Matthew L. Wright
Assistant Professor, St. Olaf College

# Differential Equations

## Math 230 ⋅ Fall 2016

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; office hours are Mon. 1:15–1:45 & 3–3:30, Wed. 9–10, Thurs. 10–11 & 1–2, Fri. 1:15–1:45 & 3–3:30, or by appointment in RMS 409.

Below is a tentative outline of the course. Use the controls at right to make the page easier to view.

Unless otherwise noted, homework listed below is assigned on the day indicated and due in the homework mailbox at 4:00pm on the next class day. For example, homework assigned on a Wednesday is due at 4:00pm Friday.

September 5–9 − hide
DayTopicHomework Assigned
Friday
Sep. 9
Modeling with
differential equations;
230A notes; 230B notes
Do the following:
1. Watch this video: What are differential equations?
2. Read §1.1 in the textbook, and do exercises 3, 5, and 17.
3. Read this article and answer the following question: What are three ways that students with a growth mind-set approach challenges differently than students with a fixed mind-set?
4. Complete the syllabus quiz.
Your answers to #2 and #3 are due in the homework mailbox at 4:00pm Monday.
September 12–16 − hide
DayTopicHomework AssignedLabs
Monday
Sep. 12
Separation of variables;
230A notes; 230B notes
Read §1.2, do #1, 3, 5, 8, 15, 17, 25, 28
Wednesday
Sep. 14
Slope fields;
230A notes; 230B notes; mixing problem
Read §1.3, do #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.
Friday
Sep. 16
Meet in Tomson 188 computer lab
Euler's method
Read §1.4, do #1, 3, 5, 6, 11;
Watch the video Existence and Uniqueness before next class.
Lab 1 assigned;
due Sept. 28
September 19–23 − hide
DayTopicHomework Assigned
Monday
Sep. 19
Existence and uniqueness;
230A notes; 230B notes; solutions to practice problems
Read §1.5, do #2, 3, 5–8, 9ab, 11, 13
Wednesday
Sep. 21
Phase line;
230A notes; 230B notes
Read §1.6, do #1, 4, 7, 10, 13, 16, 19, 31, 32, 33
Friday
Sep. 23
Bifurcations;
230A notes; 230B notes
Read §1.7, do #4, 8, 9, 11, 12, 13, 16
September 26–30 − hide
DayTopicHomework AssignedLabs
Monday
Sep. 26
Linear differential equations;
230A notes; 230B notes
Watch the video The Integrating Factor Method before next class.
Lab 1 due Wednesday
Wednesday
Sep. 28
Integrating factor method;
230A notes; 230B notes; solutions to practice problems
Do §1.8 exercises #1, 4, 5, 8, 10, 17, 19, 23;
Read §1.9, do #1, 4, 5, 15, 19, 23
Lab 1 due today
Friday
Sep. 30
Systems of linear equations;
230A notes; 230B notes;
Lotka-Volterra plotter
Do #1–4, 7a, 8ab, 15
October 3–7 − hide
DayTopicHomework AssignedLabs
Monday
Oct. 3
Geometry of systems;
230A notes; 230B notes
Do §2.1 exercises #20, 21, 22;
Read §2.2, do #5, 9, 11, 14, 21
Lab 2 assigned;
due Oct. 21
Wednesday
Oct. 5
Damped harmonic oscillation;
230A notes; 230B notes
Read §2.3, do #1, 2, 5, 6, 7
Friday
Oct. 7
230A notes; 230B notes
Read §2.4, do #1, 2, 5, 6, 7, 10, 13
October 10–14 − hide
DayTopicHomework Assigned
Monday
Oct. 10
230A notes; 230B notes
Study for the exam
Wednesday
Oct. 12

