Matthew L. Wright
Assistant Professor, St. Olaf College

# Differential Equations

## Math 230 ⋅ Fall 2018

Prof. Wright's office hours: Mon. 1–2, Tues. 10–11, Wed. 2–3, Thurs 10–11, Fri. 1–2, whenever the door is open, or by appointment in RMS 405

Help sessions: Tuesdays 9–10pm and Thursdays 7:30–8:30pm in Tomson 186

Friday
September 7
Introduction
Modeling with differential equations
Do the following before next class:
Monday
September 10
Separation of variables
Do the following before next class:
• Homework 1: §1.1 exercises 3, 5, 17; and §1.2 exercises #1, 3, 5, 8, 15, 17, 25, 28. This is due in the homework box (RMS 3rd floor, near the fireplace) at 4pm Wednesday.
• If possible, bring a computer with Mathematica to class on Wednesday.
Wednesday
September 12
Slope fields
Do the following before next class:
Friday
September 14
Euler's method
Do the following before next class:
• Homework 3: §1.3 exercises 18, 19 and §1.4 exercises #1, 3, 5, 6, 11. (Due 4pm Monday in the homework box.)
• Watch the video Existence and Uniqueness. Also read §1.5, at least through page 67.
Monday
September 17
Existence and uniqueness
Do the following before next class:
• Homework 4: §1.5 exercises #2, 3, 5–8, 9ab, 11, 13. (Due 4pm Wednesday.)
• This week: begin work on Lab 1.
Wednesday
September 19
Phase line
Do the following before next class:
• Homework 5: §1.5 exercise 12 and §1.6 exercises 1, 4, 7, 10, 13, 16, 19, 31, 32, 33, 34. (Due 4pm Friday.)
• Work on Lab 1.
Friday
September 21
Bifurcations
Do the following before next class:
• Read §1.8. Especially note the Linearity Principle and the Extended Linearity Principle..
• Homework 6: §1.6 exercises 28, 37 and §1.7, exercises 4, 8, 9, 11, 12, 13. (Due 4pm Monday.)
• Work on Lab 1.
Monday
September 24
Linear equations
Do the following before next class:
Wednesday
September 26
Integrating factor
Lab 1
due today
Do the following before next class:
• Re-read the subsection Comparing the Methods of Solution for Linear Equations (p. 131–132). Then read §2.1, and complete the reading questions on Moodle.
• Homework 7: §1.7 exercises 14, 16; §1.8 exercises 1, 4, 5, 8, 10, 17; and §1.9 exercises 1, 4, 5, 15. (Due 4pm Friday.)
• If possible, bring a computer with Mathematica to class on Friday.
Friday
September 28
Systems of differential equations
Predator-prey systems
Do the following before next class:
• Read §2.2. Take note of how vector fields can be used to visualize the behavior of solutions to systems of differential equations.
• Homework 8: §1.8 exercises 19, 23; §1.9 exercises 19, 23; and §2.1 exercises 1–4, 7a, 8ab, 15. (Due 4pm Monday.)
• If possible, bring a computer with Mathematica to class on Monday.
Monday
October 1
Geometry of systems
Spring-mass systems
Do the following before next class:
• Homework 9: §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
October 3
Damped harmonic oscillation
Do the following before next class:
• Homework 10: §2.3 exercises 1, 2, 5, 6, 7. (Due 4pm Friday. You may use Mathematica or other technolgy instead of HPGSystemSolver.)
• Familiarize yourself with Lab 2: Bifurcation Plane, which is due on October 19.
Friday
October 5
Do the following before next class:
• Homework 11: §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
October 8
topics in Chapter 2
Study for the exam! Do the take-home problems (PDF here), distributed in class. For review, consider doing some of the following problems (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
October 10
Exam 1
• This exam will cover Chapter 1 and the first four sections of Chapter 2.
• The exam will consist of a short take-home portion and an in-class portion.
• For the take-home portion, you may (and should) use Mathematica or other technology.
• You may not use Mathematica or similar technology on the in-class exam. Calculators will be permitted, but probably not very helpful. The in-class exam will focus on conceptual understanding. It will involve basic calculus and some arithmetic, but not tedious arithmetic.
Do the following before next class:
Friday
October 12
Linear systems, linearity principle
Fall break! No class Monday, October 15.
Do the following before next class:
• Homework 12: §3.1 exercises 5, 9, 14, 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
October 17
Linear systems and straight-line solutions
Do the following before next class:
• Finish Lab 2 (bifurcation plane). You may either submit your lab report on Moodle in PDF format or place it in the homework box by 4pm Friday.
• Read §3.3. What types of phase portraits that are possible for linear systems with real eigenvalues?
• The next homework includes exercises from §3.1 and §3.2. Because the lab is due Friday, the next homework is due Monday.
Friday
October 19
Linear systems with real eigenvalues
Lab 2
due today
Do the following before next class:
Monday
October 22
Linear systems with complex eigenvalues
Do the following before next class:
• Homework 14: §3.4 exercises 1, 2, 4, 5, 10, 11, 15, 16. (Due 4pm Wednesday.)
• Read §3.5. Note what types of phase portraits can occur for linear systems with repeated (real) eigenvalue or zero eigenvalues.
Wednesday
October 24
Linear systems with repeated eigenvalues
Do the following before next class:
Friday
October 26
Linear systems with zero eigenvalues
Linear system summary
Do the following before next class:
Monday
October 29
Second-order linear systems
Do the following before next class:
Wednesday
October 31
Trace-determinant plane
Do the following before next class:
Friday
November 2
Forced harmonic oscillation
Do the following before next class:
Monday
November 5
Sinusoidal forcing
Do the following before next class:
Wednesday
November 7
Undamped forcing
Do the following before next class:
Friday
November 9
Resonance and beats
Lab 3
due today
Do the following before next class:
Monday
November 12
Review
Study for the exam! Consider the following problems for review (not to be collected):
Wednesday
November 14
Exam 2
• This exam will cover Chapter 3, sections 1 through 7, and the first three sections of Chapter 4.
Do the following before next class:
Friday
November 16
Nonlinear systems: equilibrium point analysis
Do the following before next class:
Monday
November 19
Qualitative analysis
Thanksgiving break! No class Wednesday, Nov. 22 or Friday, Nov. 24.
Do the following before next class:
Monday
November 26
Qualitative analysis
Do the following before next class:
Wednesday
November 28
Hamiltonian systems
Do the following before next class:
Friday
November 30
Laplace transforms
Do the following before next class:
Monday
December 3
Laplace tranforms, discontinuous functions
Do the following before next class:
Wednesday
December 5
Laplace transforms of second-order equations
Do the following before next class:
Friday
December 7
Delta functions and impulse forcing
Lab 4
due today
Do the following before next class:
Monday
December 10
Review
Final Exam Information: The final exam will consist of a take-home problem and an in-class exam.
Friday
December 14
Final exam for Math 230A
9:00 – 11:00am
Tuesday
December 18
Final exam for Math 230B
9:00 – 11:00am