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Continuation of CS 357. Orthogonalization methods for least squares, Krylov subspace methods, non-linear equations and optimization in multiple dimensions, initial and boundary value problems for ordinary and partial differential equations. Course Information: No graduate credit. Credit is not given for both CS 457 and CS 450. Prerequisite: CS 357.

Construct and analyze the numerical approximation to ordinary differential equations (1)(2)
Construct and analyze the numerical approximation to partial differential equations (1)(2)
Assess sparse matrix problems and their connection with graphs and partial differential equations (1)(6)
Attain a working knowledge of approximating solutions to a variety of differential and algebraic equations in the context of applications (1)

Use computer software to solve problems in numerical differential equations. (1)(6)

Initial Value Problems and Finite Differences
Boundary Value Problems and Finite Differences

Numerical Linear Algebra

Selected Elective.