Computational physics learning modules as IPython Notebooks.

Plotting a function in Python.

Very basic introduction to using and generating NumPy arrays

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

Basic linear algebra in Python.

explicit euler method, ode, implementation, basic

Basic notebook covering how to implement Euler's method, without much focus on theory

An extension of the Introduction to NumPy-notebook, going through some of the more common features in NumPy.

Basic and intermediate plotting with Python using the Matplotlib library. Topics include, figure formatting, subplots, mesh grids and 3D plots.

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.

euler, differential equation, euler explicit method, set of odes, basic

A thorough walkthrough of the theoretical aspects of Euler's method. Also covers how to solve higher order ODEs.

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).

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

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

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

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

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

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.

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

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

newton, lagrange, interpolation, chebychev nodes, runges phenomenon

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

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

Uses cubic splines to interpolate a given set of data points

discrete fourier transform, interpolation, fft, 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.

basic, quantum computers, cat states

Uses the qiskit framework to run basic quantum circuits, both locally and on real quantum computers.

Julia has to some degree already cemented itself in the scientific community, and will most likely continue to expand in the coming years. It aims at taking the middle ground between Python on one side, and Fortran and C++ on the other. In this notebook we offer a quick introduction for those who wish to venture from Python to Julia.

Making a neural network from scratch and training the network using a dataset from scikit-learn.