The Scientific Computing Group offers the following courses:
AM0016 -- Topics in Scientific Computing
For students in any discipline that may involve numerical computations. Includes instruction for programming in MATLAB. Applications include solution of linear equations (with vectors and matrices) and nonlinear equations (by bisection, iteration, and Newton's method), interpolation, and curve-fitting, difference equations, iterated maps, numerical differentiation and integration, and differential equations.
Prerequisites: MA10 or its equivalent
AM0117 -- Computational Linear Algebra
Devoted to computational linear algebra. Tailored to computer science concentrators but the topics will also appeal to other science concentrators. Topics include Newton methods, elements of basic linear algebra, Gauss elimination and matrix decompositions (Cholesky, LU, QR, etc.) Methods for computation of eigenvalues and eigenvectors, round-off errors and error analysis. Basic iterative methods such as SOR and conjugate gradient methods.
Prerequisites: MA10 or its equivalent. MA52 and AM16 recommended.
AM0118 -- Introduction to the Numerical Solution of Differential Equations
Basic numerical techniques for solving ordinary and partial differential equations. Topics include Euler, Runge-Kutta, and multistep method, error analysis, and step-size control for ordinary differential equations. Methods for partial differential equations include finite difference and finite element methods for Poisson equation, the heat equation, and wave problems and various solution techniques.
Prerequisites: AM 33, 34, or 35, 36, AM 117 is recommended, not required.
AM0191 -- Topics in Applied Mathematics
Topics course, changes from year to year.
AM0255 -- Numerical Solution of Partial Differential Equations I
Finite difference methods for solving time-depend 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.
AM0256 -- Numerical Solution of Partial Differential Equations II
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.
Prerequisites: AM255 or equivalent. Some knowledge of computer programming expected.
AM0257 -- Numerical Solution of Partial Differential Equations III
We will cover finite difference and other methods for solving hyperbolic partial differential equations. Background material in hyperbolic partial differential equations will also be covered. Algorithm development, analysis, implementation and application issues will be addressed.
Prerequisites: AM255 or equivalent. Some knowledge of computer programming expected.
AM0258 -- Computational Fluid Dynamics
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.
Prerequisites: Material from AM 117 and 118 is appropriate as prerequisite, but no prior knowledge of fluid dynamics is necessary.
Content changes from year to year.
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