# Numerical integration (brief)

In this text I will go over a few subjects related to integration and its relevance for simulation. I try to focus on the areas where I had trouble when I originally learned about these things, and I will generally focus less on the things I found
to be easy. The subjects I touch upon are...

• Very brief overview of what it means to integrate.
• Introduction to ordinary differential equations and their use.
• Example of using analytical integration to solve an initial value problem.
• Introduction to numerical integration and Taylor series as well as truncation error.
• A description of phase space and its use.
• Example of using Explicit Euler to solve the problem previously solved analytically.
• Example of using Midpoint to solve the same problem.
• Example of using Runge Kutta 4 to solve the same problem.
• Example of using Implicit Euler to solve the same problem.
Early on I will present a physical problem in form of an initial value problem in 1 which is then solved analytically by integration,  with Taylor series and numerically using three different methods.