Instructor: Tim Chumley
Office: Clapp 404b
Phone: 538-2299
e-mail: tchumley
Office Hours: tentatively Mondays 10:00–11:00, Tuesdays 4:00–5:00, Wednesdays 3:00–4:00, Thursdays 9:00–10:00, and by appointment

Textbook: Differential Equations, 4th edition, by Paul Blanchard,‎ Robert L. Devaney,‎ Glen R. Hall, ISBN: 978-1133109037;
on library reserve under QA371 .B63 2011


Announcements will be posted here throughout the semester.

April 29: Here are office hours for the coming week:

  • Monday, April 30: 10:00 – 11:00
  • Tuesday, May 1: 11:00 – 12:00, 4:00 – 5:00
  • Wednesday, May 2: 2:00 – 3:00

and by appointment. Please note that I’ll be away Thursday and Friday, but I’ll be able to reply to email, albeit with some delay.

April 28: The final exam was handed out in class and is posted here.

Apr 17: Here is a nice resource for notes on generalized eigenvectors. It summarizes and includes some proofs of things we discussed.

Apr 16: Information on quiz 3 is posted here and below.

Feb 5: We’ll have to stop using Gradescope and go back to handing in paper copies.
Starting with this week’s problem set 2, I’m hoping you’ll turn in your assignments in a folder which I’ll have on the board next to my office door, Clapp 404b. The due date and time will continue to be 7pm on Wednesdays. I’m sorry to make the change if you found Gradescope convenient.

Feb 2: Here is another modeling competition opportunity taking place at Amherst College April 21 called SCUDEM (in addition to the one I wrote to you about taking place next week).

Jan 24: Chapter 1 of our textbook is posted on Moodle in case your copy hasn’t arrived yet.


Check the syllabus for all the important class policies (grades, attendance, etc.).


There will be weekly homework assignments throughout the semester to be turned in, as well as suggested problems to be considered as additional practice.

  • Written assignments. A selection of problems taken from the textbook or other sources will be assigned to be due Wednesdays at 7pm.
    • These assignments are given so that you can practice writing mathematics and receive feedback on your progress.
    • If you would like feedback on a particular step in a problem, then you can indicate this on your assignment.
    • Each problem will be given a score out of 5. A score of 1 will be given to indicate that to stay on track you should get help from your instructor.
    • Please refer to these guidelines when writing your homework.
  • Submitting to Gradescope. We’ll be using an online submission tool called Gradescope to collect, grade, and return homework. Here are some notes:
    • Begin by signing up as a student on the Gradescope home page with Entry Code MD5GVZ.
    • I’ve posted a short tutorial to help with Gradescope if you haven’t used it before.
    • Gradescope has also made a guide to help with scanning and submitting.
    • More information is available in this general help guide.
    • Please let me know of any issues that come up!
  • Suggested problems. The book has a good variety of problems, both in terms of content and difficulty level. As you study throughout the semester, you might consider browsing and trying the problems at the end of the chapter for extra practice. I’ll always be happy to help over email or in office hours if you’re stuck.
Assignment Due
Problem set 0 (solutions) Jan 29
Problem set 1 (solutions) Jan 31
Problem set 2 (solutions) Feb 7
Problem set 3 (solutions) Feb 14
Problem set 4 (solutions) Feb 21
Problem set 5 (solutions) Mar 2
Problem set 6 (solutions) Mar 7
Problem set 7 (solutions) Mar 21
Problem set 8 (solutions) Mar 28
Problem set 9 (solutions) Apr 6
Problem set 10 (updated April 6) (solutions) Apr 11
1-2 page project topic summary Apr 16
Problem set 11 (solutions) Apr 18
Problem set 12 (solutions) Apr 25


There will be a few quizzes during the semester—roughly 3 total, one midway between each exam. These are intended to break up the material between exams and get everyone studying. The precise sections covered will be listed below and the types of problems will be discussed in class.

