## Differential Equations

### Welcome to Differential Equations!

Differential Equations

Homework Solutions are offline during the exam.

9/5: The exercises assigned today are due on 9/10 except as noted. Do these exercises on a separate sheet of paper (not in your notes) and have them ready to turn in at the beginning of class on the indicated date. Of course, there is nothing to turn in for reading assignments, but there could be a quiz.

* DO THIS BEFORE OUR NEXT CLASS: Read Chapter 0 in the notes carefully. There is some inportant information in there!
* DO THIS BEFORE OUR NEXT CLASS: Read Section 1.1 in the notes.
* DO THIS BEFORE OUR NEXT CLASS: Do exercise 3 from Section 1.1 in the notes. Do these exercises (and all future exercises) on a separate sheet of paper so you can turn them in, not in your notes!
* DO THIS BEFORE OUR NEXT CLASS: Take this short media survey. (Yes, this is required!) You will need to log in to your Carthage account.

*(Due 9/10) Do exercises 1, 2, and 4-6 from Section 1.1.

9/7: The exercises assigned today are due on 9/12.

* Read Section 1.2 in the notes.
* Do the exercises in Section 1.2 of the notes.

Week 2

9/10: Due 9/14.

* Read Section 1.3 in the notes.
* Do the exercises in Section 1.3 of the notes.

9/12: Due 9/17. We will have a short quiz at the beginning of class today over Sections 1.1 and 1.2.

* Read Section 1.4 in the notes.
* Do the exercises in Section 1.4 of the notes.

9/14: Due 9/19.

* Read Section 1.5 in the notes.
* Do the exercises in Section 1.5 of the notes.

Week 3

9/17: Due 9/21.

* Read Section 1.6 in the notes.
* Do the exercises in Section 1.6 of the notes. Problems 1 and 2 should be done by hand on paper. Problems 3 and 4 should be submitted via e-mail as described in the notes. There is an example of that I want for problem 3 in the Homework Solutions section of the course website.

9/19: Due 9/24. We will have a short quiz today at the beginning of class over Sections 1.3-1.5. Last day to drop a class without a W appearing on your transcript.

* Read Section 1.7 in the notes.
* Do the exercises in Section 1.7 of the notes.

9/21: Due 9/26.

* Read Section 1.8 in the notes.
* Do exercises 1-7 in Section 1.8 of the notes.

Week 4

9/24: Due 10/3.

* Read Section 1.9 in the notes.
* Do the exercises in Section 1.9 of the notes.

9/26: Due 10/3.

* Read Section 2.1 in the notes.
* Do the exercises in Section 2.1 of the notes.

9/28: Due 10/5. We will spend half of today's class on this material, and half of the class reviewing for Monday's exam.

* Read Section 2.2 in the notes.
* Do the exercises in Section 2.2 of the notes.

Week 5

10/1: Exam 1 over the material from 9/5-9/26.

10/3: Due 10/8

* Read Section 3.1 in the notes.
* Do the exercises in Section 3.1 of the notes.

10/5: Due 10/10.

* Read Section 3.2 in the notes.
* Do the exercises in Section 3.2 of the notes.

Week 6

10/8: Due 10/12.

* Read Section 3.3 in the notes, excluding the section on Integrating Factors.
* Do exercises 1acdefh, 2, 3abcdj, 4a-d, 4i-j.

10/10: Due 10/15.

* Read Section 3.4 in the notes, excluding the section on Integrating Factors.
* Do exercises 1-4 in Section 3.4 of the notes.
* Complete the quiz distributed in class. You can download another copy here.

10/12: Due 10/17.

* Read Section 3.5 in the notes, excluding the section on Integrating Factors.
* Do exercises 1, 2abe in Section 3.5 of the notes.

Week 7

10/15: Due 10/19.

* Do exercises 4, 5, and 6 in Section 3.5 of the notes.
* Read Section 3.6 in the notes, excluding the section on Integrating Factors.
* Do the exercises in Section 3.6 of the notes.

10/17: Due 10/22. Today's demonstration file.

* Read Section 3.7 in the notes.
* Do exercises 1, 2, 3acefg in section of the notes.

10/19: Due 10/24.

* Read Section 3.8 in the notes, up to Section 3.8.1.
* Do exercises 1abceg and 2abe in Section 3.8 in the notes.

Week 8

10/22: Due 10/26.

* Read Section 3.3.3 on Integrating Factors for Linear Equations in the notes.
* Read Section 3.8.1 in the notes.
* Do exercises 5abeg from Section 3.3 in the notes.
* Do exercise 3 from Section 3.8 in the notes (after doing the exercises from Section 3.3).
* Do problem 3b from Section 3.7 using the closed form method.

10/24: Due 11/5.

* Read Section 2.3 in the notes.
* Plot solutions to the following systems of differential equations. Use the format described in the homework section of the website.
(a) $$\dot x = 2x+3y,\ \dot y = 4y-x,\ x(0)=1,\ y(0)=-1,\ t\in[0,2]$$
(b) $$\dot x = y^{-2},\ \dot y = -2x^{-2},\ x(0)=2,\ y(0)=1,\ t\in[0,1]$$
* Do exercises 1ac, 2a, and 3 from Section 2.3 in the notes. Use the format described in the homework section of the website. Turn in one WORD file for this entire assignment via e-mail.

