Courses:

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This course is an advanced introduction to applications and theory of numerical methods for solution of differential equations, especially of physically-arising partial differential equations, with emphasis on the fundamental ideas underlying various methods. Topics include finite differences, spectral methods, well-posedness and stability, boundary and nonlinear instabilities. The course assumes familiarity with basic (numerical) linear algebra and will involve a certain amount of programming in MATLAB® or another programming language of your choice.

Introduction to Numerical Analysis (18.330) and Introduction to Numerical Methods (18.335J).

Trefethen, Lloyd N. Spectral Methods in MATLAB®. Philadelphia, PA: Society for Industrial and Applied Mathematics, 2000. ISBN: 0898714656.

Strikwerda, John C. Finite Difference Schemes and Partial Differential Equations. The Wadsworth & Brooks/Cole Mathematics Series. Pacific Grove, CA: Wadsworth & Brooks/Cole Advanced Books & Software, 1989. ISBN: 053409984X.

There will be six homework assignments, two of which may be projects. You may cooperate on the problem sets, but you must write up and turn in your own solutions, and be able to explain them.