# Math 450: Applied mathematics modelling

Timothy Reluga

December, 2018

Copyright 2018 by Timothy Reluga

posted version

Course web page

# Lectures

- Preface

## Algebra and Geometry

- Fermi models
- Cartesian geometry
- Trigonometry
- Least squares
- Scaling and exponential laws
- Dimensional analysis
- Symmetry and fractals

## Simulation

- Modelling uncertainty
- Probability and Distributions
- Horse kicks and Height
- Zipf and preferential attachment
- Markov chains
- Telephones and Shooting stars

## Reactions

- Pharmacodynamics
- Modeling in-host Hepatitis C infection
- Orange mites and bean-bags
- Epidemics and zombies

## Mechanics

- Geometric optics
- Cannons and Space ships
- The two-body problem
- From hanging chains to Eadâ€™s bridge
- The pendulum

## Space

- Percolation
- Lattices for space (2 days)
- Telegraphs to Geosciences (2 days)
- Fluids
- Lubrication theory

## Miscellaneous

- Climate and snowball earth (3 days)
- Optimization
- Decision processes (4 lectures)
- Difference equations and chaos

# Appendices

- Preceding modelling textbooks
- Introduction to python programming
- Calculating with python
- Complex numbers
- The calculation of curves
- Functional calculus
- Probability laws
- Project ideas