Math 134: Dynamical Systems

Late breaking news

(12/23) Solutions to the final exam are finally here. Please email me if you would like to find out your grade.

Happy holidays and enjoy your winter break!

(12/12, part 2) There's a typo in the final exam: in problem 5, the first equation should have a minus sign in front of 0.1 cos x inside the parenthsis, so the first equation should read:

x' = sin x (-0.1 cos x - cos y).

Here the correct version of the exam. Sorry about that!

(12/12) I just posted solutions to HW 9.

A slight change in my office hours next week (due to a meeting of the hiring committee fo which I am a member): on Monday, December 17, I will not have an office hour from 10 to 12, but instead my afternoon office hours will be from 1 to 4. Those of you who wanted to present on Monday morning will have to come in the afternoon. Sorry about the change.

(12/10) The final exam has been posted and is due on December 17 by 2 PM. You can give it either directly to me or to staff in MH 308 and they wil put it in my mailbox. Good luck!

Also, I will put all the remaining graded homework assignments in an envelope just outside my office.

(12/8) Solutions to Homework 8 have been posted.

(12/5) My office hours after the last day of class will be (modified on 12/12):

Wed. 12/12: 10-12, 2-4
Mon., 12/17: 1-4
Thu., 12/20: TBA

(12/1) The last homework assignment, number 9, has been posted. It's due on the last day of class, December 10. The take-home final exam will be assigned on the same day. I'll post it on the web in the morning and distribute copies in class. The final will be due on December 17 at 2 PM.

(11/28) Solutions to HW 7 have finally been posted.

(11/26) If you chose to do a presentation, please email me your topic as soon as you can. The first (and possibly only) round of presentations will be on December 12 (exact time TBA).

(11/25) Homework 8 has been posted and is due on Monday, December 3.

(11/21) As I said in class today, Homework 7 is now due on Monday, November 26. Happy Thanksgiving, everyone!

(11/14, part 2) I'm afraid my lecture today wasn't very clear, so here's a little handout on the Hartman-Grobman and Stable Curve Theorem to clarify things.

(11/14) If you liked Math 134 or are just curious about "chaos" beyond popular science literature (or Hollywood), you may want to take Math 234: Advanced Dynamical Systems next semester. Here's the announcement.

(11/13) Very few of you have told me about your choice of the presentation topic. Since I assume more people are interested in presenting, I am extending the deadline for choosing a topic (and telling me about it) until November 21. The first round of presentations will be on Wednesday, December 12.

(11/12) Homework 7, just posted, is due on Wednesday, November 21.

(11/8) I just posted Midterm 2 solutions.

(11/6) Solutions to HW 6 have been posted.

(11/4) Remember that Midterm 2 this coming Wednesday will cover the material from homework assignments 4-6. To prepare, check out midterm 2 from two years ago, although be aware that our midterm will have at least one problem about a nonlinear system.

(11/1) Rember that Midterm 2 will be on Wednesday, Nov. 7. It will cover the all material we talked about after Midterm 1. Here are some practice problems for the exam. You are allowed to bring a 3 X 5 inch index with your notes.

(10/30) I have a meeting tomorrow from 10:30 until at least 11:30, so I will only have office hours from 10 to 10:30 and after my meeting until noon. Sorry about that.

(10/28) Check out a handout on flows I just posted.

(10/27) I just posted Homework 6 (due on Monday, November 5) and solutions to HW 5. To give us more time to review, I have decided to move the second midterm to November 7. (I know that some people have two other midterms on Nov. 5, so I hope this will help.) And here's one more possible presentation topic:

7.5 Exploration: Numerical Methods.

(10/21) Here's a list of some possible presentation topics:

6.2 Harmonic oscillators

11.1 Infectious diseases

11.2 Predator/prey systems

12.1 An RLC circuit and 12.2 The Lienard equation (combined)

12.5 Exploration: Neurodynamics

17.3 Continuoud dependence of initial conditions

17.4 Extending solutions

I'm open to other suggestions. You need to let me know if and what you would like to present by November 7. The presentations will be scheduled on a day (or two) after the end of classes. A presentation is worth a maximum of 10 extra credit points.

(10/19) Just posted: HW 4 solutions and Homework 5 due on Wednesday, October 24.

(10/7) Tomorrow morning I have to do a peer evaluation of somebody's teaching, so I will have to cancel my AM office hours. Sorry about that!

(10/6) I just posted Homework 4, which is due on Wednesday, October 17.

(10/3) I just posted Midterm 1 solutions.

(10/2) Yesterday I forgot to mention that you are allowed to bring a 3X5 inch index card with your notes to the midterm tomorrow.

(9/28) I posted Midterm 1 review questions. You don't have to turn in your solutions. To prepare for the midterm, check out also the first midterm from two years ago.

Oh yeah, I also posted Homework 3 solutions.

(9/26) To give us more time for reviewing, I am postponing Midterm 1 to Wed., October 3.

