| source MIT (X) |
level |
department Mathematics (X) |
18.01 Calculus ( , ) Prereq: None Units: 5-0-7 Credit cannot also be received for 18.014 , 18.01A URL: http://www-math.mit.edu/18.01/ Lecture: TR1,F2 ( 54-100 ) Recitation: MW10 ( 2-142 ) or MW11 ( 2-142 , 2-143 ) or MW12 ( 2-142 , 2-143 ) or MW1 ( 2-143 , 4-265 , 26-328 ) or MW2 ( 4-265 , 26-328 , 2-135 ) or MW3 ( 4-265 ) +final Differentiation and integration of functions of one variable, with applications. Informal treatment of limits and continuity. Differentiation: definition, rules, application to graphing, rates, approximations, and extremum problems. Indefinite integration; separable first-order differential equations. Definite integral; fundamental theorem of calculus. Applications of integration to geometry and science. Elementary functions. Techniques of integration. Polar coordinates. L'Hopital's rule. Improper integrals. Infinite series: geometric, p-harmonic, simple comparison tests, formal power series for some elementary functions. Fall: B. B. Brubaker Spring: Staff
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18.01A Calculus ( ) Prereq: Knowledge of differentiation and elementary integration Units: 5-0-7 Credit cannot also be received for 18.01 , 18.014 URL: http://math.mit.edu/~apm/1801A.html Lecture: TR1,F2 (ENDS OCT 18) ( 26-100 ) Recitation: MW11 ( 2-139 ) or MW12 ( 2-139 , 4-159 ) or MW1 ( 4-159 , 26-142 ) or MW2 ( 4-159 , 26-142 , 2-102 , 24-121 ) or MW3 ( 4-159 , 24-121 ) Six-week review of one-variable calculus, emphasizing material not on the high-school AB syllabus: integration techniques and applications, polar coordinates, improper integrals, infinite series. Prerequisites: one year of high-school calculus or the equivalent, with a score of 4 or 5 on the AB Calculus test (or the AB portion of the BC test, or an equivalent score on a standard international exam), or equivalent college transfer credit, or a passing grade on the first half of the 18.01 advanced standing exam. A. P. Mattuck
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18.014 Calculus with Theory ( ) Prereq: None Units: 5-0-7 Credit cannot also be received for 18.01 , 18.01A Lecture: TR1,F2 ( 2-147 ) Recitation: MW2 ( 2-147 ) +final Covers the same material as 18.01, but at a deeper and more rigorous level. Emphasizes careful reasoning and understanding of proofs. Assumes knowledge of elementary calculus. Topics: axioms for the real numbers; the Riemann integral; limits, theorems on continuous functions; derivatives of functions of one variable; the fundamental theorems of calculus; Taylor's theorem; infinite series, power series, rigorous treatment of the elementary functions. G. K. Lyo
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18.02 Calculus ( , ) Prereq: Calculus I (GIR) Units: 5-0-7 Credit cannot also be received for 18.022 , 18.023 , 18.024 , 18.02A URL: http://www-math.mit.edu/18.02/ Lecture: TR1,F2 ( 10-250 ) Recitation: MW10 ( 2-131 , 2-146 ) or MW11 ( 2-131 , 2-146 ) or MW12 ( 2-131 , 2-146 ) or MW1 ( 2-131 , 2-142 , 2-146 , 2-136 ) or MW2 ( 2-131 , 2-142 , 2-146 , 2-136 , 2-143 ) or MW3 ( 2-131 , 4-163 , 2-146 , 2-143 ) +final Calculus of several variables. Vector algebra in 3-space, determinants, matrices. Vector-valued functions of one variable, space motion. Scalar functions of several variables: partial differentiation, gradient, optimization techniques. Double integrals and line integrals in the plane; exact differentials and conservative fields; Green's theorem and applications, triple integrals, line and surface integrals in space, Divergence theorem, Stokes' theorem; applications. Fall: B. Poonen Spring: A. P. Mattuck
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18.02A Calculus ( , , ) Prereq: Calculus I (GIR) Units: 5-0-7 Credit cannot also be received for 18.02 , 18.022 , 18.023 , 18.024 URL: http://math.mit.edu/~mahlburg/07-1802A.html Lecture: TR1,F2 (BEGINS OCT 21) ( 26-100 ) +final First half is taught during the last six weeks of the Fall term; covers material in the first half of 18.02 (through double integrals). Second half of 18.02A can be taken either during IAP (daily lectures) or during the first half of the Spring term; it covers the remaining material in 18.02. Fall: J. W. Bush Spring: K. Wehrheim
