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

Simulation

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

Reactions

  1. Pharmacodynamics
  2. Modeling in-host Hepatitis C infection
  3. Orange mites and bean-bags
  4. Epidemics and zombies

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. Telegraphs to Geosciences (2 days)
  4. Fluids
  5. Lubrication theory

Miscellaneous

  1. Climate and snowball earth (3 days)
  2. Optimization
  3. Decision processes (4 lectures)
  4. Difference equations and chaos

Appendices

  1. Preceding modelling textbooks
  2. Introduction to python programming
  3. Calculating with python
  4. Complex numbers
  5. The calculation of curves
  6. Functional calculus
  7. Probability laws
  8. Project ideas