Credits: 3 (3-0-0)
Description
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.
Prerequisite Tree
flowchart TD
MTL260-610[MTL260]
MTL260-610 --> MTL101-610[MTL101]
MTL260-610 --> MTL100-610[MTL100]
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