Computational physics learning modules as IPython Notebooks.
Numerical integration using the trapezoidal and Simpson's rules.
Numerical integration in one dimension using the Monte Carlo method.
Numerical integration in D dimensions using the Monte Carlo method.
Solving a first-order ordinary differential equation with Euler's method.
Solving a second-order ordinary differential equation (Newton's second law) using Verlet integration.
Solving a first-order ordinary differential equation using the implicit Euler method (backward Euler method).
Solving a first-order ordinary differential equation using the Runge-Kutta method.
Solving a first-order ordinary differential equation using Runge-Kutta methods with adaptive step sizes.
This module shows two examples of how to discretize partial differential equations: the 2D Laplace equation and 1D heat equation.
The Jacobi, Gauss-Seidel and Successive overrelaxation (SOR) methods are introduced and discussed with the Poisson equation as an example.
Using polynomial interpolation to interpolate a set of points and to approximate a function or a curve.
Introduction to cubic splines.
Using trigonometric interpolation and the discrete Fourier transform to fit a curve to equally spaced data points.
Making use of the Fortran to Python package F2PY which enables creating and compiling a Fortran routine before converting it to a Python Module, which can be imported to any Python script.