Computational physics learning modules as IPython Notebooks.

Basics 8

  Basic Plotting


Plotting a function in Python.

  Introduction to NumPy

Very basic introduction to using and generating NumPy arrays

  Discrete Fourier Transform

fft, dft

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

  Linear Algebra in Python

Basic linear algebra in Python.

  Simple implementation of Euler's method

explicit euler method, ode, implementation, basic

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

  Intermediate NumPy


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

  Intermediate plotting


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

  Classes in Python


Introduction to object oriented programming in Python.

Numerical Integration 3

  Numerical Integration

method, simpson's

Numerical integration using the trapezoidal and Simpson's rules.

  Monte Carlo Integration in One Dimension

monte, carlo

Numerical integration in one dimension using the Monte Carlo method.

  Monte Carlo Integration in D Dimensions

monte, carlo

Numerical integration in D dimensions using the Monte Carlo method.

Root Finding 3

  Bisection Method

Determining a root using the bisection method.

  Newton-Raphson Method


Determining a root with the Newton-Raphson algorithm.

  Fixed-Point Iteration

method, Newton-Rhapson

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

Ordinary Differential Equations 5

  Euler's 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.

  Verlet Integration


Solving a second-order ordinary differential equation (Newton's second law) using Verlet integration.

  Implicit Euler Method

euler, ode

Solving a first-order ordinary differential equation using the implicit Euler method (backward Euler method).

  Runge-Kutta Methods

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

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

  Adaptive Runge-Kutta Methods

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.

Partial Differential Equations 3

  Partial Differential Equations - Two Examples

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.

  Relaxation Methods for Solving PDE's

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.

  Iterative Gauss-Seidel Method

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.

Curve Fitting 3

  Polynomial Interpolation

newton, lagrange, interpolation, chebychev nodes, runges phenomenon

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

  Cubic Splines

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

Uses cubic splines to interpolate a given set of data points

  Trigonometric Interpolation

discrete fourier transform, interpolation, fft, least squares

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

Python Packages 1

  Calling Fortran(95) Routines from a Python Script

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.

Modern 3

  Quantum computing - Basics

basic, quantum computers, cat states

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

  A quick introduction to the Julia programming language

fortran, basic, Julia

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.

  Neural Network From Scratch


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