Math 22B Fall 2026

Course Information

Lectures: MWF at 11:00-11:50am at Giedt Hall 1001.

Textbook: Elementary Differential Equations and Boundary Value Problems by W.E. Boyce, R.C. DiPrima and D.B. Meade (11th Edition).
Please note that there is an abridged and more affordable version of this textbook available for UC Davis students.
We will use Chapters 1,2,3,6 and 7 of the above textbook, which are available in the abridged version.

Syllabus: The course syllabus contains the basic guidelines for the course, it will be uploaded closer to the start of the Quarter.

Office Hours: Mondays 3:00-4:00pm at MSB 3214 (Casals). Always feel free to ask after class.
TA Can Gormez: Monday & Wednesdays (4-6pm in QMAP 3030). TA Alex Simons: Tuesday (11am-12:30pm) and Thursday (1-2:30pm) in MSB 3151.
In addition, Academic Assistance and Tutoring Centers offers support workshop for this class Tuesdays and Thursdays 2:10-3pm at 3218 Dutton Hall.

Teaching Assistants: The Teaching Assistants are Can Gormez (cgormez@ucdavis.edu) and Alex Simons (asimons@ucdavis.edu).

Important Dates: First Day (Sep 23), First Midterm (Oct 23), Second Midterm (Nov 20), Final Exam (Dec 7).

Problem Sets: Weekly assignments are due on Fridays at 11:00am, at the beginning of class.
Problem Sets must be submitted online through Canvas. Problem Set 1 will be due Friday Oct 2.

Problem Sets

Problem Set 1: Due Friday Oct 2.
Problem Set 2: Due Friday Oct 9.

Math Diaries

Wednesday Sep 23: Introduction to Differential Equations.

Definition of a

Differential Equation

The Fundamental Theorem of Calculus

Newton's Second Law

Growth Rate Modeling

Oscillating Pendulum

Textbook Reading (Sep 23): Sections 1.1 and 1.3. Section 1.2 also recommended.

Friday Sep 25: Integrating Factors.

Motivating example: falling object with drag. The Method of Integrating Factors.
Explicit computation of the integrating factor. Comparison of free fall and fall with drag.
Examples: current in a resistor-inductor circuit and Streeter-Phelps model.

Textbook Reading (Sep 25): Section 2.1.

Monday Sep 28: Separation of Variables.

The Method of Separation of Variables. General recipe. First Examples.
Detailed example of a falling object with linear drag via separation of variables.
The Differential Equation for Pareto's Law and its Solution.

Textbook Reading (Sep 28): Section 2.2.

Wednesday Sep 30: The Geometry of First-Order ODEs.

Qualitative Solutions: understanding plots for falling object with drag.
Long-term Behaviour: Analytic Solution and Geometric Solution.
Method of Direction Fields (Isoclines). Example: Logistic Model .

Textbook Reading (Sep 30): Sections 1.1, 1.2 and Section 2.5.

Friday Oct 2: Autonomous ODEs and Population Dynamics.

Autonomous Differential Equations . Behaviour in terms of f(y).
Example in Logistic Model. Recipe for stable and unstable solutions.
Application to Harvesting: Solution for the case of Constant Quota.
(The case of non-constant quota: Gordon-Schaefer model .)

Textbook Reading (Oct 2): Section 2.5, Problems 19 and 20 (Harvesting a Renewable Resource).

Monday Oct 5: Numerical Methods in ODEs.

Numerical Approximations: Values and Errors. Euler's Method,
Geometric Perpsective. Algorithmic Perpsective: The Recipe.
Comprehensive Case Study: Analytical and Numerical Solutions.
Error Analysis. Error in terms of h and upper bound for global error.

Textbook Reading (Oct 5): Section 2.7.

Wednesday Oct 7: Homogeneous ODEs with Constant Coefficients.

Textbook Reading (Oct 7): Section 3.1.

Mathematical Resources

Books: Chapters 1-4 and 9-10 in the book "Differential Equations with Applications and Historical Notes" by G.F. Simmons are aligned with our course. The book "Ordinary Differential Equations" by M. Tenenbaum and H. Pollard is extremely well-written and clear. The book "Differential Equations and Linear Algebra " by G. Strang, with this associated website is also useful.

Additional Books: The books "Differential Equations and Their Applications" by M. Braun, and "Ordinary Differential Equations and Dynamical Systems" by G. Teschl might also be interesting. For students interested in mathematics, my favourite reference in the subject is "Ordinary Differential Equations" by V.I. Arnol'd.

Online resources: Arthur Mattuck's Course in Differential Equations provided by MIT OpenCourseWare is a wonderful video series. The recorded lectures "Differential Equations and Linear Algebra" by G. Strang is also a good source. The Differential Equations Video Series in 3Blue1Brown is both instructive and entertaining. The Khan Academy Differential Equations Series is useful and clear. This An Interactive Guide To The Fourier Transform is a wonderful introduction to the Fourier transform, and thus the Laplace transform. The online resource Paul's Online Notes in Differential Equations can be helpful as well.

There are many additional resources online, let me know if you are interested in more references for a particular topic.