10/26: Due 11/7.

* Read Section 4.1 in the notes.
* Do the exercises from Section 4.1 in the notes.
* Fill out this survey as soon as possible!

Week 9

10/29: No additional assignment. We will start Section 4.2 and review for Exam 2 today.

10/31: Exam 2 over the material covered from 9/26-10/26.
1:30 group: Steve K., Toni, Cory, Patrick, Matt J., Emma, Steve M., Mitch, Collin, Balor
2:45 group: Jackson, Kelsey, Ben W., John, Connor, DaZahn, Sean, Tom, Brennan, Mike, Sam, Amelia, Matt K., Benjamin M., Kyle

11/2: Class canceled due to St. Norbert Conference.

Week 10

11/5: Due 11/9.

* Read Section 4.2 in the notes.
* Do the exercises from Section 4.2 in the notes.

11/7: Due 11/12.

* Read Section 4.3 in the notes.
* Do the exercises from Section 4.3 in the notes.

11/9: Due 11/14.

* Read Section 4.4 in the notes.
* Do exercise 1 from Section 4.4 in the notes.
* Don't forget to read the blog from time to time, at least once a week!

Week 11

11/12: Due 11/16.

* Read Section 4.5 in the notes.
* Do exercises 1bdefgh from Section 4.5 in the notes.

11/14: Due 11/26.

* Do exercises 2aceg, 3ac and 4 from Section 4.5 in the notes.
* Read appropriate parts of Section 4.7 in the notes.

11/16: Due 11/28.

* Read Section 4.7 in the notes.
* Do exercises 1ace, 2ace, 3acf from Section 4.7 in the notes.
* Remember to read the blog once in a while!

For those of you who are interested in a structured review for the final exam, I will include recommended review assignments along with our regular homework. These optional assignments will appear in green, and will not be collected. If you follow these guidelines, you will review most of the course by the time of the cumulative final exam.

* Over break, study equations with constant coefficients by reviewing Sections 1.1, 1.2, 1.3, 1.4, the linear equations in Section 3.1, and Section 4.1, 4.3 (skipping reduction of order for now), and 4.4. Also, review differentiation and integration to sharpen those skills.

Week 12

Thanksgiving Break November 11/19-11/23!

Week 13

11/26: Due 11/30.

* Read Section 4.8 in the notes.
* Do exercises 1abe, 2cde, and 4 from Section 4.8 in the notes.

* Review the rest of Section 3.1, Section 1.5, and Section 3.8.

11/28: Due 12/3. A table of Laplace transforms. Today's very short Mathematica file.

* Read Section 5.1 in the notes.
* Do the exercises from Section 5.1 in the notes.

* Review Sections 1.6, 2.1, and 2.2.

11/30: Due 12/5. Quiz today over second order linear equations with constant coefficients, homogeneous and non-homogeneous.

* Read Section 5.2 in the notes.
* Do the exercises from Section 5.2 in the notes.

* Review Sections 3.3 and Section 4.5.

Week 14

12/3: Nothing to be collected from today's class.

Course evaluations are available on the eRacer site. Please fill out a course evaluation.

* Read Sections 5.3 and 5.4 in the notes.
* Do the exercises at the end of Sections 5.3 and 5.4 in the notes.

* Review Section 1.7, Section 1.9, and Section 2.3.

12/5: Nothing to be collected from today's class.

* Read Section 5.5 in the notes.
* Do the exercise 1d at the end of Section 5.5 in the notes.
* Solve the differential equation $$y''+y=f(x)$$ where $$f(x)$$ is the function defined in problem 1d of Section 5.5.

* Review Sections 3.6, 3.7, and 4.8.

12/7: Nothing to be collected from today's class.

Review for Exam 3 and the cumulative final exam.

Week 15

12/10: Exam 3 over the material covered from 10/26-12/5. There will be a pencil and paper part to this exam (no calculators) and a part on which you can use Mathematica.
1:30 group: Steve K., Toni, Cory, Patrick, Matt J., Emma, Mitch, Balor. WE WILL MEET IN DSC 225.
2:45 group: Jackson, Kelsey, Ben W., John, Connor, DaZahn, Sean, Tom, Brennan, Mike, Sam, Amelia, Matt K., Benjamin M., Kyle, Steve M., Collin

* Study for the final exam!

* Review everything we haven't covered yet. We skipped reduction of order, applications of first order equations, substitution, integrating factors (optional), and you should review Laplace Transforms.

Finals

12/12: Our final exam is from 3:30-5:30 on Wednesday, December 12.

10:30-12:30 group: Steve K., Toni, Cory, Patrick, Matt J., Emma, Mitch, Balor. WE WILL MEET IN DSC 225.
3:30-5:30 group: Jackson, Kelsey, John, Connor, DaZahn, Sean, Tom, Brennan, Mike, Sam, Amelia, Matt K., Benjamin M., Steve M., Collin, Kyle

* The comprehensive final exam will cover all of the material in the course. There will be a pencil and paper part (no calculators), and a part on which you can use Mathematica.