Syllabus

Topic I: Discovering the tools for measuring and modeling the world

1. Jan.28 Introduction and the big picture
2. Jan.30 Babylonians and sexagesimals
3. Feb.2 Greeks and measuring astronomical distances
4. Feb.4 The 14th century: Oresme and graphing
5. Feb.6 Galileo and falling bodies

Topic II: Differential Equations, or how best to predict the future

6. Feb.9 Newton, F=ma and fluxions
7. Feb.11 The pendulum and the clock
8. Feb.13 Simple harmonic motion
9. Feb.18 Phase-plane plots and the predator-prey equation
10. Feb.20 Van der Pol and verge-and-foliot clocks
11. Feb.23 The planets

Topic III: Music, Sound and the superposition of waves

12. Feb.25 Musical chords - Pythagoras and Galileo again
13. Feb.27 The vibrating string as a PDE
14. Mar.1 Two ways of solving the vibrating string equation
15. Mar.3 Superposition of harmonics
16. Mar.5 Fourier analysis
17. Mar.8 Power, phase and spectrograms
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18. Mar.10 Recap and review
19. Mar.12 MID TERM EXAM

Topic IV: PDE Technologies

20. Mar.15 Stress and strain in matter
21. Mar.17 Buckling columns
22. Mar.19 Waves in earth, air and water
23. Mar.22 Some interesting water waves
24. Mar.24 Electromagnetic waves and the transatlantic cable
25. Mar.26 Modulation: how TV and radio work

SPRING BREAK

Topic V: The non-linear world of chaos: the real limits of predict-ability and computability

26. Apr.5 Weather, convection cells and the Lorenz equation
27. Apr.7 Lorenz's eqn is unpredictable
28. Apr.9 The strange attractor at its heart
29. Apr.12 Ferns and other fractals in nature
30. Apr.14 Measuring 2½ dimensions

Topic VI: Harnessing chance: how throwing dice is not so unpredict-able and can be useful

31. Apr.16 Brown's observations of microscopic motion
32. Apr.19 Random walks
33. Apr.21 Elections and standard deviation
34. Apr.23 Making the atomic bomb at Los Alamos by coin flipping
35. Apr.26 Fingerprints and ROC curves
36. Apr.28 Misuse of statistics: IQ's and heavy tails