# Math 450: Applied mathematics modelling

Timothy Reluga

December, 2018

Copyright 2018 by Timothy Reluga

posted version

Course web page

# Lectures

- Preface

## Algebra and Geometry

- Trigonometry
- Cartesian geometry
- Symmetry and fractals
- Least squares
- Earth’s figure
- Scaling and exponential laws
- Dimensional analysis

## Reactions

- Differential equations
- Pharmacokinetics
- Fruit mites and bean-bags
- Fire
- Epidemics and zombies
- Metaphors and models

## Stochastic Simulation

- Modelling uncertainty
- Distributions
- Horse kicks and Height
- Markov chains
- Radioactivity and Telephones
- Zipf and preferential attachment

## Mechanics

- Geometric optics
- Cannons and Space ships
- The two-body problem
- From hanging chains to Ead’s bridge
- The pendulum

## Space

- Percolation
- Lattices for space (2 days)
- Heat and the Age of the earth
- Option pricing
- Fluids
- Lubrication theory

## Miscellaneous

- Fermi models
- Climate and snowball earth (3 days)
- Optimization
- Modeling in-host Hepatitis C infection
- Decision processes (4 lectures)
- Difference equations and chaos

# Appendices

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