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

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Friday
August 28
Euler's method
Homework 1
due at 4pm
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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
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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
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
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Wednesday
September 30
Linear systems with complex eigenvalues
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
Do the following before next class:
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

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
Exam 2
No homework before Friday's class.
Friday
October 23
Nonlinear systems: equilibrium point analysis

Bonus video: Francis Su — Mathematics for Human Flourishing

Do the following before next class:
Monday
October 26
Nonlinear systems: nullclines
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
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Friday
October 30
Hamiltonian systems
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Monday
November 2
Hamiltonian systems
Homework 13
due at 4pm
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Wednesday
November 4
Revisiting Euler's Method: Quantifying Numerical Error
Do the following before next class:
• Read §7.2. There are no reading questions on Moodle for Friday, but as you read, answer the question: How is the improved Euler's method similar to the trapezoid rule from calculus?
• Finish Homework 14 (due Friday).
• Start work on Lab 3.
• Bring a computer with Mathematica to class next time, if possible.
Friday
November 6
Improving Euler's Method
Homework 14
due at 4pm
Do the following before next class:
• Read §7.3. Note that the Runge-Kutta is more sophisticated than Improved Euler's method.
• Begin Homework 15 (due Wednesday).
• Start work on Lab 3, if you haven't done so already.
• If possible, bring a computer with Mathematica to class on Monday.
Monday
November 9
Runge-Kutta Method
Do the following before next class:
• Read Appendix B: Power Series (pages 742–748). Pay special attention to the examples, observing how power series can be used to find solutions to differential equations.
• Finish Homework 15 (due Wednesday).
• Work on Lab 3.
Wednesday
November 11
Power Series Solutions
Homework 15
due at 4pm
Do the following before next class:
• Re-read Appendix B: Power Series (pages 742–748).
• Finish Lab 3.
• Begin Homework 16 (due Monday).
Friday
November 13
Power Series Solutions
Lab 3
due at 4pm
Do the following before next class:
• Finish Homework 16 (due Monday).
• Review the final exam information (below).
Monday
November 16
Homework 16
due at 4pm
Complete the final exam take-home problems; either bring your solutions to the exam session or upload them to Moodle here. See the final exam information below, and make sure you are familiar with St. Olaf College's final exam policies.
Thursday
November 19
Final exam
9:00 – 11:00am