Welcome to Differential Equations! For course info and policies, please see the syllabus. For grades, log into Moodle. If you need help or have questions, please contact Prof. Wright.

**Prof. Wright's office hours:** Mon. 1–2, Tues. 10–11, Wed. 2–3, Thurs 10–11, Fri. 1–2, whenever the door is open, or by appointment in RMS 405

**Help sessions:** Tuesdays 9–10pm and Thursdays 7:30–8:30pm in Tomson 186

- Complete the Syllabus Quiz.
- Complete the Computational Assessment.
- Watch this video:
*What are differential equations?* - From the textbook, read §1.1 and §1.2, up to the heading "Missing Solutions" on page 27. Complete the reading questions on Moodle before class on Monday.

- Finish reading §1.2.
- Homework 1: §1.1 exercises 3, 5, 17; and §1.2 exercises #1, 3, 5, 8, 15, 17, 25, 28. This is due in the homework box (RMS 3rd floor, near the fireplace) at 4pm Wednesday.
- Read this article and §1.3 in the textbook. Then complete the reading questions on Moodle.
- If possible, bring a computer with Mathematica to class on Wednesday.

- Homework 2: §1.2 exercise 33 and §1.3 exercises #1, 3, 8, 11, 13, 14, 16, 17.
*Note*: You do not need to use HPGSolver; instead, you may use Mathematica, Desmos, GeoGebra, or other technology. (Due 4pm Friday in the homework box.) - Read §1.4 and complete the reading questions on Moodle.
- If possible, bring a computer with Mathematica to class on Friday. (Instructions for installing Mathematica at St. Olaf.)

- Homework 3: §1.3 exercises 18, 19 and §1.4 exercises #1, 3, 5, 6, 11. (Due 4pm Monday in the homework box.)
- Watch the video Existence and Uniqueness. Also read §1.5, at least through page 67.

- Read this article and §1.6 in the tetbook. Then complete the reading questions on Moodle.
- Homework 4: §1.5 exercises #2, 3, 5–8, 9ab, 11, 13. (Due 4pm Wednesday.)
*This week:*begin work on Lab 1.

- Read §1.7 and complete the reading questions on Moodle..
- Homework 5: §1.5 exercise 12 and §1.6 exercises 1, 4, 7, 10, 13, 16, 19, 31, 32, 33, 34. (Due 4pm Friday.)
- Work on Lab 1.

- Read §1.8. Especially note the
*Linearity Principle*and the*Extended Linearity Principle.*. - Homework 6: §1.6 exercises 28, 37 and §1.7, exercises 4, 8, 9, 11, 12, 13. (Due 4pm Monday.)
- Work on Lab 1.

- Watch the video The Integrating Factor Method. Then read §1.9.
- Finish Lab 1. You may submit your lab report on Moodle in PDF format or print it and place it in the homework box by 4pm Wednesday.
- The next homework appears below. Because the lab is due Wednesday, this homework is due Friday.

- Re-read the subsection
*Comparing the Methods of Solution for Linear Equations*(p. 131–132). Then read §2.1, and complete the reading questions on Moodle. - Homework 7: §1.7 exercises 14, 16; §1.8 exercises 1, 4, 5, 8, 10, 17; and §1.9 exercises 1, 4, 5, 15. (Due 4pm Friday.)
- If possible, bring a computer with Mathematica to class on Friday.

September 28

Predator-prey systems

- Read §2.2. Take note of how vector fields can be used to visualize the behavior of solutions to systems of differential equations.
- Homework 8: §1.8 exercises 19, 23; §1.9 exercises 19, 23; and §2.1 exercises 1–4, 7a, 8ab, 15. (Due 4pm Monday.)
- If possible, bring a computer with Mathematica to class on Monday.

- Homework 9: §2.1 exercises 20, 21, 22 and §2.2 exercises 5, 9, 11, 14, 21. (Due 4pm Wednesday. You may use
*Mathematica*or other technolgy instead of HPGSystemSolver.) - Read §2.3. Note how the "guessing" method is used to solve the differential equation in this section.

- Homework 10: §2.3 exercises 1, 2, 5, 6, 7. (Due 4pm Friday. You may use
*Mathematica*or other technolgy instead of HPGSystemSolver.) - Read §2.4 and complete the reading questions on Moodle.
- Familiarize yourself with Lab 2: Bifurcation Plane, which is due on October 19.

- Homework 11: §2.4 exercises 1, 2, 5, 6, 7, 10, 13. (Due 4pm Monday.)
- Read §2.5, and observe how a 2-D version of Euler's method can be used to solve systems of two differential equations.

- Chapter 1 review (pages 136–141) exercises 1–39, 41–46, 49, 51, 52
- Chapter 2 review (pages 224–226) exercises 1–9, 11, 13, 14–28, 31–34, 35, 36

October 10

**Exam 1**

- This exam will cover Chapter 1 and the first four sections of Chapter 2.
- The exam will consist of a short take-home portion and an in-class portion.
- For the take-home portion, you may (and should) use Mathematica or other technology.
- You may not use Mathematica or similar technology on the in-class exam. Calculators will be permitted, but probably not very helpful. The in-class exam will focus on conceptual understanding. It will involve basic calculus and some arithmetic, but not tedious arithmetic.

- Read §3.1, and complete the reading questions on Moodle.

