# Maple

## Textbook

This page is a fragment of the full course Theoretical physics in transportation which is aimed at mathematical modelling in traffic. That course is now being tought in Python and therefore I moved the Maple-related part here. However, much more topics on Maple are covered in the textbook. Unfortunately, the textbook is not finished and probably will never be. Still I believe you can find something useful there.

- Introduction (highly unfinished)
- Mathematical introduction (highly unfinished)
- Classical mechanics
- Lagrange equations (derivation, Hamilton's principle, examples, implementation in Maple)
- Hamilton equations (derivation, variational derivation, canonical transformations and Hamilton-Jacobi equation, Maple)
- Dynamical systems
- Introduction to fractals
- Fluid mechanics
- Two-dimensional potential flow
- Appendices: Maple, Eigenvalues and eigenvectors, Numerical methods, Laplace transform

## Selected topics in Maple

- First steps with Maple
- Basic algebra with Maple
- Solving differential equaions
- Hamilton's equations in Maple (worksheet with theory)
- Critical points and the stability analysis in Maple (worksheet with theory)

### Exercises in Maple

Here, you can find a set of exercises in Maple. The assignment of the exercises is always in the .pdf file. This file also contains the results, but not the solutions! Sometimes, the part of the exercise is to produce the animation. Since embedding animations in pdf files is not very reliable, I decided to publish resulting animations separately, you can download them.

## Lagrange's equations

- Lagrange's equations - pdf file
- Two body equilibrium configuration - animation
- Two body problem, non-equilibrium situation -- animation
- Three-body problem, light comet - animation
- Three-body problem, heavier comet - animation
- Three-body problem, impact - an imation

## Volterra-Lotka equations

- Maple worksheet for Volterra-Lotka equation , includes the explanation of theoretical background, several examples and also exercises

Last update of this page: June 05 2019 14:58:07.