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Jack Baskin School of EngineeringUC Santa Cruz

Lectures Notes - Winter 2010

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Lecture Notes, Winter 2010

WARNING: downloading the lecture notes and putting them under your pillow at night will not help you learn the material.

If you would like to have the movies that I showed, please come to see me to copy them directly from my computer - most of them are very large.

Please let me know if there are any mathematical errors remaining in these notes.


Week 1:
Preparation for class:
  • Preparation for Tuesday class: come and enjoy the show.
  • Preparation for Thursday class: Read Strogatz Chapter 2.
Lecture notes:
Week 2:
Preparation for class:
  • Preparation for Tuesday class: Read Strogatz Chapter 3
  • Preparation for Thursday class: TBA
  • Lectures 3 and 4 : Bifurcations in 1D systems

Week 3:
  • Preparation for Tuesday class:
  • Preparation for Thursday class: Read Strogatz Chapter 5
  • Lecture 5 : Example of population dynamics
  • Lecture 6 : Introduction to 2D systems

Week 4:
  • Preparation for Tuesday class: make sure you remember what an eigenvalue/eigenvector is, and practise finding eigenvalue/eigenvectors for 2D matrices.
  • Preparation for Thursday class: download the ODEtemplate and examples from the Homework page and make sure you know how to use them.
  • Lecture 7 : Linearization near a fixed point
  • Lecture 8 : Linearization near a fixed point (part II)
  • First inquiry : Numerical and analytical study of dynamical systems.

Week 5:
  • Preparation for Tuesday class: finish up your inquiry on your particular system. You will be expected to make a 1-2 minute presentation on your system, and what you found. Also, if you haven't done it already, read Strogatz Chapter 5 and also 6.1-3
  • Preparation for Thursday class: Read the rest of Strogatz Chapter 6
  • Lecture 9 : Linearization near a fixed point: the general case.
  • Lecture 10 : Example of applicaton: the damped Pendulum. Problems with linearization.

Week 6:
  • Preparation for Tuesday class: Read Strogatz Chapter 6.5-7
  • Preparation for Thursday class: Read Strogatz Chapter 7
  • Lecture 11 : Structural stability. Conservative systems.
  • Lecture 12 : Limit cycles (part 1).

Week 7:
  • Preparation for Tuesday midterm: practise on previous year midterms!
  • Preparation for Thursday class: work on the take-home!
  • Lecture 13 : Limit cycles (part 2).

Week 8:
  • Preparation for Tuesday class: Read Strogatz Chapter 10.1-10.4
  • Preparation for Thursday class: Read Strotatz Chapter 10.5 and 11
  • Lecture 14 and 15 : Introduction to discrete systems.

Week 9:
  • As you may have noticed, because we have taken some delay in the class schedule, I have had to skip a few things and go in less depth than I would like on others. Please read the textbook for details, or come and ask me.
  • Lecture 16 : Introduction to discrete systems. Lyapunov exponents as measure of chaos. From discrete systems to fractals.
  • Preparation for Thursday class: Bring a laptop!
  • Inquiry: The Rossler attractor and the Lorenz map. See Exams page for answers.

Week 10:
  • Lecture 17 : 2D discrete systems. Behavior of dissipative vs. non-dissipative maps.
  • Lecture 18 : Fundamental examples of dynamical systems: Synchronized Oscillations
  • If you are interested : Fundamental examples of dynamical systems: The square Map.

Final's Week:
    Schedule for the presentations:
  • 2:00 - 2:15: Ariel Kellison: The dynamics of nonlinear convection
  • 2:15 - 2:30: Claire Walton: The cubic map
  • 2:30 - 2:45: Katelyn White: Noisy dynamos
  • 2:45 - 3:00: Jen Holt: Particle trapping in vortices
  • 3:00 - 3:15: Curtis Andrus: the Newton Raphson method
  • 3:15 - 3:30: Ross Anderson: Chaotic skiing
  • 3:30 - 3:45: Justin Yeakel: Dynamics of a food web
  • 3:45 - 4:00: Chris Phelps: The restricted 3-body problem