Approved courses for the applied math/computational science requirement

AM 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.

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.

CEE 498 Computer Methods (same as CEE 490)
Credit: 4 hours
This course covers computer methods and their programming for solving common types of differential equations in engineering. Students will be exposed to state-of-the-art open-source numerical methods libraries. This course will enable students to develop high-performance and high-purpose codes in these open-source frameworks for their research problems in an efficient way.

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.

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.

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

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.

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.