MATH 441 (Fall 2026): Differential Equations

Brachistochrone by Henk Ovink, Zernike, Groningen (Netherlands). Picture taken from Wikimedia Commons. Click here for a nice video on the Brachistrochrone by Prof. Steven Strogatz.

Time: MWF 11:00-11:50 AM. The first lecture will be on Monday, August 24th.

Location: 111 Gregory Hall.

Office Hours: Tu 3:50-4:50 PM in Harker Hall, Room 314i.

Description: This is an introductory course in ordinary differential equations (ODEs). We will focus mainly on classes of ODEs that have explicit or implicit closed-form solutions (which include linear ODEs) and finding these solutions. Unlike MATH 285, this course will both emphasize techniques for solving ODEs and present a rigorous treatment of ODEs. See the syllabus for a more detailed description of the course material.

Course notes and exercises: See below for my course notes and some in-class exercises (this is a work in progress). I will provide these notes in advance and print them for you. You are encouraged to take notes in class; I may sometimes deviate from these notes or do more in-depth exercises.

Unit 1: Introduction and first-order ODEs. Warm-up exercises.
Unit 2: Second-order linear ODEs.
Unit 3: The Laplace transform.
Unit 4: Series solution of second-order ODEs.
Unit 5: Linear Systems of ODEs.
Unit 6: Nonlinear systems of ODEs.
Unit 7: Introduction to numerical methods for ODEs.

Homework assignments: Your solutions must be handwritten; I will not accept typed solutions unless you have an accommodation.

Assignment 1, due Wednesday, September 9th, in class by 11 AM.
Assignment 2 will be released around Friday, September 4th.

Course schedule: TBC. The final exam is scheduled to take place on Wednesday, December 16th, between 8:00 and 11:00 AM.