Matthew L. Wright
Assistant Professor, St. Olaf College

# Differential Equations

## Math 230 ⋅ Fall 2020

Top
Today
Bottom
Friday
August 21
Introduction; modeling with differential equations
Do the following before next class:
Monday
August 24
Separation of variables
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Wednesday
August 26
Slope fields

Bonus video: John Urschel-NFL Math Whiz

Do the following before next class:
Friday
August 28
Euler's method
Homework 1
due at 4pm
Do the following before next class:
Monday
August 31
Existence and uniqueness
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Wednesday
September 2
Phase line
Homework 2
due at 4pm

Bonus video: Hannah Fry — Beautiful equations: how insects walk on water and galaxies form (the Navier-Stokes equations are differential equations!)

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Friday
September 4
Bifurcations
Meet in RML 115 — masks required!
Do the following before next class:
• Review the problems and solutions from class (see notes posted after class).
• Finish Homework 3 (due 4pm Monday).
• Read §1.8 in the text, paying close attention to the Linearity Principle
• Work on Lab 1.
Monday
September 7
Linear equations
Homework 3
due at 4pm
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Wednesday
September 9
Integrating factor
Lab 1
due at 4pm

Bonus video: Yitang Zhang: An Unlikely Math Star Rises

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Friday
September 11
Systems of differential equations
Homework 4
due at 4pm
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. (There are no reading questions today.)
• Begin Homework 5 (due Wednesday).
• If possible, bring a computer with Mathematica to class on Monday.
Monday
September 14
Harmonic oscillation; Systems of differential equations
Do the following before next class:
Wednesday
September 16
Damped harmonic oscillation; Systems of differential equations
Homework 5
due at 4pm

Bonus video: Moon Duchin: "Political Geometry"

Do the following before next class:
• Complete Homework 6 (due Friday).
• Study for the exam. Talk with Prof. Wright if you have any questions.
Friday
September 18
Euler's method for systems; Review
Homework 6
due at 4pm
Do the following before next class:
• Complete the take-home exam problems.
• Study for the exam. Talk with Prof. Wright if you have any questions.
Monday
September 21
Exam 1
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Wednesday
September 23
Linear systems, linearity principle
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Friday
September 25
Linear systems and straight-line solutions
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Monday
September 28
Linear systems with real eigenvalues
Homework 7
due at 4pm
Do the following before next class:
• to be announced
Wednesday
September 30
Linear systems with complex eigenvalues
Do the following before next class:
• to be announced
Friday
October 2
Linear systems with repeated eigenvalues
Homework 8
due at 4pm
Do the following before next class:
• to be announced
Monday
October 5
Linear systems with zero eigenvalues
Linear system summary
Do the following before next class:
• to be announced
Wednesday
October 7
Second-order linear systems
Homework 9
due at 4pm
Do the following before next class:
• to be announced
Friday
October 9
Trace-determinant plane
Lab 2
due today
Do the following before next class:
• to be announced
Monday
October 12
Forced harmonic oscillation
Homework 10
due at 4pm
Do the following before next class:
• to be announced
Wednesday
October 14
Undamped forcing
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• to be announced
Friday
October 16
Resonance and beats
Do the following before next class:
• to be announced
Monday
October 19
to be determined
Do the following before next class:
• to be announced
Wednesday
October 21
Exam 2
Do the following before next class:
• to be announced
Friday
October 23
Nonlinear systems: equilibrium point analysis
Do the following before next class:
• To be announced
Monday
October 26
Nonlinear systems: nullclines
Do the following before next class:
• to be announced
Wednesday
October 28
Nonlinear systems: bifurcations
Do the following before next class:
• to be announced
Friday
October 30
Nonlinear systems: qualitative analysis
Do the following before next class:
• to be announced
Monday
November 2
To be determined
Do the following before next class:
• to be announced
Wednesday
November 4
Revisiting Euler's Method: Quantifying Numerical Error
Do the following before next class:
• to be announced
Friday
November 6
Improving Euler's Method
Do the following before next class:
• to be announced
Monday
November 9
Runge-Kutta Method
Do the following before next class:
• to be announced
Wednesday
November 11
Power Series Solutions
Do the following before next class:
• to be announced
Friday
November 13
Power Series Solutions
Do the following before next class:
• to be announced
Monday
November 16
Power Series Solutions
Final Exam Information: The final exam will consist of a short take-home portion and an in-class exam.
Thursday
November 19
Final exam
9:00 – 11:00am