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18.022 Calculus ( ) Prereq: Calculus I (GIR) Units: 5-0-7 Credit cannot also be received for 18.02 , 18.023 , 18.024 , 18.02A URL: http://www-math.mit.edu/18.022/ Lecture: TR1,F2 ( 4-370 ) Recitation: MW12 ( 2-132 ) or MW1 ( 2-255 , 2-132 ) or MW2 ( 2-132 ) or MW3 ( 2-132 ) +final Calculus of several variables. Topics as in 18.02 but with more focus on mathematical concepts. Vector algebra, dot product, matrices, determinant. Functions of several variables, continuity, differentiability, derivative. Parametrized curves, arc length, curvature, torsion. Vector fields, gradient, curl, divergence. Multiple integrals, change of variables, line integrals, surface integrals. Manifolds with boundary, Stokes' theorem in one, two, and three dimensions. T. A. Kemp
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18.023 Calculus with Applications ( ) Prereq: Calculus I (GIR) Units: 5-0-7 Credit cannot also be received for 18.02 , 18.022 , 18.024 , 18.02A Lecture: TR1,F2 ( 4-270 ) Recitation: TR2 ( 4-163 ) or TR3 ( 4-163 ) Calculus of several variables, emphasizing applications. Vector algebra, partial differentiation, multiple integrals, and vector calculus. Asymptotic and numerical methods. D. J. Benney
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18.024 Calculus with Theory ( ) Prereq: Calculus I (GIR) and permission of Instructor Units: 5-0-7 Credit cannot also be received for 18.02 , 18.022 , 18.023 , 18.02A Continues 18.014. Parallel to 18.02, but at a deeper level, emphasizing careful reasoning and understanding of proofs. Considerable emphasis on linear algebra and vector integral calculus. G. K. Lyo
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18.03 Differential Equations ( , , ) Prereq: None. Coreq: Calculus II (GIR) Units: 5-0-7 Credit cannot also be received for 18.034 , 18.036 URL: http://math.mit.edu/~apm/1803.html Lecture: MWF3 ( 54-100 ) Recitation: WF10 ( 4-265 ) or TR10 ( 2-105 ) or TR11 ( 2-143 , 2-146 , 2-139 ) or TR12 ( 2-143 , 2-146 ) or TR1 ( 26-142 , 4-153 ) or TR2 ( 4-153 ) +final Study of ordinary differential equations (ODEs), including modeling physical systems. Solution of first-order ODEs by analytical, graphical, and numerical methods. Linear ODEs, primarily second order with constant coefficients. Complex numbers and exponentials. Inhomogeneous equations: polynomial, sinusoidal, and exponential inputs. Oscillations, damping, resonance. Fourier series inputs; resonant terms. Laplace transform methods; convolution and delta function. Matrix methods for first order linear systems: eigenvalues and eigenvectors, matrix exponentials, variation of parameters. Nonlinear autonomous systems: critical point analysis, phase plane diagrams, applications to modeling. Fall: D. A. Vogan Spring: H. R. Miller
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18.034 Differential Equations ( ) Prereq: None. Coreq: Calculus II (GIR) Units: 5-0-7 Credit cannot also be received for 18.03 , 18.036 Covers much of the same material as 18.03 with more emphasis on theory. The point of view is rigorous and results are proven. Local existence and uniqueness of solutions. First order equations, separation, initial value problems. Systems, linear equations, independence of solutions, undetermined coefficients. R. Bezrukavnikov
