Dynamics and Differential Equations

Welcome to the homepage for Math 489, Fall 2018.

Course Information

Instructor: Katelyn Leisman
Office: Altgeld Hall 165
Email: kleisman at illinois dot edu

Course Class Room: Altgeld Hall 341
Class Time: 11:00 am - 12:20 pm

Office Hours:
Tuesdays 3:30-5:30 pm (no appointment needed)
Most weeks an additional hour will be posted below
Also available by email or by appointment

Additional Office Hours: (no appointment needed)
Tuesday, December 18, 10:00-11:00 am
Tuesday, December 18, 3:45-4:45 pm

Textbook

Chaos: An Introduction to Dynamical Systems, by K Alligood, T Sauer, J Yorke


Course Syllabus (Consult syllabus for information you don't find here)

Midterm Exams

There will be three midterm exams:
Tuesday, September 25, during class (Altgeld 341) Review for Midterm 1 and Solutions to class problems
Tuesday, October 30, during class (Altgeld 341) Review for Midterm 2
Thursday, December 6, during class (Altgeld 341) Review for Midterm 3

Final Exam

8:00 am - 11:00 am Wednesday December 19 in Altgeld 341

Homework Assignments

Homework will be due most Thursdays, with an occasional Tuesday thrown in. Solutions posted on Compass.
Homework 1 (Due Thursday, September 6)
Homework 2 (Due Thursday, September 13)
Homework 3 (Due Thursday, September 20)
Homework 4 (Due Thursday, October 4)
Homework 5 (Due TUESDAY, October 16, worth more, no additional problems will be added)
Homework 6 (Due Thursday, October 25, worth more)
Homework 7 (Due Thursday, November 1)
Homework 8 (Due TUESDAY, November 13) (has been updated with additional problems)
Homework 9 (Due Thursday, November 29) (has been updated with two coding problems to final version)
Homework 10 (Due Thursday, December 6) (has been updated to final version)

Expected Schedule

I will be more or less following the suggested syllabus provided by the department, which you can find here, though it will be modified to fit a Tuesday/Thursday schedule.
Day 1: Tuesday, Aug 28: 1.1-1.3
Day 2: Thursday, Aug 30: 1.3-1.6
Day 3: Tuesday, Sept 4: 1.6-1.8
Day 4: Thursday, Sept 6: Challenge 1
Day 5: Tuesday, Sept 11: 2.1-2.3
Day 6: Thursday, Sept 13: 2.3-2.5
Day 7: Tuesday, Sept 18: 2.6
Day 8: Thursday, Sept 20: Review
Day 9: Tuesday, Sept 25: Exam 1
Day 10: Thursday, Sept 27: 3.1, 3.2
Day 11: Tuesday, Oct 2: 3.2, 3.3
Day 12: Thursday, Oct 4: 3.3
Day 13: Tuesday, Oct 9: 3.4, 4.1
Day 14: Thursday, Oct 11: 4.1, 4.2, 4.3, 4.4
Day 15: Tuesday, Oct 16: 4.5, 4.6
Day 16: Thursday, Oct 18: 5.1, 5.4, 5.5
Day 17: Tuesday, Oct 23: 5.5, 5.6
Day 18: Thursday, Oct 25: Review
Day 19: Tuesday, Oct 30: Exam 2
Day 20: Thursday, Nov 1: 7.1, 7.2, 7.3
Day 21: Tuesday, Nov 6: 7.3, 7.4, 7.5
Day 22: Thursday, Nov 8: 7.5, 7.6
Day 23: Tuesday, Nov 13: 7.6, 8.1
Day 24: Thursday, Nov 15: 8.1, 8.2, 8.3
Day 25: Tuesday, Nov 27: 11.1, 11.2, 11.4, 11.7
Day 26: Thursday, Nov 29: 11.7, 11.8
Day 27: Tuesday, Dec 4: Review
Day 28: Thursday, Dec 6: Exam 3
Day 28: Tuesday, Dec 11: Review

Class Documents:

Worksheet from Tuesday, August 28, and solutions.
cobweb_mod.m matlab code from Thursday, August 30 - makes the cobweb plots
plotsforday2.m matlab code from Thursday, August 30 - makes the successive plots of $g^k(x)$
Worksheet from Tuesday, September 4, and solutions.
plotsforday3.m matlab code from Tuesday, September 4 - various things.
Solution to Challenge 1 from Thursday, September 6.
plotsforday6.m matlab code from Thursday, September 13 - visualizing 2D maps (code sort of reproduces plots in book figures 2.3 and 2.17.
plotsforday10.m matlab code from Thursday, September 27 - compare bifurcation plot with Lyapunov exponents
Section from Strogatz book on countable and uncountable sets I mentioned this in class on Tuesday, October 9. Take a look at it if you are less familiar with countability/uncountability/1-1 correspondence of sets.
plotsforday14.m matlab code from Thursday, October 11 - plotting Fractals
plotsforday24.m matlab code from Thursday, November 15 - numerical solutions and plotting phase planes.

All code posted above as text

Other Documents:

Flow Chart for solving first order ODEs

Introduction to LaTeX

Basic Notes/Instructions for using ShareLatex
Latex Cheat Sheet
Share-Latex: You can go to this site and register with your email address (it's free and they don't spam). Then you can write and compile documents from there.
Sciweavers: If you need help with the syntax of the math equations, you can go here to create your equations, then copy and paste the syntax into the actual LaTeX document.
Art of Problem Solving Wiki for LaTeX: A useful wiki with lots of LaTeX syntax help
Detexify: This site recognizes handwritten symbols and gives appropriate LaTeX commands

Useful Links:

Dfield:
Dfield solver embedded in website
Pplane:
Go to the link for Dfields, and click on the "System" tab at the top. You will want to expand "Numerical solution tables, and timeplots (for systems)" at the bottom and uncheck "lock t=0 on the left".

Useful references for homework help:
Paul's Online Notes
Khan Academy Lecture videos

Other Stuff:
Wolfram Alpha


This site was created by and is maintained by Katelyn Leisman. Last update: 11:00 AM on December 14, 2018.