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

Jump to today

Do the following before next class:

- 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.

Do the following before next class:

- 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.

Do the following before next class:

- 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.)

Do the following before next class:

- 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.

Do the following before next class:

- 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.

Do the following before next class:

- 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.

Do the following before next class:

- 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.

Do the following before next class:

- 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.

Do the following before next class:

- 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.

Friday

September 28

September 28

Systems of differential equations

Predator-prey systems

Predator-prey systems

Do the following before next class:

- 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.

Do the following before next class:

- 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.

Do the following before next class:

- 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.

Do the following before next class:

- 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.

Study for the exam! Do the take-home problems (PDF here), distributed in class. For review, consider doing some of the following problems (not to be collected):

- 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

Wednesday

October 10

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.

Do the following before next class:

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

Fall break! No class Monday, October 15.

Do the following before next class:

- 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?*

Do the following before next class:

- 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.

Do the following before next class:

- 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.

Monday

October 22

October 22

Linear systems with complex eigenvalues

Do the following before next class:

- 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.

Wednesday

October 24

October 24

Linear systems with repeated eigenvalues

Do the following before next class:

Friday

October 26

October 26

Linear systems with zero eigenvalues

Linear system summary

Linear system summary

Do the following before next class:

Monday

October 29

October 29

Second-order linear systems

Do the following before next class:

Wednesday

October 31

October 31

Trace-determinant plane

Do the following before next class:

Friday

November 2

November 2

Forced harmonic oscillation

Do the following before next class:

Monday

November 5

November 5

Sinusoidal forcing

Do the following before next class:

Wednesday

November 7

November 7

Undamped forcing

Do the following before next class:

Do the following before next class:

Monday

November 12

November 12

Review

Study for the exam! Consider the following problems for review (not to be collected):

Wednesday

November 14

November 14

**Exam 2**

- This exam will cover Chapter 3, sections 1 through 7, and the first three sections of Chapter 4.
- More information will be posted here.

Do the following before next class:

Friday

November 16

November 16

Nonlinear systems: equilibrium point analysis

Do the following before next class:

Monday

November 19

November 19

Qualitative analysis

Thanksgiving break! No class Wednesday, Nov. 22 or Friday, Nov. 24.

Do the following before next class:

Monday

November 26

November 26

Qualitative analysis

Do the following before next class:

Wednesday

November 28

November 28

Hamiltonian systems

Do the following before next class:

Friday

November 30

November 30

Laplace transforms

Do the following before next class:

Monday

December 3

December 3

Laplace tranforms, discontinuous functions

Do the following before next class:

Wednesday

December 5

December 5

Laplace transforms of second-order equations

Do the following before next class:

Do the following before next class:

Monday

December 10

December 10

Review

Final Exam Information: The final exam will consist of a take-home problem and an in-class exam.

Friday

December 14

December 14

Final exam for Math 230

9:00 – 11:00am

**A**9:00 – 11:00am

Tuesday

December 18

December 18

Final exam for Math 230

9:00 – 11:00am

**B**9:00 – 11:00am