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18.036 Differential Equations (New) ( ) Prereq: None. Coreq: Calculus II (GIR) Units: 5-0-7 Credit cannot also be received for 18.03 , 18.034 Subject Cancelled Study of ordinary differential equations (ODEs), including modeling physical systems. Solution of first-order ODEs by analytical, graphical, and numerical methods. Linear ODEs, primarily second order with constant coefficients. Complex numbers and exponentials. Inhomogeneous equations: polynomial, sinusoidal, and exponential inputs. Oscillations, damping, resonance. Fourier series inputs; resonant terms. Matrix methods: eigenvalues and eigenvectors, matrix powers and exponentials. Applications to linear systems. Nonlinear autonomous systems: critical point analysis, phase plane diagrams, applications to modeling. Enrollment limited. Information: H. R. Miller
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18.04 Complex Variables with Applications ( ) Prereq: Calculus II (GIR) ; 18.03 or 18.034 Units: 4-0-8 Credit cannot also be received for 18.075 URL: http://math.mit.edu/18.04/ Complex algebra and functions; analyticity; contour integration, Cauchy's theorem; singularities, Taylor and Laurent series; residues, evaluation of integrals; multivalued functions, potential theory in two dimensions; Fourier analysis and Laplace transforms. H. Cheng
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18.05 Introduction to Probability and Statistics ( ) Prereq: Calculus I (GIR) Units: 3-0-9 Credit cannot also be received for 6.041 URL: http://math.mit.edu/~pak/courses/1805.htm Elementary introduction with applications. Basic probability models. Combinatorics. Random variables. Discrete and continuous probability distributions. Statistical estimation and testing. Confidence intervals. Introduction to linear regression. L. Wang
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18.06 Linear Algebra ( , , ) Prereq: Calculus II (GIR) Units: 4-0-8 Credit cannot also be received for 18.700 URL: http://web.mit.edu/18.06/www/ Lecture: MWF10 ( 54-100 ) Recitation: T10 ( 4-257 , 2-132 , 4-231 ) or T11 ( 2-132 , 2-131 ) or T12 ( 2-132 , 2-131 ) or T1 ( 2-131 , 2-132 , 2-146 ) or T2 ( 2-131 , 2-146 , 12-142 ) or T3 ( 2-131 , 2-146 ) +final Basic subject on matrix theory and linear algebra, emphasizing topics useful in other disciplines, including systems of equations, vector spaces, determinants, eigenvalues, singular value decomposition, and positive definite matrices. Applications to least-squares approximations, stability of differential equations, networks, Fourier transforms, and Markov processes. Uses MATLAB. Compared with 18.700, more emphasis on matrix algorithms and many applications. Fall: A. Postnikov Spring: G. Strang
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18.062J Mathematics for Computer Science ( , ) (Same subject as 6.042J ) Prereq: Calculus I (GIR) Units: 5-0-7 URL: http://theory.csail.mit.edu/classes/6.042 Lecture: MWF11-12.30 ( 32-082 ) or MWF3-4.30 ( 32-082 ) +final Elementary discrete mathematics for computer science and engineering. Emphasis on mathematical definitions and proofs as well as on applicable methods. Topics: formal logic notation, proof methods; induction, well-ordering; sets, relations; elementary graph theory; integer congruences; asymptotic notation and growth of functions; permutations and combinations, counting principles; discrete probability. Further selected topics such as: recursive definition and structural induction; state machines and invariants; recurrences; generating functions. A. R. Meyer, T. Leighton
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18.075 Advanced Calculus for Engineers ( , ) (H except 2, 6, 8, 12, 13, 16, 18, 22) Prereq: Calculus II (GIR) ; 18.03 Units: 3-0-9 Credit cannot also be received for 18.04 Lecture: MWF12 ( 2-102 ) Functions of a complex variable; calculus of residues. Ordinary differential equations; Bessel and Legendre functions; Sturm-Liouville theory; partial differential equations. Fall: H. Cheng Spring: T. Gilet
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18.085 Computational Science and Engineering I ( , , ) Prereq: Calculus II (GIR) ; 18.03 or 18.034 Units: 3-0-9 URL: http://www-math.mit.edu/~kasimov/teaching/18.085.html Lecture: MWF11 ( 2-190 ) Review of linear algebra, applications to networks, structures, and estimation, finite difference and finite element solution of differential equations, Laplace's equation and potential flow, boundary-value problems, Fourier series, discrete Fourier transform, convolution. Frequent use of MATLAB in a wide range of scientific and engineering applications. Fall: G. Strang Spring: L. Demanet