Exam 1

• This exam will cover Chapter 1 and the first four sections of Chapter 2.
• Calculators will be permitted, but probably not very helpful, and certainly not necessary. Computer algebra systems (including the TI-89, TI-92, and TI-Nspire calculators) and internet-capable devices will not be permitted.
• Consider the following problems for review (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
Friday
Oct. 14
Linearity principle for systems;
230A notes; 230B notes
Read §3.1, do #5, 9, 15, 16, 24, 27, 29
October 17–21 − hide
DayTopicHomework AssignedLabs
Monday
Oct. 17
Fall Break — no class!
Wednesday
Oct. 19
Straight-line solutions;
230A notes; 230B notes
Read §3.2Lab 2 due Friday
Friday
Oct. 21
Linear systems with real eigenvalues;
230A notes; 230B notes
Do §3.2 exercises 1, 2, 4, 5, 11, 12, 21;
Read §3.3, do #1, 2, 9, 10, 13
Lab 2 due today
October 24–28 − hide
DayTopicHomework AssignedLabs
Monday
Oct. 24
Linear systems with complex eigenvalues;
230A notes; 230B notes;
Bonus: video on e
Read §3.4, do #1, 2, 9, 10, 11
Wednesday
Oct. 26
Linear systems with complex or repeated eigenvalues;
230A notes; 230B notes
Do §3.4 exercises #6, 12, 15, 16, 23;
Read §3.5, do #1, 9, 10
Lab 3 assigned;
due Nov. 11
Friday
Oct. 28
Linear systems with repeated or zero eigenvalues;
230A notes; 230B notes
Do §3.5 exercises 3, 7, 11, 17, 18, 21, 22
October 31 – November 4 − hide
DayTopicHomework Assigned
Monday
Oct. 31
Linear system summary
and trace-determinant plane;
230A notes; 230B notes
Wednesday
Nov. 2
Trace-determinant plane;
Second-order linear equations;
230A notes; 230B notes
Do §3.7 exercises #1, 2, 3, 5, 11, 12;
Read §3.6, do #1, 2, 6, 7, 10
For these problems, a "brief essay" can be a sentence or two.
Friday
Nov. 4
Second-order linear equations;
Forced harmonic oscillation;
230A notes; 230B notes
Do §3.6 exercises #13, 16, 21, 24, 33;
November 7–11 − hide
DayTopicHomework AssignedLabs
Monday
Nov. 7
Forced harmonic oscillation;
230A notes; 230B notes
Re-read §4.1, do #1, 5, 9, 13, 16, 22, 26, 33, 37
Wednesday
Nov. 9
Sinusoidal forcing;
230A notes; 230B notes
Read §4.2Lab 3 due Friday
Friday
Nov. 11
Undamped forcing and resonance;
230A notes; 230B notes;
Desmos: forced oscillator, undamped forced oscillator
Do §4.2 exercises #1–4, 11, 17, 19;
Read §4.3, do #5
Lab 3 due today
November 14–18 − hide
DayTopicHomework AssignedLabs
Monday
Nov. 14
Forced oscillation and resonance;
230A notes; 230B notes;
Desmos: Undamped forced oscillator
Do §4.3, #15, 17, 21 (not to be collected);
Study for the exam
Wednesday
Nov. 16

Exam 2

• This exam will cover Chapter 3, sections 1 through 7, and the first three sections of Chapter 4.
• Calculators will be permitted, but probably not very helpful, and certainly not necessary. Computer algebra systems (including the TI-89, TI-92, and TI-Nspire calculators) and internet-capable devices will not be permitted.
• Consider the following problems for review (not to be collected):
• Chapter 3 review (pages 376–380) exercises 1–32
• Chapter 4 review (pages 449–451) exercises 1–4, 10–12, 15–23
Friday
Nov. 18
Nonlinear systems: equilibrium point analysis;
230A notes; 230B notes
Read §5.1, do #1, 4, 5, 9ab, 18, 21Lab 4 assigned;
due Dec. 9
November 21–25 − hide
DayTopicHomework Assigned
Monday
Nov. 21
Qualitative analysis of nonlinear systems;
230A notes; 230B notes
Read §5.2, do #3, 7, 8, 17, 19, 21
Wednesday
Nov. 23
Thanksgiving Break — no class!
Friday
Nov. 25
Thanksgiving Break — no class!
November 28 – December 2 − hide
DayTopicHomework Assigned
Monday
Nov. 28
Qualitative analysis of nonlinear systems;
230A notes; 230B notes
Do §5.2, #9, 16, 18; Read §5.3, do #1, 2, 3
In problems #1–3, you may ignore "saddle connections" for now.
Wednesday
Nov. 30
Hamiltonian systems;
230A notes; 230B notes
Do §5.3 exercises 9, 10, 11, 12, 14, 15, 18
Friday
Dec. 2
The Laplace transform;
230A notes; 230B notes
Read §6.1, do #1, 2, 6–10, 15, 16
December 5–9 − hide
DayTopicHomework AssignedLabs
Monday
Dec. 5
Laplace transform for discontinuous functions;
230A notes; 230B notes
Read §6.2, do #1, 2, 3, 5, 7, 9, 11
Wednesday
Dec. 7
Laplace transform for second-order equations;
230A notes; 230B notes
Read §6.3Lab 4 due Friday
Friday
Dec. 9
Delta functions and impulse forcing;
230A notes; 230B notes
Do §6.3 exercises #5, 11, 15, 27, 30;
Read §6.4, do #2, 3, 5, 7
Lab 4 due today
December 12–16 − hide
DayTopic
Monday
Dec. 12

Review for final exam. Solutions to in-class problems.

Final Exam Information:

• This exam will cover the sections we have studied from Chapters 1 through 6, with emphasis on Chapters 5 and 6.
• Calculators will be permitted, but probably not very helpful, and certainly not necessary. Computer algebra systems (including the TI-89, TI-92, and TI-Nspire calculators) and internet-capable devices will not be permitted.
• A Laplace Transform Reference will be provided during the exam.
• As you study, consider working the problems from these old exams by the textbook authors:
• Also consider problems from the chapter review sections in the text.
• Lastly, make sure you are familiar with the St. Olaf final exam policies.
Friday
Dec. 16
Final exam for Math 230B
2:00 – 4:00pm
December 19–23 − hide
DayTopic
Monday
Dec. 19
Final exam for Math 230A
9:00 – 11:00am