Differential Equations

• Read the syllabus, then complete the Syllabus Quiz (on Moodle).
• Watch this video: What are differential equations?
• From the textbook, read §1.1 and §1.2, at least up to the heading "Missing Solutions" on page 27. Complete the reading questions on Moodle before class on Monday.

• Finish reading §1.2, if you haven't done so already. Review the solutions to the problems from class (see the notes which will be posted after class).
• Read The Secret to Raising Smart Kids by Carol Dweck and §1.3 in the textbook. Then complete the reading questions on Moodle.
• Begin Homework 1 (due 4pm Friday).
• If possible, install Mathematica on your computer. We'll use it in class on Wednesday. See this help page for installation information.

Bonus video: John Urschel-NFL Math Whiz

• Finish Homework 1 (due 4pm Friday).
• Read §1.4 and complete the reading questions on Moodle.
• If possible, install Mathematica on your computer. We will use it in class on Friday. See this help page for installation information.

• Watch the video Existence and Uniqueness. Also read §1.5, at least through page 67. (There are no reading questions for Monday.)
• Begin Homework 2 (due 4pm Wednesday).

• Review the problems and solutions from class (see notes posted after class).
• Finish Homework 2 (due 4pm Wednesday).
• Read §1.6 in the textbook and complete the reading questions on Moodle.
• This week: begin work on Lab 1: Euler's Method, due September 9.

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

• Review the problems and solutions from class (see notes posted after class).
• Read §1.7 and complete the reading questions on Moodle..
• Begin Homework 3 (due 4pm Monday).
• Work on Lab 1.

• 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.

• Please complete the Week 3 Survey. Responses are voluntary and anonymous.
• Watch the video The Integrating Factor Method. Then read §1.9 in the textbook.
• Finish Lab 1 and submit your lab report to the Lab 1 assignment on Moodle.
• Begin Homework 4 (due 4pm Friday).

Bonus video: Yitang Zhang: An Unlikely Math Star Rises

• Please complete the Week 3 Survey, if you haven't done so already. Responses are voluntary and anonymous.
• Re-read the subsection Comparing the Methods of Solution for Linear Equations (p. 131–132).
• Read §2.1 and complete the reading questions on Moodle.
• Finish Homework 4 (due 4pm Friday).
• If possible, bring a computer with Mathematica to class on Friday.

• 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.

• Read §2.3 and complete the reading questions on Moodle.
• Finish Homework 5 (due Wednesday).
• Review the Exam 1 Information. Talk with Prof. Wright if you have any questions.

Bonus video: Moon Duchin: "Political Geometry"

• Complete Homework 6 (due Friday).
• Study for the exam. Talk with Prof. Wright if you have any questions.

• Complete the take-home exam problems.
• Study for the exam. Talk with Prof. Wright if you have any questions.

• Read §3.1, and complete the reading questions on Moodle.

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

• Read §3.2 and complete the reading questions on Moodle.
• Begin Homework 7 (due Monday).
• Take a look at Lab 2, which is due on October 9.

• Read §3.3 and complete the reading questions on Moodle.
• Finish Homework 7 (due Monday).

• Read §3.4 and complete the reading questions on Moodle.
• Begin Homework 8 (due Friday).
• If you want to know more about Euler's formula, watch this video by 3Blue1Brown.

Bonus video: Talitha Washington — Big Ideas in STEM Innovation

• 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).

• 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.

• Read §3.6 and complete the reading questions on Moodle.
• Finish Homework 9 (due Wednesday).
• Work on Lab 2 (due Friday). If you have questions about the lab, talk with Prof. Wright.

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

• Read §3.7 and complete the reading questions on Moodle.
• Finish Lab 2.

• Read §4.1 and complete the reading questions on Moodle. Take special note of the Extended Linearity Principle.
• Begin Homework 10 (due Wednesday).

• 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).

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.

• Read §4.3 and complete the reading questions on Moodle.
• Begin Homework 11 (due Monday).

• Review §4.1–4.3.
• Finish Homework 11 (due Monday).
• Read the Exam 2 Information. Talk with Prof. Wright if you have any questions.

• Complete the take-home exam problems.
• Study for the exam. Talk with Prof. Wright if you have any questions.

Bonus video: Francis Su — Mathematics for Human Flourishing

• Read §5.1 and complete the reading questions on Moodle.
• Begin Homework 12 (due Wednesday).

MSCS Colloquium: Monday, 3:15–4:15pm

• 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).

• Read §5.3 and complete the reading questions on Moodle.
• Begin Homework 13 (due Monday).
• Take a look at Lab 3.

• Review §5.1–5.3.
• Finish Homework 13 (due Monday).

MSCS Colloquium: Monday, 3:30–4:30pm

• Read §7.1 and complete the reading questions on Moodle.
• Begin Homework 14 (due Friday).
• Start work on Lab 3.

• 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.

• 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.

MSCS Colloquium: "Sharing Secrets" on Monday, November 9, 3:30–4:30pm

• 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.

• Re-read Appendix B: Power Series (pages 742–748).
• Finish Lab 3.
• Begin Homework 16 (due Monday).

• Finish Homework 16 (due Monday).
• Review the final exam information (below).

Bonus: Living Proof: Stories of Resilience Along the Mathematical Journey