Math 302: Introduction to Differential Equations I (Fall 2021)

Class Meets Mondays/Wednesdays/Fridays 9:30–10:20

• See here for the syllabus.

• Class meetings will be conducted over Zoom. Access info can be found on the Laulima site or the Discord for the class.

• Outside of Zoom there are two main ways I will communicate with you: (1) This site, the public site for the class, where I will post announcements and any lecture notes; (2) a Discord channel, where I will also post announcements, where you can ask questions and discuss things with your classmates. Assignment submission will be done through Gradescope, and online homework will be done through UHM’s WeBWorK site.

Announcements

• Here is a study guide for the second midterm.

• Here is the schedule for the second midterm, which will be a take-home exam. Wednesday, April 21 we will use class time for a review session. The exam will be available on gradescope starting at the end of class. It will be due by 11pm on Sunday, April 25. I will post a study guide for the exam soon.

• For your convenience, here is a pdf with a table of Laplace transforms.

• See here for info about the final project for the class.

• No class Friday, April 3rd on account of Good Friday

• No class Friday, March 26th on account of Prince Kūhiō Day

• Here is a study guide for the first midterm.

• The first midterm will be a take-home exam. I will release it on gradescope on Wednesday, February 17th after class, and it will be due by the end of Sunday, February 21st.

• No class Monday, February 15th on account of Presidents Day

• No class Monday, January 18th on account of MLK Day

Lecture notes

• 1/11: Introduction

• 1/13: Introduction, part II

• 1/20: Separable differential equations

• 1/25: ODEs with homogeneous coefficients

• 1/27: ODEs with linear coefficients

• 2/1: Exact differential equations

• 2/3: Integrating factors

• 2/8: Linear ODEs

• 2/10: More on solving first-order ODEs

• 2/19: The catenary

• 2/22, 2/24: Complex numbers and linear independence

• 3/1, 3/3: Homogeneous linear ODEs

• 3/8, 3/10: The method of undetermined coefficients

• 3/22, 3/24: The method of variation of parameters

• 3/29: Operators

• 3/31: The Laplace transform, part I

• 4/5, 4/7: The Laplace transform, part II

• 4/12, 4/14: Series methods

• 4/19: Series methods, II

• 4/23: The Legendre equation

• 4/26, 4/28: Existence and uniqueneness

In-class worksheets

• 1/15: Direction fields.

  For this worksheet you will need to use a direction field plotter, such as the one found here (or a different online direction field plotter).

• 1/22: Dilution problems.

• 1/29: Orthogonal trajectories.

• 2/5 No worksheet this week

• 2/12: Newton’s Law of Cooling.

• 2/26: Wronskians.

• 3/5: Simple harmonic motion.

• 3/12: Damped harmonic motion.

• 4/9: Forced undamped harmonic motion.

• 4/16: Error with approximating solutions.

• 4/30: The Lotka–Volterra model.

Schedule

(Tentative, may change)

• Week 1 (Jan 11) Introduction: Chapters 1, 3, 5

• Week 2 (Jan 18) Separable equations: Chapters 4, 6

• Week 3 (Jan 25) Equations with homogeneous coefficients: Chapters 7, 8

• Week 4 (Feb 1) Exact equations: Chapters 9, 10

• Week 5 (Feb 8) Linear first-order equations: Chapter 11

• Week 6 (Feb 15) Review and midterm 1

• Week 7 (Feb 22) Linear ODEs of degree > 1: Chapters 18, 19

• Week 8 (Mar 1) Homogeneous linear ODEs: Chapter 20

• Week 9 (Mar 8) Nonhomogeneous linear ODEs, I: Chapter 21

• Spring break!

• Week 10 (Mar 22) Nonhomogeneous linear ODEs, II: Chapter 22

• Week 11 (Mar 29) Operators: Chapters 24, 25

• Week 12 (Apr 5) The Laplace transform: Chapter 27

• Week 13 (Apr 12) Series solutions: Chapter 37

• Week 14 (Apr 19) Overspill, review, and midterm 2

• Week 15 (Apr 26) Existence and uniqueness theorems, I

• Week 16 (May 3) Existence and uniqueness theorems, II