Mathematical Methods




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Course Contents

Multiple Integral Theorems and their Applications: Greens theorem, Stokes theorem and Gauss divergence theorem. Integral Transforms: Fourier, Fouriersine/cosine and Hankel 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 functional containing first order derivatives and Euler equations. Functional containing higher order derivatives and several independent variables. Variational problem with moving boundaries. Boundaries with constraints. Higher order necessary conditions, Weiretrass function, Legendres and Jacobiscondition. Existence of solutions of variational problems. Rayleigh Ritz method, statement of Ekelands variational principle; Self ad joint, normal and unitary operators; Banach algebras. 



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