming, transportation and assignment models, network algorithms, queues, inventory models and simulation will be considered. Introduction to concepts of modelling of engineering problems, including model formulation, dimensional analysis, solution procedures, comparisons with reality, and shortcomings, with examples from elementary mechanics, structures, hydrostatics, one-dimensional heat, diffusion and fluid motion. Further development of problem-solving skills and group project work. The use of computer tools in engineering design, including advanced spreadsheeting integrated with solid modelling. A selection from: ordinary differential equations, systems of equations, analytical and numerical methods, non-linear ODEs, partial differential equations, separation of variables, numerical methods for solving PDEs, models for optimisation, industrial statistics, data analysis, regression, experimental design reliability methods, regression. Complex Analysis, including complex numbers, analytic functions, complex integration, Cauchy's theorem, Laurent series, residue theory; Laplace transforms; Modelling with partial differential equations, including electronic and electrical applications; Fourier Analysis, Fourier transform, Fast Fourier transform; Optimisation, including unconstrained and constrained models, linear programming and nonlinear optimisation. Mathematical modelling using ordinary and partial differential equations. Probability. Conditional probability, random variables as models of a population, common distribution models, the Poisson process, applications to reliability. Exploratory data analysis, confidence intervals, tests of hypothesis, t-tests, sample tests and intervals, paired comparisons. Introduction to one-way ANOVA. Linear and polynomial regression, regression diagnostics. Numerical algorithms and their translation to computer code. A selection of topics from numerical solution of linear equations, eigen problems, ordinary differential equations, numerical integration, nonlinear equations, finite differences and partial differential equations. Vector calculus and integral theorems. Continuum hypothesis, indicial notation, deformation, strain, traction, stress, principal directions, tensors, invariants, constitutive laws, isotropy, homogeneity. Navier-Stokes and Navier's equations. Isotropic elasticity, elastic moduli, plane stress and plane strain. Airy stress function, Viscous flow, simple solutions of the Navier-Stokes equations. Flow over flat plates, boundary layers. Ideal flow, velocity potential, stream function, 2-D flows. Use of optimisation modelling languages, simulation software and databases, with an emphasis on practical problem solving and laboratory-based learning. Applications of elasticity and fluid dynamics theory to engineering problems including design and analysis of mechanical assemblies. Group projects to formulate design proposals, including costings for development and manufacture. Underlying Finite Element Modelling (FEM) and Continuum Mechanics concepts. Utilisation of 3D CAD and FEM software during both design and analysis phases. Linear programming, the revised simplex method and its computational aspects, duality and the dual simplex method, sensitivity and post-optimal analysis. Network optimisation models, maximum flow, shortest path and spanning tree algorithms. Transportation, assignment and transhipment models, and the network simplex method. An investigation carried out under the supervision of a member of staff on a topic assigned by the Head of Department of Engineering Science. A written report on the work must be submitted. An advanced course on topics to be determined each year by the Head of Department of Engineering Science. A selection of modules on mathematical modelling methods in engineering, including theory of partial differential equations, integral transforms, methods of characteristics, similarity solutions, asymptotic expressions, theory of waves, special functions, non-linear ordinary differential equations, calculus of variations, tensor analysis, complex variables, wavelet theory and other modules offered from year to year. Advanced topics in mathematical modelling and computational techniques, including linear algebra and its applications (topics on singular value decomposition, ill-conditioning, orthogonal factorisation, least squares, eigen-problems and iterative methods), perturbation theory (topics on dimensional analysis, regular and singular perturbation analysis) and signal processing (topics on neural network models such as the multi-layer perception and self organising map). An advanced course on finite elements, boundary elements and finite differences. Applications of continuum mechanics to problems in biomechanics, fluid mechanics and solid mechanics. Including topics such as large deformation elasticity theory applied to soft tissues, inviscid flow theory, compressible flows, viscous flows, meteorology, oceanography, coastal ocean modelling, mixing in rivers and estuaries. Fracture, composite materials and geomechanics. Turbulence and turbulence modelling. Advanced numerical techniques in computational fluid dynamics (CFD). Application of CFD to environmental flows and aerodynamics. A variety of topics in engineering solid mechanics which could include composite materials, geomechanics, contact mechanics, fracture mechanics, rheology, thermomechanics, constitutive theory and computational methods. An advanced course in continuum mechanics covering topics in the mechanics of solids and fluids and other continua. Theoretical and applied finite element and boundary element methods for static and time dependent problems of heat flow, bioelectricity and linear elasticity. Meta-heuristics and local search techniques such as Genetic Algorithms, Simulated Annealing, Tabu Search and Ant Colony Optimisation for practical optimisation. Introduction to optimisation under uncertainty, including discrete event simulation, decision analysis, Markov chains and Markov decision processes and dynamic programming. Computational methods for solving optimisation problems, including branch and bound and cutting plane methods for integer programming and a selection of methods for convex, nonlinear and network optimisation, such as Lagrangean relaxation.
Score: 10.682133 Details | Listing | Web page