# Applied mathematics modelling – a sampler and pragmatist’s hodgepodge

Timothy Reluga

March, 2019

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

## Introduction

- Linear Perspective
- Fermi models
- Description
- Cartography
- Least squares
- Surveying closure problems
- Simple laws

## Mechanics

- Dimensional analysis
- Kinematics
- Geometric optics
- The cannon
- Flight
- Simulations of newtonian systems

## Astronomy

- Pendulum and circular motion
- Kepler and Mars
- The two-body problem
- Approximation
- The figure of the earth

## From few to many

- Stable Distributions
- Zipf and preferential attachment
- Horse kicks and Height
- Shooting stars
- Telephone Systems (3 days)
- Markov chains
- Simulations
- Percolation
- Lattices for space (2 days)
- Fractals

## Reactions

- Optimization
- The catenary and functional calculus
- Pharmacokinetics
- Mass action
- Fruit mites and Zombies
- Metaphors and models

## Space and time

- Heat and the Age of the earth
- Waves, telegraphs, and telephones
- Climate and snowball earth (3 days)
- Fluids

# Appendices

- Complex numbers
- Differential equations
- Introduction to python
- Calculating with python
- Preceding modelling textbooks