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. Fermi models
  2. Geometry
  3. Shape of the earth
  4. Least squares
  5. Scaling and exponential laws
  6. Dimensional analysis
  7. Complex numbers
  8. Symmetry and fractals

Mechanics

  1. Differential equations
  2. Geometric optics
  3. Cannons and Space ships
  4. The two-body problem
  5. Flight

Stochastic Simulation

  1. Pendulums and hanging chains
  2. Simulations
  3. Distributions
  4. Horse kicks and Height
  5. Markov chains
  6. Telephone Systems

Reactions

  1. Pharmacokinetics
  2. Mass action
  3. Fruit mites and Zombies
  4. Optimization
  5. Metaphors and models

Space

  1. Zipf and preferential attachment
  2. Percolation
  3. Lattices for space (2 days)
  4. Heat and the Age of the earth
  5. Waves, telegraphs, and telephones
  6. Fluids

Miscellaneous

  1. Climate and snowball earth (3 days)
  2. Option pricing
  3. Modeling in-host Hepatitis C infection
  4. Decision processes
  5. 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