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18.086 Computational Science and Engineering II ( ) Prereq: Calculus II (GIR) ; 18.03 or 18.034 Units: 3-0-9 URL: http://math.mit.edu/18086/ Initial value problems: finite difference methods, accuracy and stability, heat equation, wave equations, conservation laws and shocks, level sets, Navier-Stokes. Solving large systems: elimination with reordering, iterative methods, preconditioning, multigrid, Krylov subspaces, conjugate gradients. Optimization and minimum principles: weighted least squares, constraints, inverse problems, calculus of variations, saddle point problems, linear programming, duality, adjoint methods. Information: G. Strang
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18.089 Review of Mathematics ( ) Prereq: Permission of instructor Units arranged One-week review of one-variable calculus (18.01), followed by concentrated study covering multivariable calculus (18.02), two hours per day for five weeks. Primarily for graduate students in Course 2N. Degree credit allowed only in special circumstances. Information: A. P. Mattuck
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18.094J Teaching College-Level Science and Engineering ( ) (Same subject as 5.95J , 6.982J , 7.59J , 8.395J ) Prereq: None Units: 2-0-2 [P/D/F] URL: http://web.mit.edu/5.95/ Participatory seminar focuses on the knowledge and skills necessary for teaching science and engineering in higher education. Topics include: theories of adult learning; course development; promoting active learning, problem solving, and critical thinking in students; communicating with a diverse student body; using educational technology to further learning; lecturing; creating effective tests and assignments; and assessment and evaluation. Students research and present a relevant topic of particular interest. Subject is appropriate for both novices and those with teaching experience. L. Breslow
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18.095 Mathematics Lecture Series ( ) Prereq: Calculus I (GIR) Units: 2-0-4 [P/D/F] URL: http://www-math.mit.edu/~davis/18.095.html Ten lectures by mathematics faculty members on interesting topics from both classical and modern mathematics. All lectures accessible to students with calculus background and an interest in mathematics. At each lecture, reading and exercises are assigned. Students prepare these for discussion in a weekly problem session. Information: H. R. Miller
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18.098 Independent Activities ( ) Prereq: Permission of instructor Units arranged [P/D/F] Studies or special individual reading arranged in consultation with individual faculty members and subject to departmental approval. Information: H. R. Miller
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18.099 Independent Activities ( , , , ) Prereq: Permission of instructor Units arranged Studies (during IAP) or special individual reading (during regular terms). Arranged in consultation with individual faculty members and subject to departmental approval. Information: H. R. Miller
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18.100A Analysis I ( , ) (H except 18) Prereq: Calculus II (GIR) ; 18.03 or 18.034 Units: 3-0-9 Credit cannot also be received for 18.100B , 18.100C URL: http://math.mit.edu/~apm/18100A.html Lecture: MWF1 ( 4-163 ) +final
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18.100B Analysis I ( , ) (H except 18) Prereq: Calculus II (GIR) ; 18.03 or 18.034 Units: 3-0-9 Credit cannot also be received for 18.100A , 18.100C URL: http://math.mit.edu/~lenzmann/18-100B-2.html Lecture: MW9.30-11 ( 4-149 ) or TR11-12.30 ( 4-163 ) +final
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