Math 450: Applied mathematics modelling

Timothy Reluga

December, 2018

Copyright 2018 by Timothy Reluga

posted version

Course web page

Lectures

  1. Preface

Algebra and Geometry

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

Reactions

  1. Differential equations
  2. Pharmacokinetics
  3. Fruit mites and bean-bags
  4. Fire
  5. Epidemics and zombies
  6. Metaphors and models

Stochastic Simulation

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

Mechanics

  1. Geometric optics
  2. Cannons and Space ships
  3. The two-body problem
  4. From hanging chains to Ead’s bridge
  5. The pendulum

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. Complex numbers
  5. Functional calculus
  6. Probability laws
  7. Project ideas