Differential Equations
Math 244, Spring 2020

Due to the ongoing pandemic, all courses at Whitman College have gone online as of March 30th. Therefore, some changes to the course are necessary.

Looking for the original page? It's here.

Course Links

Changes to the Syllabus

Schedule:

Week 9

In our first week back, we have an exam to make up. The exam is given below in the exam links. Please read the instructions carefully- You'll be given a week to write solutions (more than usual since this is our first week back). During Week 9, we start Chapter 6, and work through Sections 6.1 and 6.2 below. For future reference, if you want a link to the entire Youtube playlist for Chapter 6, here it is: This is a link to the entire playlist on Youtube.

(Mon, Wed) Section 6.1: Introduction to the Transform.
- L001 - Section 6.1, part 1
- Overhead slides for L001 and L002
- L002 - Section 6.1, part 2
- L003 - Section 6.1, Examples part 1
- Notes
- L004 - Section 6.1, Examples part 2
- Notes
- Homework for 6.1 (Due Thursday, Apr 2): 1, 3, 4*, 5(a), 22.
(Wed, Fri) Section 6.2: Solving DEs with the transform.
- L005 - Section 6.2 Solving DEs
- Notes
- L006 - Section 6.2 - Examples
- Notes
- Homework for 6.2 (Due Tuesday, Apr 7): 1, 3, 5, 10*, 13, 15, 20, 21*

Week 10

Please turn in your solutions to the exam on/before the past weekend.

(Mon, Wed) Section 6.3-4: The Heaviside Function (and solving ODEs with the Heaviside function)
- L007 - Section 6.3 - Heaviside L008 - Section 6.3-4 - Examples, part 1
- L009 - Section 6.3-4 - Examples, part 2
- L010 - Section 6.3-4 - Examples, part 3
- L011 - Section 6.3-4 - Examples, part 4
- Homework for 6.3: 1, 5, 7, 21, 23*, 33
- Homework for 6.4: 1(a), 3(a), 8(a)*, 15, 21(b)*
- Homework for 6.3-6.4 will be due on Thursday.
(Fri) Section 6.5: The Dirac delta function
- L012 - Section 6.5 Dirac
- L013 - Section 6.5 Examples
- Homework for 6.5: 1(a), 3(a)*, 14(a)-just solve, 17(b), 18(b)*
- Homework for 6.5 will be due on Tuesday.

Week 11

Not much left now in Chapter 6. We'll finish it this week, Wednesday will be a summary day. The exam over Chapter 6 will be given out at the end of the week, April 17, and will be due on Tuesday, April 21.

Section 6.6: The Convolution
- L014 - Section 6.6 Convolution
- L015 - Section 6.6 Examples
- Homework for 6.6: 5, 6, 9, 10, 17, 23, 24
A Summary of Chapter 6, Review problems.
Exam 3 will be released on Friday.

Week 12

The first two sessions are an introduction to systems of DEs, and a review of parametric equations. The "text" for Monday and Wednesday is an excerpt from another book, available on Canvas. On Friday, we'll return to our text.

(Mon, Apr 20)
- L016 - Viewing Parametric Equations
- L017 - The Predator-Prey Model
- L018 - Graphing the Predator-Prey Solutions
- L019 - Conversions between known DEs and systems (and vice versa)
- Notes from L017 and L019 (also see notes on Canvas, Section 2.1)
- L020 Homework solution, Section 2.1 #7(c)
- Homework for today: (1) From the new text on Canvas, Section 2.1: 2, 7-10. Turn in solutions to 8 and 9. (2) From the handout below, work on all the problems, but only turn in solutions to 1(a), 2(a), 3(a), 4(a), 6(a). These will be the only things due on Thursday this week.
- Conversion Homework (Practice01.pdf)
(Wed, Apr 22)
- Reading: Look over Section 2.2 of the notes from Canvas.
- L021 Connecting Vector Fields and ODEs
- Homework: Section 2.2: 9, 10*, 11*, 12, 16*. Due next Tuesday.
(Thu, Apr 23) Homework from Section 2.1 and the Conversion handout due (11:59PM)
(Fri, Apr 24) Linear Systems and Tanks (replaces 7.1-7.2 in Boyce/DiPrima)
- L022 Systems and Matrices
- L023 Inverses, Determinants and Parametric Lines
- L024 Lines, and Verify a Solution
- L025 Tanks! Part 1
- L026 Tanks! Part 2
- PDF notes from the above 5 videos!
- Homework: Work over all the problems, but just turn in solutions to 6, 8, 9 and 10(b). Due next Tuesday.

