Matthew L. Wright
Assistant Professor, St. Olaf College

Differential Equations

Math 230 ⋅ Fall 2017

Prof. Wright's office hours: Mon. 2–3, Tues. 9:45–10:45, Wed. 9–10, Thurs 1–2, Fri. 10:30–11:30, or by appointment in RMS 405

Help sessions: Tues. 7–8pm and Sat. 3–4pm in RNS 206

Jump to today
Friday
Sep. 8
Introduction
Modeling with differential equations
Do the following before next class:
Monday
Sep. 11
Separation of variables
Do the following before next class:
  • Finish reading §1.2. Then do exercises #1, 3, 5, 8, 15, 17, 25, 28.
  • 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?
  • Your answers to the two items above are due 4pm Wednesday in the homework box.
  • Read §1.3. Come to class knowing how to interpret a slope field.
Wednesday
Sep. 13
Slope fields
Do the following before next class:
  • Do §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.
  • Read this article and answer the following questions: According to Devlin, what is the secret to doing mathematics? How does this relate to the growth mind-set from the article you read last week? How might Devlin’s secret be relevant in this course?
  • Your answers to the two items above are due 4pm Friday in the homework box.
  • Read §1.4, up to the middle of page 59.
  • If possible, bring a computer with Mathematica to class on Friday. (Instructions for installing Mathematica at St. Olaf.)
Friday
Sep. 15
Euler's method
Do the following before next class:
  • Finish reading §1.4, then do exercises #1, 3, 5, 6, 11. (Solutions due 4pm Monday.)
  • Watch the video Existence and Uniqueness. Also read §1.5, at least through page 67.
Monday
Sep. 18
Existence and uniqueness
Do the following before next class:
  • Finish reading §1.5, then do #2, 3, 5–8, 9ab, 11, 13. (Solutions due 4pm Wednesday.)
  • Read from the beginning of §1.6 through page 79. Take note of the definition of autonomous differential equation and pay special attention to how a phase line can be used to sketch solutions.
Wednesday
Sep. 20
Phase line
Do the following before next class:
  • Finish reading §1.6, then do #1, 4, 7, 10, 13, 16, 19, 31, 32, 33, 34. (Solutions due 4pm Friday.)
  • Read from the beginning of §1.7 through page 99. Take special note of the definition of a bifurcation.
Friday
Sep. 22
Bifurcation
Do the following before next class:
  • Finish reading §1.7, then do #4, 8, 9, 11, 12, 13, 16. (Solutions due 4pm Monday.)
  • Read §1.8. Take note of the Linearity Principle and the Extended Linearity Principle, and how they are used in solving linear differential equations.
Monday
Sep. 25
Linear equations
Do the following before next class:
Wednesday
Sep. 27
Integrating factor
Lab 1
due today
Do the following before next class:
  • Finish reading §1.9, especially the subsection Comparing the Methods of Solution for Linear Equations (p. 131–132).
  • Do §1.8, #1, 4, 5, 8, 10, 17, 19, 23 and §1.9 #1, 4, 5, 15, 19, 23. (Due 4pm Friday.)
  • Read §2.1, through the end of the predator-prey discussion on page 156. Take special note of how the R(t) and F(t) graphs relate to the solution curves in the phase portrait.
Friday
Sep. 29
Systems of differential equations
Do the following before next class:
  • Do §2.1 exercises 1–4, 7a, 8ab, 15. (Due 4pm Monday.)
  • Read the spring-mass discussion in §2.1 (pages 156–160). Also read §2.2 and note how direction fields can be used to understand phase portraits.
Monday
Oct. 2
Geometry of systems
Do the following before next class:
  • Do §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.
Wednesday
Oct. 4
Damped harmonic oscillation
Do the following before next class:
  • Do §2.3 exercises 1, 2, 5, 6, 7. (Due 4pm Friday. You may use Mathematica or other technolgy instead of HPGSystemSolver.)
  • Read §2.4. Note how a decoupled system can be solved by solving each differential equation separately.
Friday
Oct. 6
Additional analytic methods
Do the following before next class:
  • Do §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.
Monday
Oct. 9
topics in Chapter 2
Study for the exam! 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
Wednesday
Oct. 11
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.
exam
Do the following before next class:
  • Read §3.1. Note how the concepts of determinate, linear combination, and linear independence from linear algebra can be applied to systems of differential equations.
Friday
Oct. 13
Linear systems, linearity principle
Fall break! No class Monday, October 16.
Do the following before next class:
  • Do §3.1 exercises 5, 9, 14, 16, 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?
Wednesday
Oct. 18
Linear systems and straight-line solutions
Do the following before next class:
  • Finish Lab 2 (bifurcation plane)
  • Read §3.3. What types of phase portraits that are possible for linear systems with real eigenvalues?
  • The next homework includes §3.2, exercises 1, 4, 5, 11, 12, 21. Because the lab is due Friday, the next homework is due Monday.
Friday
Oct. 20
Linear systems with real eigenvalues
Lab 2
due today
Do the following before next class:
  • Do §3.2 exercises 1, 4, 5, 11, 12, 21 and §3.3 exercises 17, 18. For each of these problems, identify the type of equilibrium point that you find.
  • Read §3.4, at least through the box at the top of page 305. Pay attention to the how the authors solve the example linear system, especially to how two linearly-independent real solutions are obtained from the complex solution.
  • If you want to know more about Euler's formula, watch this video by 3Blue1Brown.
This weekend, the help session will be Sunday, 1–2pm in RNS 206.
Monday
Oct. 23
Linear systems with complex eigenvalues
Do the following before next class:
  • TBA...
Wednesday
Oct. 25
Linear systems with complex or repeated eigenvalues
Do the following before next class:
  • TBA...
Friday
Oct. 27
Linear system summary
Do the following before next class:
  • TBA...
Monday
Oct. 30
Trace-determinant plane
Do the following before next class:
  • TBA...
Wednesday
Nov. 1
Second-order linear systems
Do the following before next class:
  • TBA...
Friday
Nov. 3
Forced harmonic oscillation
Do the following before next class:
  • TBA...
Monday
Nov. 6
Sinusoidal forcing
Do the following before next class:
  • TBA...
Wednesday
Nov. 8
Undamped forcing
Do the following before next class:
  • TBA...
Friday
Nov. 10
Resonance and beats
Do the following before next class:
  • TBA...
Monday
Nov. 13
Review
Do the following before next class:
  • TBA...
Wednesday
Nov. 15
Exam 2
exam
Do the following before next class:
  • TBA...
Friday
Nov. 17
Nonlinear systems: equilibrium point analysis
Do the following before next class:
  • TBA...
Monday
Nov. 20
Qualitative analysis
Thanksgiving break! No class Wednesday, Nov. 22 or Friday, Nov. 24.
Do the following before next class:
  • TBA...
Monday
Nov. 27
Qualitative analysis
Do the following before next class:
  • TBA...
Wednesday
Nov. 29
Hamiltonian systems
Do the following before next class:
  • TBA...
Friday
Dec. 1
Laplace transforms
Do the following before next class:
  • TBA...
Monday
Dec. 4
Laplace tranforms, discontinuous functions
Do the following before next class:
  • TBA...
Wednesday
Dec. 6
Laplace transforms of second-order equations
Do the following before next class:
  • TBA...
Friday
Dec. 8
Delta functions and impulse forcing
Do the following before next class:
  • TBA...
Monday
Dec. 11
Review
Study for the final exam!
Thursday
Dec. 14
Final exam for Math 230A
2:00 – 4:00pm
exam
Tuesday
Dec. 19
Final exam for Math 230B
2:00 – 4:00pm
exam