## Math 488. Math Methods in Engineering

Instructor Syllabus

**Text: **Erwin Kreyszig, *Advanced Engineering Mathematics, *9th Edition, John Wiley and Son Inc.

This course covers a variety of topics in applied mathematics including: systems of linear equations and matrices, eigenvalues and diagonalization of matrices, first order systems of differential equations, stability of planar non-linear systems of differential equations, iterative and least squares methods, orthogonal series including Fourier, Bessel and Legendre series, boundary value problems for partial differential equations, discrete and continuous Fourier transforms including the mathematics of the Fast Fourier Transform. The course will stress the application of mathematical results and methods to solve problems, rather than the derivation of mathematical theorems.

Prerequisites: Calculus (including mulivariate calculus) and some background in introductory matrix algebra and introductory differential equations is assumed.

This course will cover the following topics:

- Matrices and linear systems, eigenvalues and diagonalization of matrices; iterative methods for solving linear systems and for finding eigenvalues and eigenvectors. (Some familiarity with basic matrix operations will be assumed but a brief review will be provided.)
- Solution of linear differential equations and systems of linear differential equations. (Some familiarity with basic differential equations will be assumed but a brief review will be provided.)
- Planar systems of nonlinear differential equations; stability and asymptotic behavior of solutions.
- The separation of variables method for solving linear partial differential equations with applications to the heat, wave and Laplace equations in various dimensions for various domains.
- Fourier, Bessel and other orthogonal series; continuous and discrete Fourier transforms; applications to the solution of boundary value problems for partial differential equations.