PHYS 400 Computational physics

Introduction:The need for computers in science, What is computational physics?, Operating systems and programming languages.

Interpolation: Lagrange interpolation, Neville's algorithm, Linear interpolation, Polynomial interpolation, Cubic spline, Rational function interpolation.

Numerical differentiation: Forward difference, Central difference and higher order methods, Higher order derivatives.

Numerical Integration: Rectangular method, Trapezoid method, Simpson method.

Solution of nonlinear equations:Bisection method, Newton's method, Method of secants, Brute force method.

Differential equations: Euler method, Numerical errors and instabilities, Runge-Kutta method.

Monte-Carlo methods: Random number generators, Distribution functions, Acceptance and rejection method, Inversion method.