**PH-308 Methods of Mathematical and Computational Physics (Pre-req: PH-301)**

- Vector spaces, basis vectors, linear independence, function spaces.
- Review of differentiation and integration, continuity and differentiability, functions of many variables.
- First order differential equations, general solution by integration, uniqueness property.
- Second order differential equations with constant coefficients, Euler linear equations, singular points, series solution by Frobenius' method, solution space, Wronskian, uniqueness.
- Special functions: gamma and beta functions, Stirling's series, Legendre equation, Associated Legendre functions, Hermite equation and polynomials, Laguerre equation and associated polynomials, Bessel’s equation and solutions, spherical Bessel functions.
- Use of Mathematica for items 2-5 above: students will be given practice questions to solve using a computer.
- Second order linear partial differential equations, Laplace equation, wave equation, solution of Poisson equation
- Definition of probability, simple properties, random variables, binomial distribution, Poisson and Gaussian distributions, central limit theorem, statistics.
- Numerical methods: interpolation, root finding, numerical integration, matrix manipulation, numerical solutions of ODE’s, least square fit.

**Recommended texts:**

*Mathematical Methods for Physicists*, by Arfken & Weber, publisher: Academic Press; 6th Edition, (2005).*Mathematical Methods for Physicists,*by Tai L. Chow, publisher: Cambridge University Press (2000).*Numerical Analysis,*by J. Douglas Faires and Richard L. Burden, publisher: Brooks, 8th Edition (2005).