Matthew L. Wright
Assistant Professor, St. Olaf College

# Differential Equations

## Math 230 ⋅ Spring 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. 1–2, Tues. 2–3, Wed. 9–10, Thurs. 9:30–10:30, Fri. 1–2 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 Tuesday is due at 4:00pm Thursday.

February 8–12 − hide
DayTopicHomework Assigned
Tuesday
Feb. 9
Modeling with differential equationsRead §1.1, do exercises #3, 5, 13, 15, 17;
Thursday
Feb. 11
Separation of varibles and slope fieldsRead §1.2, do #1, 3, 5, 7, 9, 15, 17, 23, 35;
Read §1.3, do #1, 3, 5, 7, 15
February 15–19 − hide
DayTopicHomework AssignedOther
Tuesday
Feb. 16
Slope fields and Euler's method
Mathematica notebook; PDF
Do §1.3 #11, 13, 16, 17 and §1.4 #1, 3, 5;
Watch this video before next class
Lab 1 due
Feb. 25
;
LaTeX file
Thursday
Feb. 18
Existence and uniqueness of solutions
solutions to practice problems; LaTeX file;
Phase line
Read §1.5, do exer. #2, 3, 5–9, 11, 13;
Read §1.6, do exer. #1, 4, 7, 10
February 22–26 − hide
DayTopicHomework Assigned
Tuesday
Feb. 23
Phase line and bifurcationsDo §1.6 exercises #13, 16, 19, 32, 33, 34;
Read §1.7, do exer. #4, 8, 9, 11, 12, 13, 16;
Lab 1 due Thursday (Moodle link)
Thursday
Feb. 25
Linear equations and integrating factorRead §1.8, do #1, 4, 5, 8, 10, 13, 17, 23;
Read §1.9, do #1, 4, 5, 12, 19
February 29 – March 4 − hide
DayTopicHomework AssignedOther
Tuesday
Mar. 1
Systems of linear equationsDo Ch. 1 review #29, 32 (p. 137);
Read §2.1, do #1–4, 7a, 8a, 15, 20–22
Lotka-Volterra
plotter
Thursday
Mar. 3
Geometry of systems and
damped harmonic oscillator
Read §2.2, do #1, 2, 9, 10, 11, 14, 21;
Lab 2 due Mar. 17;
LaTeX file
March 7–11 − hide
DayTopicHomework Assigned
Tuesday
Mar. 8
(not on Exam 1)
Do §2.3 #1, 2, 5, 6;
Read §2.4, do #1, 2, 4, 5, 6, 7, 10
(due Mar. 15)
Thursday
Mar. 10

Exam 1:

• This exam will cover Chapter 1 and the first three 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 1–8, 11, 13, 14–28
March 14–18 − hide
DayTopicHomework Assigned
Tuesday
Mar. 15
Linear systems and
straight-line solutions
Read §3.1, do #5, 9, 15, 16, 24, 27, 28, 29, 33;
Lab 2 due Thursday (Moodle link)
Thursday
Mar. 17
Linear systems with
real eigenvalues
Do §3.2 #1–6, 11, 12, 21;
Read §3.3, do #1–4, 9, 10, 13
March 21–25 − hide
Spring Break
no class
March 28 – April 1 − hide
DayTopicHomework AssignedOther
Tuesday
Mar. 29
Complex eigenvaluesRead §3.4, do #1, 3–6,
9–12, 15, 16, 23
Thursday
Mar. 31
Repeated and zero eigenvaluesRead §3.5, do #1, 2, 5,
6, 9, 11, 17, 18, 21, 22
Lab 3 due April 21;
LaTeX file
April 4–8 − hide
DayTopicHomework Assigned
Tuesday
Apr. 5
Trace-determinant planeRead §3.7, do #1, 2, 3, 4, 5, 11, 12
Thursday
Apr. 7
Second-order linear equationsRead §3.6, do #1, 2, 6, 7, 10, 13, 16, 21, 24
April 11–15 − hide
DayTopicHomework Assigned
Tuesday
Apr. 12
Forced harmonic oscillatorsRead §4.1, do #1, 4, 7, 9, 13, 16, 22, 26, 33, 37
Thursday
Apr. 14
Sinusoidal and undamped forcing
Desmos graph: forced oscillator
Read §4.2, do #1–4, 11, 12, 17, 19
April 18–22 − hide
DayTopicHomework Assigned
Tuesday
Apr. 19
Resonance and beats
Desmos graph: beats
Lab 3 due Thurs., April 21 (Moodle link)
Thursday
Apr. 21

Exam 2:

• This exam will cover Chapter 3, sections 1 through 7, and the first two 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, 3, 4, 10, 11, 12, 15–22
April 25–29 − hide
DayTopicHomework AssignedOther
Tuesday
Apr. 26
Nonlinear systems:
equilibrium point analysis
Read §5.1, do #1, 4, 5, 8ab, 16ab, 18, 21
Thursday
Apr. 28
Qualitative analysis
(nullclines, etc.)
Read §5.2, do #3, 7, 8, 17, 18, 19, 21Lab 4 due May 17;
LaTeX file
May 2–6 − hide
DayTopicHomework Assigned
Tuesday
May. 3
Hamiltonian systemsRead §5.3, do #1, 9–12, 14, 15
Thursday
May. 5
Laplace transformsRead §6.1, do #1, 2, 6–10, 15, 16, 22, 23, 26
May 9–13 − hide
DayTopicHomework Assigned
Tuesday
May. 10
Laplace transforms of discontinuous functions and
second-order equations
; Mathematica plot
Read §6.2, do #1, 2, 3, 5, 7, 9, 11;
Read §6.3, do #5, 11, 15
Thursday
May. 12
Laplace transforms of second-order equations
and delta functions
; Mathematica plot
Do §6.3 #27;
Read §6.4, do #2, 3, 5, 7;
Lab 4 due Tues., May 17 (Moodle link)
May 16–20 − hide
DayTopic
Tuesday
May. 17

Review for final exam—notes from class.

Final Exam Information:

• This exam will cover the sections we have studied from Chapters 1 through 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.
Thursday
May. 19
Final exam for Math 230B
2:00 – 4:00pm
May 23–27 − hide
DayTopic
Monday
May. 23
Final exam for Math 230A
9:00 – 11:00am