SE 360. Mathematical Methods
(3 - 1 - 0 - 0 - 4)
Multiple Integral Theorems and their Applications: Green's theorem, Stoke's theorem and Gauss divergence theorem. Integral Transforms: Fourier, Fourier sine/cosine and Hankle Transforms with their inverse transforms (properties, convolution theorem and application to solve differential equation). Perturbation Methods: Perturbation theory, Regular perturbation theory, Singular perturbation theory, Asymptotic matching. Calculus of Variation: Introduction, Variational problem with functionals containing first order derivatives and Euler equations. Functionals containing higher order derivatives and several independent variables. Variational problem with moving boundaries. Boundaries with constraints. Higher order necessary conditions, Weiretrass function, Legendre's and Jacobi's condition. Existence of solutions of variational problems. Rayleigh-Ritz method, statement of Ekeland's variational principle and applications.
- REFERENCES:
- Calculus of Variation with Applications - A.S. Gupta
- Introduction to Perturbation Techniques - A.H. Nayfeh
- Integral Transform in Applied Mathematics - J.W. Miles
- Mathematical Physics - Dattman
- Concerned Department: Mathematics