ROWAN
UNIVERSITY

Department
of Mathematics

Syllabus

**Math 01.515
Engineering Applications of Analysis
**

**Course Description:**

** **

**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.

**Objectives:**

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:

- Use analytical techniques such as separation of
variable, Fourier series, Green’s functions for solving linear multi-dimensional
PDEs.
- Use numerical methods such as finite-difference,
finite-element, and Monte-Carlo to solve PDEs.
- Use method of characteristics and method of
inverse scattering to solve nonlinear PDEs.
- Identify mathematical models for describing
various physical and engineering applications.
- Use a computer algebra system, e.g. Mathematica,
to solve problems.

**Topical Outline:**

Topics that may be covered include:

- Separation of variables, superposition
principle, Fourier series.
- Heat equation, Laplace’s equation, wave equation.
- Green’s functions, nonhomogeneous problems.
- Finite-difference methods, finite-element
method, Monte-Carlo.
- Fourier transforms, Laplace transforms,
infinite-domain problems.
- Method of characteristics, shock waves.
- Solitons, inverse scattering.

**Texts:**

The following books may be used as texts for the course.

1.
Haberman, R., Elementary Applied Partial Differential
Equations, 3^{rd} edition, Prentice-Hall, 1998.

2.
Kreyszig, E., Advanced Engineering Mathematics, 8^{th}
edition, Wiley, 1999.

3.
Strauss, W. A., Partial Differential Equations: An
Introduction, Wiley, 1992.