# Our Courses ## CS357 · Numerical Methods I

Offered Fall and Spring.

Credit: 3 hours.

This introductory course on numerical methods prepares undergraduate CS majors for applications of numerical methods they will encounter as part of the undergraduate and early graduate Computer Science curriculum.

Fundamentals of numerical methods for students in science and engineering; floating-point computation, systems of linear equations, approximation of functions and integrals, the single nonlinear equation, and the numerical solution of ordinary differential equations; various applications in science and engineering; programming exercises and use of high quality mathematical library routines.

Same as MATH357. Credit is not given for CS357 if credit for CS450 has been earned. (Counts for advanced hours in LAS). Prerequisite: A 100-level computer science course; MATH225 or MATH415; MATH241. ## CS450 · Numerical Analysis

Offered Fall and Spring.

Credit: 3 OR 4 hours.

This fast-moving course builds up numerical analysis from the very basics up to advanced topics, including a glimpse of PDE solving technology. It is commonly taken by beginning graduate students in scientific computing as well as the engineering disciplines.

Linear system solvers, optimization techniques, interpolation and approximation of functions, solving systems of nonlinear equations, eigenvalue problems, least squares, and quadrature; numerical handling of ordinary and partial differential equations.

Same as CSE401, ECE491, and MATH450. 3 undergraduate hours. 3 or 4 graduate hours. Credit is not given for both CS450 and CS457. Prerequisite: CS101 or CS125; CS357 or MATH415; MATH285. ## CS457 · Numerical Methods II

Offered Spring.

Continuation of CS357. 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. No graduate credit. Credit is not given for both CS457 and CS450. Prerequisite: CS357. ## CS554 · Parallel Numerical Algorithms

Offered Fall, odd years.

Credit: 4 hours.

Numerical algorithms for parallel computers: parallel algorithms in numerical linear algebra (dense and sparse solvers for linear systems and the algebraic eigenvalue problem), numerical handling of ordinary and partial differential equations, and numerical optimization techniques. Same as CSE512. Prerequisite: One of CS450, CS457, CS555. ## CS555 · Numerical Methods for PDEs

Offered Spring.

Credit: 4 hours.

Numerical techniques for initial and boundary value problems in partial differential equations. Finite difference and finite element discretization techniques, direct and iterative solution methods for discrete problems, and programming techniques and usage of software packages. Same as CSE510. Prerequisite: CS450 or CS457. ## CS556 · Iterative and Multigrid Methods

Offered Fall, even years.

Credit: 4 hours.

Comprehensive treatment of algebraic and multigrid iterative methods to solve systems of equations, primarily linear equations arising from discretization of partial differential equations.

Same as CSE511. ## CS558 · Topics in Numerical Analysis

Offered Irregularly.

Select topics in numerical analysis. For example, Functional Analysis for Numerical Computations. ## CS598 · Special Topics

Offered Irregularly.

Special topics in Numerical Analysis. For example, spectral element methods, computational topology, and integral equations.