Matthew L. Wright
Assistant Professor, St. Olaf College

Differential Equations

Math 230 ⋅ Fall 2020

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Friday
August 21
Introduction; modeling with differential equations
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Monday
August 24
Separation of variables
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Wednesday
August 26

Bonus video: John Urschel-NFL Math Whiz

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Friday
August 28
Euler's method
Homework 1
due at 4pm
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Monday
August 31
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Wednesday
September 2
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
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
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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
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Wednesday
September 23
Linear systems, linearity principle

Bonus video: How Not to Be Wrong: The Power of Mathematical Thinking - with Jordan Ellenberg

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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
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Wednesday
September 30
Linear systems with complex eigenvalues

Bonus video: Talitha Washington — Big Ideas in STEM Innovation

Do the following before next class:
  • Review the problems and solutions from class (see notes posted after class).
  • Read §3.5. Note what types of phase portraits can occur for linear systems with repeated (real) eigenvalue or zero eigenvalues. There are no reading questions today.
  • Finish Homework 8 (due Friday).
Friday
October 2
Linear systems with repeated eigenvalues
Homework 8
due at 4pm
Do the following before next class:
  • Review the problems and solutions from class (see notes posted after class).
  • Review §3.3 through §3.5. Note the different types of phase portraits that can occur for linear systems, and how they are determined by the eigenvalues of the matrix of coefficients.
  • Begin Homework 9 (due Wednesday).
  • Work on Lab 2, due on October 9.
Monday
October 5
Linear systems with zero eigenvalues
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Wednesday
October 7
Second-order linear systems
Homework 9
due at 4pm

Bonus: Why is Mathematics Useful, and Applied Dynamical Systems Vol. 2 — Robert Ghrist

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Friday
October 9
Trace-determinant plane
Lab 2
due today
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Monday
October 12
Forced harmonic oscillation
Do the following before next class:
  • Read §4.2. Focus on the qualitative analysis and phase portraits. We will discuss "complexification" in class. There are no reading questions for Wednesday.
  • Finish Homework 10 (due Wednesday).
Wednesday
October 14
Undamped forcing
Homework 10
due at 4pm

Bonus video: Dr. Erika Camacho on Horizonte and LATMATH: Erika Camacho - "Modeling Photoreceptor Death and Rescue"

Extra credit opportunity: attend Explore MSCS on Thursday, Oct. 15, 4:00–5:00pm to earn 2 extra-credit points for your homework grade.

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Friday
October 16
Resonance and beats
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Monday
October 19
Review
Homework 11
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.
Wednesday
October 21
No homework before Friday's class.
Friday
October 23
Nonlinear systems: equilibrium point analysis

Bonus video: Francis Su — Mathematics for Human Flourishing

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Monday
October 26
Nonlinear systems: nullclines

MSCS Colloquium: Monday, 3:15–4:15pm

Do the following before next class:
  • Read §5.2. Notice how analysis of equilibrium points and nullclines can provide a lot of qualitative information about solutions to systems of differential equations, even if you can't write down formulas for the solutions.
  • Finish Homework 12 (due Wednesday).
Wednesday
October 28
Nonlinear systems: bifurcations
Homework 12
due at 4pm
Do the following before next class:
  • to be announced
Friday
October 30
Nonlinear systems: qualitative analysis
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  • to be announced
Monday
November 2
Hamiltonian systems
Homework 13
due at 4pm
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  • to be announced
Wednesday
November 4
Revisiting Euler's Method: Quantifying Numerical Error
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  • to be announced
Friday
November 6
Improving Euler's Method
Homework 14
due at 4pm
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  • to be announced
Monday
November 9
Runge-Kutta Method
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  • to be announced
Wednesday
November 11
Power Series Solutions
Homework 15
due at 4pm
Do the following before next class:
  • to be announced
Friday
November 13
Power Series Solutions
Lab 3
due at 4pm
Do the following before next class:
  • to be announced
Monday
November 16
Review
Homework 15
due at 4pm
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