Quiz Date Material Solutions
Quiz 1 Feb 12 1.1 – 1.3 (pdf)
Quiz 2 Mar 23 2.1 – 2.4, 2.6 (pdf)
Quiz 3 (info) Apr 20 3.5, 3.6, 3.8 (pdf)


There will be three exams. The dates for the two mid-terms are subject to change slightly:

Exam Date Time and Location Material Study material
Exam 1 Feb 23 in class, take home Chapter 1 study guide
Exam 2 Mar 30 in class, take home Chapter 2, 3.1 – 3.3 study guide
Final May 3-7 take home 3.4 – 3.8, 5.1, 5.2, 5.5

Course plan

Our plan is to cover the textbook chapters 1-3, and parts of 4 and 5. Below is a rough outline of what is to be covered week by week through the semester. Please check back regularly for precise details on what is covered, as well as postings of in-class worksheets and other activities. Also note that the days of the week under Sections in the table below provide links to class notes.

Week Sections In-class activities Problems
Jan 22 - Jan 26 Wednesday: 1.1
Friday: 1.1
First day info, Big picture, Exponential growth
Logistic model, Worksheet1.m
1.1: 1, 2, 3, 6, 7, 11
1.1: 17, 18
1.2: 1
Jan 29 - Feb 2 Monday: 1.2
Wednesday: 1.3, 1.4
Friday: 1.4
Separation of variables, (solutions)
Slope fields, Slopefield.m
Euler’s method, euler.m, example
1.2: 6, 8, 9, 20, 30, 32, 39, 40
1.3: 1, 5, 6, 11, 12, 13, 14, 15, 16
1.4: 2, 4, 6, 8, 11
Feb 5 - Feb 9 Monday: 1.5
Wednesday: 1.6
Friday: 1.7
Existence and uniqueness
Phase lines
1.5: 2, 5, 7, 9, 11
1.6: 1,5, 8, 13, 17, 20, 30, 34, 39
1.7: 3, 5, 7, 17, 19
Feb 12 - Feb 16 Monday: 1.7
Wednesday: 1.8
Friday: 1.9
Bifurcations (part 3)
Linear equations

1.8: 3, 5, 19, 20, 21
1.9: 10, 23
Feb 19 - Feb 23 Monday: 2.1
Wednesday: review
Friday: exam
Predator-prey systems, Matlab file 1, Matlab file 2 2.1: 1, 2, 4, 6, 7a, 8, 9, 10, 16a
Feb 26 - Mar 2 Monday: 2.2
Wednesday: 2.3, 2.4
Friday: 2.6
Lotka-Volterra systems, PhasePortrait2.m

Existence and uniqueness for systems, NonautonomousExtended.m
2.2: 8, 11, 21
2.3: 3, 7; 2.4: 1, 3, 7, 8, 11
2.6: 2, 3, 4, 5
Mar 5 - Mar 9 Monday: 2.7
Wednesday: 2.7
Friday: 2.8
SIR Model
SIR part II, SIRPhasePortrait.m, SIRparameterized.m
LorenzMovie.m, Chaotic water wheel, Steven Strogatz water wheel, Chapter 9 of Strogatz on Lorenz equations (posted if you’re curious)
2.7: 2, 7, 8

2.8: 1, 5
Mar 12 - Mar 16 spring break
Mar 19 - Mar 23 Monday: 3.1
Wednesday: 3.2
Friday: 3.3
Linear algebra review (solutions)
Eigenstuff review (solutions)
3.1: 6, 8, 10, 11, 17, 19, 26, 29
3.2: 1, 2, 9, 14ab, 23
3.3: 1, 2, 7, 15
Mar 26 - Mar 30 Monday: 3.4
Wednesday: review
Friday: exam
Complex eigenvalues (solutions)
Real eigenvalues, review questions (solutions)
3.4: 2, 3, 4, 5, 9, 10, 11, 15, 23
Apr 2 - Apr 6 Monday: 3.5, 3.6
Wednesday: 3.6, 3.8
Friday: matrix exponential
Second-order linear equations
Harmonic oscillators, HarmonicOscillatorParameterized.m
3.5: 1, 2, 17, 18
3.6: 13, 15, 16, 21, 23, 24
3.5: 5, 6
Apr 9 - Apr 13 Monday: generalized eigenvectors Wednesday: generalized eigenvectors
Friday: 5.1
  Generalized eigenvectors
More on generalized eigenvectors
3.8: 7, 10

