Fall 2025 MATH 53 Lecture Notes

Preface

This is a collection of lecture notes for MATH 53: Differential Equations with Linear Algebra, Fourier Methods, and Modern Applications taught at Stanford during the Autumn 25-26 quarter.

How to use

Each lecture will roughly correspond to one chapter in the textbook. It is highly recommended that you consult the textbook for learning objectives and key concepts for each lecture. The lecture will often contain one or two curated examples to illustrate the main concepts.

These notes are meant to be very cursory, and they may not faithfully represent the actual lecture. The contents of the lecture may deviate from what is written on the notes, possibly guided by student questions.

This set of notes is NOT meant to replace the textbook in any way; it is simply meant to complement the text and to allow easier access to course contents. In particular, the contents of the exam will be based on the contents of the actual text, not of these lecture notes.

Circulation outside of class, including providing the contents of these notes to AI, is STRICTLY PROHIBITED.