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.

INTENDED LEARNING OUTCOMES

The students would be able to understand the types of transformations and their practical use. Also, they would be able to know their importance in higher education in particular research.

COURSE CONTENTS

1. The Fourier transforms.
2. Fourier analysis of the generalized functions.
3. The Laplace transforms.
4. Hankel transforms for the solution of PDEs and their application to boundary value problems.
5. Green’s Functions and Transform Methods: Expansion for Green’s functions.
6. Transform methods. Closed form Green’s functions. Perturbation Techniques.
7. Perturbation methods for algebraic equations.
8. Perturbation methods for differential equations.
9. Variational Methods: Euler-Lagrange equations.
10. Integrand involving one, two, three and n variables.
11. Special cases of Euler-Lagrange’s equations.
12. Necessary conditions for existence of an extremum of a functional.
13. 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).

Suggested Books

1. J. W. Brown and R. V. Churchil, Fourier Series and Boundary Value Problems, (McGraw Hill, 2006).
2. A. D. Snider, Partial Differential Equations: (Sources and Solutions, Prentice Hall Inc., 1999).

RESEARCH PROJECT /PRACTICALS/LABS/ASSIGNMENTS

Assignments would be given related topics. These may cover to interesting fields related to mathematics. Main purpose would be to learn about various kind of transformations and their importance in field.

ASSESSMENT CRITERIA

Sessional: 20 (Presentation / Assignment 10, Attendance 05, Quiz 05)

Mid-Term Exam:   30

Final-Term Exam: 50

Key Dates and Time of class meeting

Monday : 8:00 am -9:30 am.    

Tuesday: 9:30am-11:00am.

Commencement of Classes                                                   January 13, 2020

Mid Term Examination                                                            March 09-13, 2020

Final Term Examination                                                          May 04-08, 2020

Declaration of Result                                                              May 19, 2020