MTL260: Boundary Value Problems

3 Credits (3-0-0)

Pre-requisites: MTL100, MTL101

Sturm Liouville problem, Boundary Value Problems for nonhomogeneous ODEs, Green’s Functions. Fourier Series and Integrals: Periodic Functions and Fourier Series, Arbitrary Period and Half-Range Expansions, Fourier Integral theorem and convergence of series Parabolic equations: Heat equation, Fourier series solution, Different Boundary Conditions, Generalities on the Heat Conduction Problems on bounded and unbounded domains and applications in Option pricing.

The Wave Equation: The Vibrating String, Solution of the Vibrating String Problem, d’Alembert’s Solution, One-Dimensional Wave Equation

The Potential Equation: Potential Equation in a Rectangle, Fourier series method, Potential equation in Unbounded Regions, Fourier integral representations, Potential in a Disk and Limitations.

Higher Dimensions and Other Coordinates: Two-Dimensional Wave Equation: Derivation, Parabolic equation, Solution by Fourier series, Problems in Polar Coordinates, Temperature in a Cylinder, Vibrations of a Circular Membrane.

Finite dimensional approximations of solutions, piecewise linear polynomials and introduction to different methods like Galerkin and Petrov-Galerkin method.