| source Brown University (X) |
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Solution methods and basic theory for first and second order partial differential equations. Geometrical interpretation and solution of linear and nonlinear first order equations by characteristics; formation of caustics and propagation of discontinuities. Classification of second order equations and issues of well-posed problems. Green's functions and maximum principles for elliptic systems. Characteristic methods and discontinuous solutions for hyperbolic systems. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Graduate School College Applied Mathematics Department Return to Previous New Search
Score: 5.0149603 Details | Listing | Web page
Integral equations. Fredholm and Volterra theory, expansions in orthogonal functions, theory of Hilbert-Schmidt. Singular integral equations, method of Wiener-Hopf. Calculus of variations and direct methods. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Graduate School College Applied Mathematics Department Return to Previous New Search
Score: 5.0149603 Details | Listing | Web page
Calculus of asymptotic expansions, evaluation of integrals. Solution of linear ordinary differential equations in the complex plane, WKB method, special functions. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Graduate School College Applied Mathematics Department Return to Previous New Search
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Topics vary according to interest of instructor and class. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Graduate School College Applied Mathematics Department Return to Previous New Search
Score: 5.0149603 Details | Listing | Web page
Basic theory of ordinary differential equations, flows, and maps. Two-dimensional systems. Linear systems. Hamiltonian and integrable systems. Lyapunov functions and stability. Invariant manifolds, including stable, unstable, and center manifolds. Bifurcation theory and normal forms. Nonlinear oscillations and the method of averaging. Chaotic motion, including horseshoe maps and the Melnikov method. Applications in the physical and biological sciences. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Graduate School College Applied Mathematics Department Return to Previous New Search
Score: 5.0149603 Details | Listing | Web page
Basic theory of ordinary differential equations, flows, and maps. Two-dimensional systems. Linear systems. Hamiltonian and integrable systems. Lyapunov functions and stability. Invariant manifolds, including stable, unstable, and center manifolds. Bifurcation theory and normal forms. Nonlinear oscillations and the method of averaging. Chaotic motion, including horseshoe maps and the Melnikov method. Applications in the physical and biological sciences. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Graduate School College Applied Mathematics Department Return to Previous New Search
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This topics course focuses on applications of dynamical systems to nonlinear waves and patterns such as travelling waves and spiral waves. Among the topics that will be covered are exponential dichotomies, spectral theory of travelling waves, Fredholm theory, and Lyapunov-Schmidt reduction for homoclinic orbits with applications to waves in nonlinear optics and fluids. The prerequisite for the course is a solid (rigorous) grounding in nonlinear dynamics, typically APMA 2190-2200 or equivalent. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Graduate School College Applied Mathematics Department Return to Previous New Search
Score: 5.0149603 Details | Listing | Web page
The theory of the classical partial differential equations, as well as the method of characteristics and general first order theory. Basic analytic tools include the Fourier transform, the theory of distributions, Sobolev spaces, and techniques of harmonic and functional analysis. More general linear and nonlinear elliptic, hyperbolic, and parabolic equations and properties of their solutions, with examples drawn from physics, differential geometry, and the applied sciences. Generally, semester II of this course concentrates in depth on several special topics chosen by the instructor. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Graduate School College Applied Mathematics Department Return to Previous New Search
Score: 5.0149603 Details | Listing | Web page
The theory of the classical partial differential equations, as well as the method of characteristics and general first order theory. Basic analytic tools include the Fourier transform, the theory of distributions, Sobolev spaces, and techniques of harmonic and functional analysis. More general linear and nonlinear elliptic, hyperbolic, and parabolic equations and properties of their solutions, with examples drawn from physics, differential geometry, and the applied sciences. Generally, semester II of this course concentrates in depth on several special topics chosen by the instructor. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Graduate School College Applied Mathematics Department Return to Previous New Search
Score: 5.0149603 Details | Listing | Web page
The course serves as an introduction to the theory of stochastic control and dynamic programming technique. Optimal stopping, total expected (discounted) cost problems, and long-run average cost problems will be discussed in discrete time setting. The last part of the course deals with continuous time determinstic control and game problems. The course requires some familiarity with the probability theory. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Graduate School College Applied Mathematics Department Return to Previous New Search
Score: 5.0149603 Details | Listing | Web page
No description available. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Graduate School College Applied Mathematics Department Return to Previous New Search
Score: 5.0149603 Details | Listing | Web page
Devoted to one or more advanced topics in continuum mechanics not covered in detail by the regular courses. Examples are: nonlinear viscoelastic constitutive equations, strain gradient and micropolar theories of elasticity, coupled mechanical and thermal or electromagnetic phenomena, continuum thermodynamics. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Graduate School College Applied Mathematics Department Return to Previous New Search
Score: 5.0149603 Details | Listing | Web page
Theory of the inelastic behavior of materials with negligible time effects. Experimental background for metals and fundamental postulates for plastic stress-strain relations. Variational principles for incremental elastic-plastic problems, uniqueness. Upper and lower bound theorems of limit analysis and shakedown. Slip line theory. Representative problems in structural analysis, metal forming, indentation, strain and stress concentrations at notches, and ductile failure. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Graduate School College Applied Mathematics Department Return to Previous New Search
