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 Geodesy

  1. Fermi models
  2. Trigonometry
  3. Coordinate Geometry
  4. Approximation
  5. Least squares
  6. Complex numbers

Power Laws

  1. Power laws and exponential laws
  2. Dimensional analysis
  3. Symmetry and fractals
  4. Zipf and preferential attachment

Reactions

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

Mechanics

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

Stochastic Simulation

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

Space

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

Miscellaneous

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