## Approved courses for the applied math/computational science requirement

TAM 541 Mathematical Methods I

Credit: 4 hours.

Vector and tensor algebra and complex-variable methods; ordinary differential equations, qualitative questions of existence and uniqueness; analytic solution methods, numerical methods, power-series solution and special functions; eigenvalue problems, Green’s functions, Laplace transforms, stability of solutions; engineering applications drawn from mechanics.

TAM 470 Computational Mechanics (same as CSE 450)

Credit: 3 OR 4 hours.

Modercomputational mechanics: mappings and iterative methods; stability; convergence; consistency; numerical and symbolic solutions of ordinary and partial differential equations; finite-difference methods; the finite-element method; spectral methods. Applications to problems in solid mechanics, fluid mechanics, and dynamics.

ME 471 Finite Element Analysis (same as CSE 451)

Credit: 3 OR 4 hours.

The finite element method and its application to engineering problems: truss and frame structures, heat conduction, and linear elasticity; use of application software; overview of advanced topics such as structural dynamics, fluid flow, and nonlinear structural analysis.

CSE 510 Numerical Methods for PDEs (same as CS 555)

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.

MATH 442 Intro Partial Diff Equations

Credit: 3 OR 4 hours.

Introduces partial differential equations, emphasizing the wave, diffusion and potential (Laplace) equations. Focuses on understanding the physical meaning and mathematical properties of solutions of partial differential equations. Includes fundamental solutions and transform methods for problems on the line, as well as separation of variables using orthogonal series for problems in regions with boundary. Covers convergence of Fourier series in detail.

4 hours of credit requires approval of the instructor and completion of additional work of substance

CS 450 (same as CSE 401, ECE 491, and MATH 450) Numerical Analysis

Credit: 3 OR 4 hours.

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.

MATH 487 Advanced Engineering Math (same as ECE 493)

Credit: 3 OR 4 hours.

Complex linear algebra, inner product spaces, Fourier transforms and analysis of boundary value problems, Sturm-Liouville theory.

MATH 488 Math Methods in Engineering

Credit: 3 OR 4 hours.

Matrices, determinants, bounds and approximations to eigenvalues, introduction to linear operator theory and inner product spaces, orthogonal expansions, and Fourier transforms.