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

  1. Preface

Algebra and Geometry

  1. Trigonometry
  2. Cartesian geometry
  3. Symmetry and fractals
  4. Least squares
  5. Scaling and exponential laws
  6. Dimensional analysis

Reactions

  1. Differential equations
  2. Pharmacokinetics
  3. Mass action
  4. Fruit mites and Zombies
  5. Metaphors and models
  6. Fire

Stochastic Simulation

  1. Modelling uncertainty
  2. Distributions
  3. Horse kicks and Height
  4. Markov chains
  5. Telephone Systems
  6. Zipf and preferential attachment

Mechanics

  1. Complex numbers
  2. Geometric optics
  3. Cannons and Space ships
  4. Flight
  5. Pendulums and hanging chains
  6. The two-body problem

Space

  1. Percolation
  2. Lattices for space (2 days)
  3. Heat and the Age of the earth
  4. Option pricing
  5. Fluids
  6. Lubrication theory

Miscellaneous

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

Appendices

  1. Preceding modelling textbooks
  2. Introduction to python programming
  3. Calculating with python
  4. Functional calculus
  5. Probability laws
  6. Project ideas