(9/21) Solutions to Homework 2 have been posted. On Wednesday, I talked about matrices as linear transformations and how one can get a matrix from every linear transformation. Here's a little handout I wrote about this two years ago.

(9/16) I posted Homework 3 (due on Sept. 26) and the solutions to Homework 1.

(9/10) I'm sorry for having to cancel my morning office hours today (it was due to factors beyond my control). To make up for that, I'll have additional office hours from 3 to 4 both this Wednesday and next Wednesday (9/19). Also, I'm moving the deadline for submitting Homework 1 to this Wednesday (9/12).

(9/8) On Monday, September 10, I will be about half an hour late to my morning office hours, which will therefore be from 10:30 to noon. But I'll have afternoon office hours on Wednesday (9/12), from 2:45 to 3:45.

(9/4) Homework 2 has been posted and is due on September 17.

(8/29) Since Monday, Sept. 3, is a holiday, Homework 1 is actually due on September 10, not Sept. 5, as previously announced.

(8/27) I posted Homework 1, which is due on Wednesday, September 5.

A nice short article about the history of dynamical systems can be found here.

(8/7) Good news: 9 students are officially enrolled (and I know one more who will soon register), which should be enough. So see you on August 27!

(7/24) As of today, there are only 6 registered students. Hope we can get at least 3 more soon! If you know someone who may be interested, please spread the word!

(7/13) IMPORTANT: only 7 students have so far registered for this class, and we need at least 9 for it to run. If we don't have enogh people by the beginning of August, the class may get cancelled. So if you are thinking of taking the class or just want to check it out, it would be helpful to register as soon as possible.

(6/14) Welcome to the home page of Math 134 for Fall 2007! If you are planning to take this class, please register as soon as possible. If you need a permission number, please email me to get one. We need at least nine people in order for the class to run. Math 134 is offered only every two years, so it would be a shame if it gets cancelled.

If you are still not sure if you want to take the class, feel free to email me for more information. You can also check out the home page for Math 134 for Fall 2005.

Syllabus

First-order equations refresher (Chapter 1).

Planar linear systems (Chapter 2): second-order ODEs and planar systems, preliminaries from algebra, planar linear systems, eigenvalues and eigenvectors, solving linear systems, linearity principle.

Phase portraits depending on the eigenvalues (Chapter 3).

Classification of planar systems (Chapter 4).

Nonlinear systems (Chapter 7): dynamical systems, existence and uniqueness theorem, continuous dependence of solutions.

Equilibria in nonlinear systems (Chapter 8): examples, sinks, sources, saddles, stability, bifurcations.

Closed orbits and limit sets (parts of Chapter 10).

Applications: RLC circuit (parts of Chapter 12), Newtonian mechanics (parts of Chapter 13), predator/prey systems (parts of Chapter 11, time permitting).

Basics of discrete dynamical systems (parts of Chapter 15, time permitting).

Exams

How to...

Grading policy

Handouts

Homework

#	Due date	Assignment	Solutions
1	9/12	Ch. 1, ex. 5, 8, 9, 11, 13, 14. Extra credit (XC), ex. 15.	HW 1
2	9/17	Chapter 2, all exercises (on p.36-38) except 5, 8, 10, 13	HW 2
3	9/26	Chapter 3, ex. 1, 2(vi), 3, 5, 8, 9, 11, 12, 14, 15	HW 3
*	*	Midterm 1 review: Ch. 1: #2, 4, 8, 10. Ch. 2: #1, 2, 9, 10. Ch. 3: #2, 3, 6, 11.
4	10/17	Chapter 4, ex. 1-4, 5a, 6-9	HW 4
5	10/24	Chapter 6, ex. 12abcd, 13, 14	HW 5
6	11/5	Chapter 7, ex. 1a, 2, 5, 6, 8. Extra credit: ex. 9	HW 6
*	11/7	Practice problems for Midterm 2
7	11/26	Chapter 8, ex. 1, 2, 3	HW 7
8	12/3	Chapter 9, ex. 7ab, 8b, 10, 11	HW 8
9	12/10	Chapter 9, ex. 8c, 16. Chapter 13, ex. 1, 5	HW 9

Policy on calculators

We will be using some dynamical systems and ODE software, such as Matlab and pplane6.

Math 134: Dynamical Systems
Fall 2007

Contents of this page

Late breaking news

Lecture time and location

Prerequisite

Office hours

Textbook

Syllabus

Exams

How to...

Grading policy

Handouts

Homework

Policy on calculators

Academic integrity

Anonymous feedback

Math 134: Dynamical Systems Fall 2007

Contents of this page

Late breaking news

Lecture time and location

Prerequisite

Office hours

Textbook

Syllabus

Exams

How to...

Grading policy

Handouts

Homework

Policy on calculators

Academic integrity

Anonymous feedback

Math 134: Dynamical Systems
Fall 2007