Applied mathematics modelling – a sampler and pragmatist’s hodgepodge

Timothy Reluga

March, 2019

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

Introduction

  1. Linear Perspective
  2. Fermi models
  3. Description
  4. Cartography
  5. Least squares
  6. Surveying closure problems
  7. Simple laws

Mechanics

  1. Dimensional analysis
  2. Kinematics
  3. Geometric optics
  4. The cannon
  5. Flight
  6. Simulations of newtonian systems

Astronomy

  1. Pendulum and circular motion
  2. Kepler and Mars
  3. The two-body problem
  4. Approximation
  5. The figure of the earth

From few to many

  1. Stable Distributions
  2. Zipf and preferential attachment
  3. Horse kicks and Height
  4. Shooting stars
  5. Telephone Systems (3 days)
  6. Markov chains
  7. Simulations
  8. Percolation
  9. Lattices for space (2 days)
  10. Fractals

Reactions

  1. Optimization
  2. The catenary and functional calculus
  3. Pharmacokinetics
  4. Mass action
  5. Fruit mites and Zombies
  6. Metaphors and models

Space and time

  1. Heat and the Age of the earth
  2. Waves, telegraphs, and telephones
  3. Climate and snowball earth (3 days)
  4. Fluids

Appendices

  1. Complex numbers
  2. Differential equations
  3. Introduction to python
  4. Calculating with python
  5. Preceding modelling textbooks