Department of Mathematics
Math 01.515 Engineering Applications of Analysis
Math 01. 515 Engineering Applications of Analysis†††††††††††††††††††††††††††††††††††††† 3 s.h.
††††††††††† This course will cover various techniques for solving linear and nonlinear partial differential equations (PDEs) arising from physical and engineering applications; this includes both analytical and numerical methods.† More specifically, students will learn the method of separation of variables for solving multi-dimensional problems, Fourier/Laplace transforms for solving infinite-domain problems, numerical methods (finite-difference, finite-element, Monte-Carlo), Green's functions, method of characteristics, and inverse scattering.† Basic applications include a vibrating membrane (wave equation), heat flow along a metal plate (heat equation), steady-state fluid flow (Laplace's equation), traffic flow (shock waves), and solitary waves (solitons).† Students will be required to use a computer algebra system, e.g. Mathematica, to solve problems. †
Students in this course will become familiar with various analytical and numerical techniques for solving partial differential equations (PDEs).† At the end of this course, students will be able to:
Topics that may be covered include:
The following books may be used as texts for the course.
1. Haberman, R., Elementary Applied Partial Differential Equations, 3rd edition, Prentice-Hall, 1998.
2. Kreyszig, E., Advanced Engineering Mathematics, 8th edition, Wiley, 1999.
3. Strauss, W. A., Partial Differential Equations: An Introduction, Wiley, 1992.