Schedule, Suggested Readings, homework assignments/solutions, (occasional) lecture notes, etc

Winter 2020

Preliminary Course Outline:

  1. Introduction
  2. Planar Linear Systems
  3. Phase Portraits for Planar Systems
  4. Classification of Planar Systems
  5. Higher-Dimensional Linear Algebra
  6. Higher-Dimensional Linear Systems
  7. Nonlinear Systems
  8. Equilibria in Nonlinear Systems
  9. Global Nonlinear Techniques (as time allows)

Readings:

Ideally, you will have had a chance to do the readings (at least at a skim level) before class. After class, you would do the readings at a deeper level. Try all of the exercises. I expect that you're at a level of sophistication where you can recognize when some subset of problems are quite similar to one another. If you're able to do this mental "clumping" then work the problems in order until you feel that you've mastered whatever it is that you think the author is trying to get you to master. If you haven't exhausted the problems, now try the last problem in the clump. If you can do it, then you can check that clump off your list.

Errors in "Differential Equations, Dynamical Systems, and an Introduction to Chaos" by Hirsch, Smale, and Devaney.

Jan 7 & 9 : What is a differential equation? Types of differential equations. Initial value problems versus boundary value problems. What it means to be a solution, interval of existence. Added twists caused by nonlinearities. First-order ODEs: qualitative methods. First-order separable ODEs: how to solve them
Please read sections 1.1 and 1.2 in the book as well as the "Definitions" section and "Final Thoughts" section in of Chapter 1 of Paul's Online Notes on ODEs.

First homework set Due Jan 25. Here are the solutions, including four different solutions to the eighth question.

First Webwork Assignment (due Jan 15) both without and with answers. Each student got a different assignment but they were all roughly similar.

Jan 14 & 16 : Chapter 2 --- Planar linear systems. Chapter 3 --- Phase Portraits for Planar Systems: distinct real eigenvalues. For additional material, see Chapter 5 of Paul's Online Notes on ODEs.

Jan 21 & 23 : Chapter 3 --- Phase Portraits for Planar Systems: complex eigenvalues, repeated eigenvalues. Chapter 4 --- Classification of Planar Systems.

Second Webwork Assignment (due Jan 22) both without and with answers. Each student got a different assignment but they were all roughly similar.

Second homework set Due Feb 8. Here are solutions and sketches of solutions. Please bear in mind that some of the given information is more of a sketch/scaffold upon which a complete solution could be built. (Specifically, would not be given full credit if provided on an exam.)

Jan 28 & 30 : Chapter 4 --- Classification of Planar Systems.

Third Webwork Assignment (due Jan 29) without and with answers. Each student got a different assignment but they were all roughly similar.

February 3 First midterm exam. Held in BA1130. You can choose between starting at 5:10pm and finishing by 7 or starting at 6:10pm and finishing by 8. The midterm will cover chapters 1 (excluding section 1.5), 2, 3 and section 4.1 of the text. The material from webwork and the HW will also be fair game. Material that I discussed in class will also be fair game. Here's the current version of the help page that will come with the midterm. Here are the solutions to the midterm.

Fourth Webwork Assignment (due Feb 8) without and with answers. Each student got a different assignment but they were all roughly similar.

Feb 4 & 6: Finish section 4.2. Sections 5.1 and 5.2 you should read on your own. Section 5.3 Section 5.4 you should read on your own. Section 5.5. Section 5.6.

Here's a nice parametric curve plotter by Christopher Chudzicki that can help you visualize solutions in R^3. There are also demos for parametric curves in R^2 and parametric surfaces in R^3.

Fifth Webwork Assignment (due Feb 12) without answers. Each student got a different assignment but they were all roughly similar.

Here's the worked through example of finding the matrix P that transforms A into Jordan Canonical Form for a specific 4x4 matrix.

Feb 11 & 13: Section 5.6, start chapter 6

Sixth Webwork Assignment (due Feb 26) without answers. Each student got a different assignment but they were all roughly similar.

Third homework set: due March 1. Here are solutions and sketches of solutions. Please bear in mind that some of the given information is more of a sketch/scaffold upon which a complete solution could be built. (Specifically, would not be given full credit if provided on an exam.)

Feb 25 & 27: Sections 6.4 and 6.5

Here's a fuller explanation of the proof of the lemma on pages 126 and 127 in the book. While the proof's technical, it's a very useful skill to learn how to approach double series and how to "change coordinates" for series. (I.e. how to view a double series using the same mentality and tools that one would bring to a double integral.)

Fourth homework set: due March 14. Here are solutions and sketches of solutions.

Mar 3 & 5: Sections 7.1, 7.2, 17.1, and 17.2

March 9 Second midterm exam. Held in EX300. You can choose between starting at 5:10pm and finishing by 7 or starting at 6:10pm and finishing by 8. New material being tested on: Section 4.2, Chapters 5 and 6, and section 7.1. (But don't forget the old material, of course!) The material from webwork and HWs 1, 2, and 3 will also be fair game. Problem 1 from HW4 is fair game. Material that I discussed in class is fair game. Here's the current version of the help page that will come with the midterm. Here are the solutions to the midterm.

Mar 10 & 12: Sections 7.1, 7.2, 17.1, and 17.2

Mar 17 & 19: Sections 7.2, 7.3, 7.4, 17.3, and 17.4. Class is meeting on zoom.

Fifth homework set: due March 29. Here are solutions.

Mar 24 & 26: Sections 8.1, 8.2, and 8.3. Class is meeting on zoom.

Mar 31 & April 2: Sections 9.1 and 9.2. Class is meeting on zoom.

Sixth homework set: due April 20 (if you're handing it in). Here are solutions.

Information about the essay: with deadlines of April 10, 17, 22, and 25 (if you're handing it in).

Seventh homework set: due April 25 (if you're handing it in). Here are solutions.