# Math 450: Applied mathematics modelling

Timothy Reluga

December, 2018

Copyright 2018 by Timothy Reluga

Mason-Dixon, Watt’s linkage, Lindenmayer Systems, Patterson’s misclosure, Cassini-Newton debate, Lotka-Volterra theory, stable distributions, Poisson process, Erlang’s B formula, Zipf’s Law, Katherine Johnson, two-body problem, catenary, percolation, Wa-Tor, Conway’s game of life, Budyko’s climate model, Karman vortex street

posted version

Course web page

# Lectures

- Preface

## Algebra and Geometry

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

## Reactions

- Differential equations
- Pharmacokinetics
- Mass action
- Fruit mites and Zombies
- Metaphors and models
- Fire

## Stochastic Simulation

- Modelling uncertainty
- Distributions
- Horse kicks and Height
- Markov chains
- Telephone Systems
- Zipf and preferential attachment

## Mechanics

- Complex numbers
- Geometric optics
- Cannons and Space ships
- Flight
- Pendulums and hanging chains
- The two-body problem

## 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
- Functional calculus
- Probability laws
- Project ideas