- Homework 12: §3.1 exercises 5, 9, 14, 24, 27, 29. (Due 4pm Wednesday.)
- Read §3.2. Look for the answer to the question:
*How do straight-line solutions of a linear system connect to eigenvectors of a matrix?*

- Finish Lab 2 (bifurcation plane). You may either submit your lab report on Moodle in PDF format or place it in the homework box by 4pm Friday.
- Read §3.3. What types of phase portraits that are possible for linear systems with real eigenvalues?
- The next homework includes exercises from §3.1 and §3.2. Because the lab is due Friday, the next homework is due Monday.

- Homework 13: §3.1 exercise 16; §3.2 exercises 1, 4, 5, 11, 12, 21; and §3.3 exercises 17, 18. (Due 4pm Monday.)
- Read §3.4, and complete the reading questions on Moodle.
- If you want to know more about Euler's formula, watch this video by 3Blue1Brown.

- Homework 14: §3.4 exercises 1, 2, 4, 5, 10, 11, 15, 16. (Due 4pm Wednesday.)
- Read §3.5. Note what types of phase portraits can occur for linear systems with repeated (real) eigenvalue or zero eigenvalues.

- Homework 15: §3.5 exercises 1, 3, 5, 7, 9, 10, 11, 13. (Due 4pm Friday.)
- Review §3.3 through §3.5. Note the different types of phase portraits that can occur for linear systems, and how they are determined by the eigenvalues of the matrix of coefficients.

- Homework 16: §3.4 exercise 23 and §3.5 exercises 17, 18, 21, 22, 23. (Due 4pm Monday.)
- For review of linear systems, complete the Linear System Summary worksheet. This will give you a catalog containing the form of the solution and the phase portrait for
*all*2x2 linear systems of differential equations. - Read §3.6. How can we use our knowledge of linear systems to solve second-order differential equations?

Extra credit opportunity: Attend the MSCS Colloquium by Minah Oh (Monday, Oct. 29, 3:30pm, in RNS 310) and answer these two questions on Moodle.

- Homework 17: §3.6 exercises 1, 6, 7, 10, 13, 16, 21, 24, 33. (Due 4pm Wednesday.)
- Start working on Lab 3.
- Read §3.7 and complete the reading questions on Moodle.

- Homework 18: §3.7 exercises 2, 3, 4, 5, 9, 10, 11, 12. (For these problems, a "brief essay" can be a sentence or two. Due 4pm Friday.)
- Start working on Lab 3.
- Read §4.1. Come to class knowing the
*Extended Linearity Principle*on page 390. Note that this is the same principle that we previously encountered in Section 1.8 (page 114).

- Homework 19: Ch. 3 review exercises 11, 12, 13, 14; §4.1 exercises 1, 5, 9, 13, 16, 22. (Due 4pm Monday.)
- Read §4.2. Focus on the qualitative analysis and phase portraits. We will discuss "complexification" in class.
- Begin Lab 3 (linear systems), if you haven't already.

- Homework 20: §4.1 exercises 26, 33, §4.2 exercises 1, 3, 5, 11, 16, 19. (Due 4pm Wednesday.)
- Read §4.3, pages 415–420. Pay special attention to the graphs of solutions that can occur when the forcing function is a sine or cosine.

- Finish Lab 3 (linear systems).
- Re-read §4.3. Understand that a forcing frequency very close to the natural frequency produces a large-amplitude forced response.

- Homework 21: §4.1 #38; §4.2 #17, 20; and §4.3 #5, 15, 17, 21. (Due 4pm Monday.)
- Study for the exam: see below for suggested review problems.

- Chapter 3 review (pages 376–380) exercises 1–32.
- Chapter 4 review (pages 449–451) exercises 1–4, 10–12, 15–23.

November 14

**Exam 2**

- This exam will cover Chapter 3, sections 1 through 7, and the first three sections of Chapter 4.
- The exam will consist of a short take-home portion and an in-class portion.
- For the take-home portion, you may use Mathematica or other technology.
- You may not use Mathematica or similar technology on the in-class exam. Calculators will be permitted, but probably not very helpful. The in-class exam will focus on conceptual understanding. It will involve basic calculus and some arithmetic, but not tedious arithmetic.

- Read §5.1. Observe how
*linearization*allows one to approximate a nonlinear system near an equilibrium point by a linear system. Come to class knowing what is a*Jacobian matrix*.

Extra credit opportunity: Attend the MSCS Research Seminar by Jasper Weinburd (Friday, Nov. 16, 3:40pm, in RNS 204) and answer these two questions on Moodle.

- Homework 22: §5.1 #1, 4, 5, 9ab, 18, 21. (Due 4pm Monday.)
- Read §5.2. Come to class knowing the definition of a
*nullcline*.

Extra credit opportunity: Attend the MSCS Colloquium by Wako Bungula (Monday, Nov. 19, 3:30pm, in RNS 310) and answer these two questions on Moodle.

- Homework 23: §5.1 #7a, 8a, 11a, and §5.2 #3, 4, 5, 6, 9. (Due 4pm next Monday.)
- Review §5.1 and §5.2. Notice how analysis of equilibrium points and nullclines can provide a lot of qualitative information about solutions to systems of differential equations, even if you can't write down formulas for the solutions.

November 26

November 28

November 30

December 3

December 5

December 10

December 12

December 14

**A**

9:00 – 11:00am

December 18

**B**

9:00 – 11:00am