Course Code: MATH-304

Mathematical Methods

Credit Hours: 3+0

Prerequisite(s): Calculus-III

Specific Objectives of course:

The main objective of this course is to provide the students with a range of mathematical methods that are essential to the solution of advanced problems encountered in the fields of applied physics and engineering. In addition this course is intended to prepare the students with mathematical tools and techniques that are required in advanced courses offered in the
applied physics and engineering programs.

Course Contents:
Fourier Methods: The Fourier transforms. Fourier analysis of the generalized functions. The Laplace transforms. Hankel transforms for the solution of PDEs and their application to boundary value problems. Green’s Functions and Transform Methods: Expansion for Green’s
functions. Transform methods. Closed form Green’s functions. Perturbation Techniques: Perturbation methods for algebraic equations. Perturbation methods for differential equations. Variational Methods: Euler-Lagrange equations. Integrand involving one, two, three and n variables. Special cases of Euler-Lagrange’s equations. Necessary conditions for existence of an extremum of a functional. Constrained maxima and minima.
 

Recommended Books:
1. Powers D. L., Boundary Value Problems and Partial Differential Equations, 5th edition,  Academic Press, 2005.
2. Boyce W. E., Elementary Differential Equations, 8th edition,  John Wiley and Sons, 2005.
3. Krasnov  M. L. Makarenko G. I. and Kiselev A. I, Problems and Exercises in the Calculus  of Variations, Imported Publications, Inc., 1985.
4. J. W. Brown and R. V. Churchil, Fourier Series and Boundary Value Problems, McGraw Hill, 2006.
5. A. D. Snider, Partial Differential Equations: Sources and Solutions, Prentice Hall Inc., 1999.

Assessment criteria:

Mid term exam.           (30 marks) 

Sessional.                    (20 marks) 

Final term exam.         (50 marks) 

Total.                           (100 marks)