Overview

Calendar

Day Topic Reading assignment Problem set
Week 1
Mon Introduction None (Read: 0.2–3, 1.1)
0.3.101
1.1.101–102, 105–106
Office hours (1–2pm).
Tue Slope fields Read: 1.21, 1.7
Do: 1.2.101, 104, 1.7.101
1.2.102–103, 105, 7–82
1.7.103, 104a
In class problems
Office hours (1–2pm).
Wed Separable equations, Linear equations Read: 1.3, 1.4
Do: 1.3.101, 103, 1.4.101
1.3.102, 104–105, 107, 12
1.4.102–105
In class problems
Office hours (1–2pm).
Writing assignment due (11:59pm). Prompt.
Thu Autonomous equations3 Read: 1.6
Do: 1.6.1, 101
1.6.2, 102, 104, 6–7
In class problems
Office hours (1–2pm).
Visiting Artist Concert: Symmetry and Fractals in Music (7:30pm in Packard Performance Hall).
Fri Linear algebra review None (ie, spend some time reminding yourself some linear algebra4) (These should all be review) 2.1.101–102
3.2.101–104
3.3.101
3.4.1, 2, 101a, 102a, 5, 11
3.7.8
3.8.9
In class problems5
Quiz 1 (in class). Sections covered: 0.2–1.4, 1.6–7.
Fearless Friday talk: Finding long cycles in graphs (2:30pm in TSC 229).
Submit self reflection form for week 1 (due Sunday by 11:59pm).
Start working on the SIR project (due third Wednesday).
Week 2
Mon First order systems Read: 2.1, 3.1, 3.3
Do: 3.1.101, 103, 3.3.103
2.1.104
3.1.104–105
3.3.104
In class problems
Quiz 1 revisions (1–2pm).
Tue Eigenvalue method: Complete real eigenvalues Read: 2.2 up through theorem 2.2.1(i), 3.4.2, 3.5 (cases 1 through 3)
Do: 2.2.1, 7 (both ways)6, 3.4.3
2.2.101 (both ways), 104, 107
3.1.102
3.4.101, 103
3.5.3–4
In class problems
Wed Eigenvalue method: Complete complex eigenvalues Read: 2.2.1–2, 3.4.3, 3.5 (cases 4 through 6)
Do: 2.2.103, 3.4.4, 102
2.2.105
3.4.104
3.5.102
In class problems
Office hours (2–3:30pm).
Thu Eigenvalue method: Defective eigenvalues Read: 3.7, finish off 2.27, 2.4
Do: 3.7.102, 2.2.2, 102 (both ways), 2.4.101
3.5.2, 103
3.7.103–104
2.4.103, 4
In class problems
Office hours (1–3:30pm).
Fri Eigenvalue method: Review None8 3.5.1, 101
In class problems
Quiz 2 (in class). Sections covered: 2.1–2, 3.1, 3.3–5, and 3.7 up through 3.7.1 (ie, homogeneous first order linear systems with constant coefficients, but don’t worry about defective eigenvalues yet).
Fearless Friday talk: A proof of Stirling’s formula (noon, in TSC 122).
Submit self reflection form for week 2 (due Sunday by 11:59pm).
Week 3
Mon Matrix exponentials Read: 3.8
Do: 3.8.101
3.8.102, 104, 6–8
In class problems
Quiz 2 revisions (1–2pm).
Tue Nonhomogeneous equations: Integrating factors and eigenvector decomposition Review: theorem 3.3.2
Read: 3.9.1 (up through the section on eigenvector decomposition)
Do: 3.9.101(a, b)
3.9.102(a, b), 103–104
In class problems
Office hours (1–2pm).
Final project proposals due (11:59pm).
Wed Nonhomogeneous equations: Undetermined coefficients Read: 2.5.1–2, 3.9.1 (the section on undetermined coefficients), 2.6
Do: 2.5.103, 3.9.101(c), 2.6.101
2.5.101–102
3.9.102(c)
2.6.103
In class problems
Office hours (1–2pm).
SIR project due (11:59pm).
Thu Review None In class problems
Quiz 3 (in class). Sections covered: Sections covered: 2.1–2, 3.1, 3.3–5, 3.7–8 (ie, everything about homogeneous first order linear systems with constant coefficients).
Fri Final project work day9
Quiz 3 revisions (1–2pm).
Fearless Friday talk: Closed chains with tetrahedral links (2:30pm in TSC 229).
Final project draft due (6pm).
Submit self reflection form for week 3 (due Sunday by 11:59pm).
Week 4
Mon Review None In class problems
Office hours (1–2pm).
Tue Final exam (in class). Sections covered: everything!
Wed Final project presentations.

  1. If you’d like to understand the proof of Picard’s existence and uniqueness theorem, see these notes by by Denise Gutermuth, and/or section 1.6 (“Existence and Uniqueness of Solutions”) in Judson’s ODEs Project.↩︎

  2. Don’t be frightened off by the word “challenging!” Both of these problems are pretty doable (and I suspect you won’t find 1.2.8 as “challenging” as 1.2.7).↩︎

  3. You might find section 1.7 (“Bifurcation”) in Judson’s ODEs Project a useful supplement to help you understand this better.↩︎

  4. Specifically, should review the following concepts:

    • Vector spaces
    • Subspaces
    • Linear independence
    • Dimension
    • Matrices
    • Determinants
    • Eigenvalues
    • Eigenvectors
    • Diagonalization

    All of this can be found in basically any linear algebra book. Check the resources page if you need some suggestions for references.↩︎

  5. We didn’t get a chance to go through these problems in class, but I’m posting them anyway in case you wanted a few more problems for practice.↩︎

  6. By “both ways,” I mean that you should try to do this problem using two methods: the method of chapter 2, and the method of chapter 3 (ie, rewrite the higher order linear ODE as a first order linear system and then apply the eigenvalue method). Then compare the two methods.↩︎

  7. Specifically, in section 2.2, look at theorem 2.2.1(ii) and example 2.2.1.

    If you’re into pure math, it’s important to point out that you’ve basically learned about Jordan Form at this point. Compare what you’ve just learned with sections Five.III-IV in Hefferon’s Linear Algebra, or chapter 8 in Axler’s Linear Algebra Done Right.↩︎

  8. You may find section 3.7 (“The Trace and Determinant Plane”) in Judson’s ODEs Project a useful resource in helping cement what’s going on with the eigenvalue method.↩︎

  9. We’ll spend class time working on final projects. I’ll be around in case you’d like to ask me questions.↩︎