“Among all the mathematical disciplines the theory of differential equations is the most important … it furnishes the explanation of all those elementary manifestations of nature which involve time.”
— Sophus Lie (lecture, 1889)
Welcome to Math 20D – Differential Equations! This summer we’ll dive into the language of change—turning real-world questions from science, engineering, and beyond into mathematical models, and exploring them through analysis, graphical intuition, and hands-on computation. Expect lively, participatory class meetings, frequent small-group problem-solving, and a capstone project where you’ll design, simulate, and present your own model. Bring curiosity, a willingness to collaborate, and the courage to ask “what if…?”—and together we’ll uncover how differential equations illuminate the dynamic world around us.
Course Information
Course Description
Ordinary differential equations: exact, separable, and linear; constant coefficients, undetermined coefficients, variation of parameters. Series solutions. Systems, Laplace transforms. Computing symbolic and graphical solutions using Matlab.
Textbook
Fundamentals of Differential Equations (9th edition), by Nagle, Saff, and Snider.
Additional textbook: The Ordinary Differential Equations Project, by Thomas W. Judson. link
Instructor
Johnny (Jingze) Li, Email: jil164@ucsd.edu
IA/TA
Minyoung Jeong (TA), Vincent Nguyen (Tutor)
MATLAB TA
Jiajia Wang, jiw133@ucsd.edu
Salma Minoo, sminoo@ucsd.edu
Time and Location of Lecture, Discussion and Exams
Lecture: MW 8:00 - 10:50am PETER* 102
Discussion: MW 11:00 - 11:50am AP&M** 2301
Midterm: Wednesday, July 16th, 10:00-10:50am, PETER* 102
Final: Friday, Aug 1st, 8:00-10:50am, PETER*102
Time and Location of Office Hours
Johnny: T, Th 2-3:30pm, at FAH*** Second floor open space, or by appointment
Minyoung: M, W 1-3pm, at AP&M 5768
*Peterson Hall Address
** Applied Physics and Mathematics Building Address
*** Franklin Antonio Hall Address
Lecture Slides
Lecture slides will be posted after class.
Homeworks
Submit your homework to Gradescope. You’re encouraged—but not required—to typeset your solution.
HW1: link (Due: Monday July 7th, 11:59pm)
HW2: link (Due: Monday July 14th, 11:59pm)
HW3: link (Due: Tuesday July 22th, 11:59pm)
HW4: link (Due: Tuesday July 29th, 11:59pm)
We have 4 homeworks. Start each one early!
MATLAB
Assignment 1: (Due: Monday, July 7th, 11:59pm)
Assignment 2: (Due: Friday, July 11th, 11:59pm)
Assignment 3: (Due: Friday, July 18th, 11:59pm)
Assignment 4: (Due: Friday, July 25th, 11:59pm)
About our in-class worksheets:
We use Inquiry-Oriented Differential Equations (IODE) by Rasmussen, C., Keene, K. A., Dunmyre, J., & Fortune, N. IODE course materials are available at https://iode.sdsu.edu. This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
The IODE content has been kindly shared by the authors for revising, remixing and redistributing. Much gratitude and thanks to the IODE team for creating and sharing amazing content with instructors and students of differential equations!
Here are the worksheets we used so far, and related material (exemplar student homework, teacher materials):
Interactive Worksheet
These materials are intended as set of activities to experiment and explore differential equations. Each interactive Jupyter notebooks is a "virtual laboratory" where we perform our experiments and summarize the results. The objectives of experimental mathematics are generally to make mathematics more tangible, lively and fun.
Lecture Notes
This is the lecture notes for a previous Math 20D class. It can be a useful summary of the key theories and examples. Note: some topics in this lecture note are NOT covered in our class.
Lecture 6 (Jul 16th): Systems of differential equations
Worksheet: link pdf version: link ploting the phase portrait: link
Lecture Slides: link
Discussion worksheet: link Solution: link
Want to have a better understanding of eigenvalue/ eigenvectors? Check out this tutorial!
Interested in knowing more about the systems of differential equations? Check out the chapter 3 of this book!
Lecture 10 (Jul 30th): Laplace Transforms
Worksheet: link (pdf) link (interactive)
Lecture Slides: link
Exit Ticket: link
Discussion worksheet: link Solution: link (Note: Content in this discussion worksheet will NOT be in the final)
Want to know more about the applications of Laplace Transforms? Check this out! link
All the course material we used in class: