Computational physics learning modules as IPython Notebooks.

Plotting a function in Python.

Brief introduction to Discrete Fourier Transform and the Fast Fourier Transform.

Introduction to vectors in NumPy, ans line plots, scatter plots and figure parameters in matplotlib.

Basic linear algebra in Python.

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.

Determining a root using the bisection method.

Determining a root with the Newton-Raphson algorithm.

Solving fixed-point problems using the Fix-Point Iteration 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).

4th order runge-kutta, ode, explicit euler method

Solving a first-order ordinary differential equation using the Runge-Kutta method.

4th order runge-kutta, trapezoidal method, ode, explicit euler method

Solving a first-order ordinary differential equation using Runge-Kutta methods with adaptive step sizes.

differential equation, stability, implicit euler method, animation, laplace's equation, finite-differences, pde

This module shows two examples of how to discretize partial differential equations: the 2D Laplace equation and 1D heat equation.

poisson's equation, iterative, laplace's equation, uniqueness theorem

The Jacobi, Gauss-Seidel and Successive overrelaxation (SOR) methods are introduced and discussed with the Poisson equation as an example.

differential equation, gauss, system of equations, iterative, laplace's equation, sparse matrix, pde

Solves a linear of system of equations using the iterative Gauss-Seidel method.

chebychev nodes, newton, interpolation, lagrange, runges phenomenon

Using polynomial interpolation to interpolate a set of points and to approximate a function or a curve.

chebychev nodes, interpolation, curve fitting, system of equations, runge's phenomenon, sparse matrix

Uses cubic splines to interpolate a given set of data points

interpolation, fft, discrete fourier transform, least squares

Using trigonometric interpolation and the discrete Fourier transform to fit a curve to equally spaced data points.

electricity, fortran, trapezoidal method

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.