Score: 5.0149603 Details | Listing | Web page
No description available. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Graduate School College Applied Mathematics Department Return to Previous New Search
Score: 5.0149603 Details | Listing | Web page
An introduction to fundamental concepts of the mechanics and thermodynamics of fluid flow. Major topics include compressible and incompressible flows, viscous and inviscid flows, and vorticity dynamics. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Graduate School College Applied Mathematics Department Return to Previous New Search
Score: 5.0149603 Details | Listing | Web page
A continuation of APMA 2410. Topics include: low Reynolds number flows, boundary layer theory, wave motion, stability and transition, acoustics, and compressible flows. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Graduate School College Applied Mathematics Department Return to Previous New Search
Score: 5.0149603 Details | Listing | Web page
Initial review of topics selected from flow stability, turbulence, turbulent mixing, surface tension effects, and thermal convection. Followed by focussed attention on the dynamics of dispersed two-phase flow and complex fluids. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Graduate School College Applied Mathematics Department Return to Previous New Search
Score: 5.0149603 Details | Listing | Web page
No description available. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Graduate School College Applied Mathematics Department Return to Previous New Search
Score: 5.0149603 Details | Listing | Web page
Finite difference methods for solving time-dependent initial value problems of partial differential equations. Fundamental concepts of consistency, accuracy, stability and convergence of finite difference methods will be covered. Associated well-posedness theory for linear time-dependent PDEs will also be covered. Some knowledge of computer programming expected. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Graduate School College Applied Mathematics Department Return to Previous New Search
Score: 5.0149603 Details | Listing | Web page
Examines the development and analysis of spectral methods for the solution of time-dependent partial differential equations. Topics include key elements of approximation and stability theory for Fourier and polynomial spectral methods as well as attention to temporal integration and numerical aspects. Some knowledge of computer programming expected. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Graduate School College Applied Mathematics Department Return to Previous New Search
Score: 5.0149603 Details | Listing | Web page
We will cover finite element methods for ordinary differential equations and for elliptic, parabolic and hyperbolic partial differential equations. Algorithm development, analysis, and computer implementation issues will be addressed. In particular, we will discuss in depth the discontinuous Galerkin finite element method. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Graduate School College Applied Mathematics Department Return to Previous New Search
Score: 5.0149603 Details | Listing | Web page
An introduction to computational fluid dynamics with emphasis on incompressible flows. Reviews the basic discretization methods (finite differences and finite volumes) following a pedagogical approach from basic operators to the Navier-Stokes equations. Suitable for first-year graduate students, more advanced students, and senior undergraduates. Requirements include three to four computer projects. Material from APMA 1170 and 1180 is appropriate as prerequisite, but no prior knowledge of fluid dynamics is necessary. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Graduate School College Applied Mathematics Department Return to Previous New Search
Score: 5.0149603 Details | Listing | Web page
This is a topics course, covering a selection of modern applications of probability and statistics in the computational, cognitive, engineering, and neural sciences. The course will be rigorous, but the emphasis will be on application. Topics will likely include: Markov chains and their applications to MCMC computing and hidden Markov models; Dependency graphs and Bayesian networks; parameter estimation and the EM algorithm; Kalman and particle filtering; Nonparametric statistics ("learning theory"), including consistency, bias/variance tradeoff, and regularization; the Bayesian approach to nonparametrics, including the Dirichlet and other conjugate priors; principle and independent component analysis; Gibbs distributions, maximum entropy, and their connections to large deviations. Each topic will be introduced with several lectures on the mathematical underpinnings, and concluded with a computer project, carried out by each student individually, demonstrating the mathematics and the utility of the approach. There will be no exams. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Graduate School College Applied Mathematics Department Return to Previous New Search
Score: 5.0149603 Details | Listing | Web page
A one-semester course on probability theory. It provides introduction to probability based on measure-theoretical approach. This course covers the following subjects: probability spaces, random variables and measurable maps, independence, integration and expectations, convergence of measures, laws of large numbers and Central Limit Theorem, conditional expectations and discrete time martingales. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Graduate School College Applied Mathematics Department Return to Previous New Search
Score: 5.0149603 Details | Listing | Web page
A one semester course on probability and stochastic processes. This course covers the following subjects: Markov chains, Poisson and birth and death processes, martingales, optional sampling theorem, martingale convergence theorem, Brownian motion, elements of Ito's, calculus, introduction to stochastic differential equations, differential equations, Feynman-Kac formula, Girsanov's theorem, Black-Scholes formula, basics of Gaussian and stationary processes. Prerequisite: AMPA 2630 or equivalent course. Prerequisite: APMA 2630. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Graduate School College Applied Mathematics Department Prerequisites: Graduate level APMA 2630 Minimum Grade of S Return to Previous New Search
Score: 5.0149603 Details | Listing | Web page
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