5.1: 1, 2, 3
Apr 16 - Apr 20 Monday: 5.1
Wednesday: 5.2
Friday: 5.2
Nullclines More nullclines practice
5.1: 5, 7
Apr 23 - Apr 27 Monday: 5.5
Wednesday: presentations
Friday: presentations
3d linearization, PhasePortrait3DLinear.m, PhasePortrait3D.m
Apr 30 - May 4 Monday: presentations


We’ll devote the last week of the semester to a mini-symposium of short group presentations. Since the field of differential equations is rich with interesting examples and topics, more than we could cover in a single semester, each group of 3-4 students will choose a topic/application that we might otherwise not have time for in class. Here are some details:

  • Presentation information and suggested topics
  • Upcoming dates:
    • Friday, April 6: select two potential topics and turn in 1-2 paragraphs about each. Give a synopsis of each topic and why you might like to present on it.
    • Monday, April 9: discuss groups/topics in class, finalize groups by Wednesday.
    • Monday, April 16: submit 1-2 page (written or typed) summary of the topic (one submission per group).
    • April 16 to 23: meet with me with a draft of slides and/or plan for the talk.
    • April 25, 27, 30: presentation days in class.
  • Presentation rubric
Group members Topic Presentation day Slides
Ashley, Xiaoxue, Young, Ziyan Hamiltonian systems Wednesday, April 25 pdf
Areeb, Faryal, Mirha Richardson arms race model Wednesday, April 25 pdf
Alina, Audrey, Ching Ching, Nikkole Discrete logistic model Friday, April 27 pdf
Claire H., Claire X., Celia Improving Euler’s method Friday, April 27 pdf
Alexis, Helen, Isahelen, Yi SIRE model Monday, April 30 pdf, Matlab files
Caledonia, Gargi, Michelle, Serena Population models, PDEs Monday, April 30 pdf
Shirley, Xingtong, Yu SIR model with vital dynamics Monday, April 30 pdf

LaTeX resources

LaTeX is a typesetting system that makes it easy to type math. Here are some resources you might find useful as you make presentation slides.

  • MacTeX/TeXLive. An installation package for getting LaTeX running on your computer. MacTeX is for macOS and TeXLive is for other operating systems.

  • LaTeXiT. This small program for macOS lets you quickly make a mathematical expression using LaTeX commands and export it as an image or pdf file that can be inserted into a PowerPoint presentation. This is an alternative to making a full LaTeX document; it doesn’t require much time investment aside from first installing MacTeX or TeXLive. (LaTeXiT comes with a full MacTeX/TeXLive installation.)

  • quick reference. This file has a list of common commands.

  • LaTeX file template. This is a simple file that lets you get started making a full LaTeX document. This is the pdf file generated by the template.

  • Beamer template. If you’d like to use LaTeX to make presentation slides, there is a package called Beamer that is an alternative to systems like PowerPoint. Here is a template for a Beamer presentation. This is the pdf file generated by the template.

Getting help

Here’s a few ways to get help:

  • Office hours (listed at the top of this page). These are times I hold on my schedule to be available for students. I like to use these times as open drop in sessions where there may be multiple students getting help simultaneously, but it’s expected that you come with specific questions about notes, homework problems, or the text that you have thought about already. If you need to schedule a time to meet with me one-on-one, either to discuss something private or because you can’t make my office hours, please send me an email with times that you are available to meet, and I will find a time that works for both of us.
  • Study groups. I strongly encourage you to form small groups and work together on problems. My advice though is to try problems by yourself before discussing them. We have several spaces on the fourth floor of Clapp where students can work together for extended periods of time.


  • We will use Matlab to do computations that complement the analytical theory in our course. Mount Holyoke provides free licenses to install Matlab on your personal computers. An installation guide is posted, along with a beginner’s tutorial.