Week 13

This week we'll start learning the nut-and-bolts of solving the linear system of equations using something called eigenvalues and eigenvectors. We'll also look at performing some graphical analysis of the solutions.

(Mon, Apr 27) These notes replace Sections 7.3-7.5 in the text.
- L027 Section 7.3-7.5, Part 1
- L028 Section 7.3-7.5, Part 2
- L029 Section 7.3-7.5, Part 3
- PDF notes for Section 7.3 (for the above videos)
- Homework problems. Work on them all, but turn in solutions to 2(a), 3(a) and 4(a) on Thursday.
(Tue, Apr 28) Homework from Apr 22 and Apr 24 due today.
(Wed, Apr 29) A Graphical Interlude
- L030 Graphical Analysis Part 1A
- L031 Graphical Analysis Part 1B
- Homework Problems. Work on them all, but turn in solutions to 2(a, b, c). Due next Tuesday.
(Thu, Apr 30) Homework from Apr 27 due today.
(Fri, May 1) Complex eigenvalues.
- L032 Complex Eigenvalues, Part 1.
- L033 Complex Eigenvalues, Part 2
- Notes about Complex Eigenvalues
- Homework for Complex Eigenvalues
- L034 A Single Eigenvalue (and summary) (An error was made and then repeated about 0:30- The trace is 2 for both matrices).
- Notes about a single eigenvalue
- Homework for Single Eigenvalue
- Homework: Complex sheet, do 1(a) and 2(a,b,c) to turn in. From the single eval sheet: 1(a,b) and 2(a). Due next Tuesday.

Week 14

(Mon, May 4) Poincare Classification
- Poincare Diagram (PDF)
- L035 Poincare Diagram Part 1
- L036 Poincare Diagram Part 2 with Examples
- Notes on Using the Poincare Diagram
- Linearization Review from Calc III (PDF) (No video- very short reading)
- Homework: From Poincare, try all, but turn in 1, 2(c) and 4(b). For the linearization handout, try them all, but turn in 1(c) and all of 2. Due on Thursday.
(Tue, May 5) HW from Apr 29 and May 1 due today.
Here's a link to an online plotter for systems of differential equations
For Wed and Fri notes in PDF form, please download the "Nonlinear Systems" notes in Canvas (in the "Files" tab). Homework will refer to those notes.
(Wed, May 6) Local Linear Analysis (Section 5.1 in the new notes- Correction from the video)
- L037 Local Linear Analysis, part 1
- L038 Local Linear Analysis, part 2
- L039 Local Linear Analysis, part 3
- Notes on local linear analysis. Also see "Chapter 5.1" from the notes on Canvas (this is also where the HW is).
- Homework: From the new notes, 5.1: #3*, 6*, 8* (use the online plotter linked above instead of the software suggested), and 17-19.
(Thu, May 7) Last HW submission: Monday's assignment due today (Poincare classification).
(Fri, May 8) Catch up day. Work on your homework from 5.1!
- Overview of the last section of new material, and a couple of notes about the final.

Week 15

(Mon, May 11) Review day.
(Fri, May 15) This is the absolute last day that I can accept any late work.
(Sat, May 16) Formal Final Exam Day. I'll give you several days for the exam- From Thursday, May 14 to Monday May 18. I cannot accept late final exams!

Exam Materials

Exam 2 (Take Home Version). Please read the instructions carefully. Due before the end of Week 9 (Sunday evening, Apr 5).
Exam 3 (Take Home Version). Please read the instructions carefully. Due Tuesday evening, 11:59PM.
Final Exam (Take Home Version). Please read the instructions carefully. Due Monday, May 18th at 11:59PM.

How Will I Upload Materials to Canvas?

There are several apps for cell phones to convert images of your work to PDF, which you can then upload to Canvas. Below, Prof. Schueller demonstrates one such app, Adobe Scan. Unfortunately, you will be asked to set up an account, but otherwise it seems like a good app (if you want to use other apps, that's fine, too- but please upload files as PDF).

Differential EquationsMath 244, Spring 2020