Mathematical methods is an important branch of mathematics. 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

*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.

*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**

- Powers, D. L. (2005).
*Boundary value problems and partial differential equations*, (5th ed.). Boston: Academic Press. - Boyce, W. E. (2005).
*Elementary differential equations,*(8th ed.). New York: John Wiley and Sons.

*Suggested Books*

- Brown, J. W. and Churchil, R. V. (2006).
*Fourier series and boundary value problems.*New York: McGraw Hill. - Snider, A. D. (2006).
*Partial differential equations .*New York: Dover Publications Inc. - Boyce, W. E. (2005).
*Elementary differential equations,*(8th ed.). New York: John Wiley and Sons. - Krasnov M. L. Makarenko, G. I. and Kiselev, A. I
*.*(1985).*Problems and exercises in the calculus of variations.*USA: Imported Publications, Inc.

*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

Wednesday 11:00 pm-12:30 pm

Thursday 11:00 pm-12:30 pm

Commencement of Classes 22-02-2021

Mid Term Examination 19-04-2021

Final Term Examination 21-06-2021

Declaration of Result 02-07-2021