EM2207 Mathematical Methods

Objectives:

This course  introduces the student  the concepts of Mathematical Methods and to their application in  engineering problems
 

Pre-requisite:

EM2105
 

Credit Hours:

3
 

Contact Hours:

35 hours of Lectures
15 hours of Assignments/Tutorials
20 hours of practical
 

Course Marks

70%  Final Exam
30% Course Work
 

Text & References

-       C. Henry Edwards, David E. Penney, “Elementary Differential Equations with Boundary Value Problems”, 4/e. Prentice-Hall, 2000, ISBN 0-13-011301-8

-       Jack L. Goldberg, Merle C. Potter, “Differential Equations: A Systems Approach” , 1/e, Prentice-Hall, 1998, ISBN 0-13-211319-8
 

Description:

Infinite series, Fourier series, Fourier integral theorem. Fourier transforms, Lapalace transform, and Special functions: Bessel’s functions, error functions, application to differential equations, partial differential
 

Outlines

1. The Laplace Transform
Introduction. Preliminaries. General Properties of the Laplace Transform. Sectionally Continuous Functions. Laplace Transforms of Periodic Functions. The Inverse Laplace Transform. Partial Fractions. The Convolution Theorem. The Solution of Initial-Value Problems. The Laplace Transform of Systems. Tables of Transforms.
2. Series Methods.
Introduction. Analytic Functions. Taylor Series of Analytic Functions. Power Series Solutions. Legendre's Equations. Three Important Examples. Bessel's Equation. The Wronskian Method. The Frobenius Method.
3. Boundary-Value Problems.
Introduction. Separation of Variables. Fourier Series Expansions. The Wave Equation. The One-Dimensional Heat Equation. The Laplace Equation. A Potential about a Spherical Surface.