About this site

Built 2026-04-20

This is an unofficial concept-per-page review of Math 53: Differential Equations with Linear Algebra, Fourier Methods, and Modern Applications as taught at Stanford in Spring 2026 (instructor: Lernik Asserian).

It is inspired by the layout of Paul's Online Math Notes (tutorial.math.lamar.edu) with a dark theme modeled after claude.ai.

## Scope

All 26 core chapters of the Math 53 textbook:

• Part I: First-order ODEs, phase lines, complex numbers, second-order linear ODEs, linear systems via eigenvectors.
• Part II: Inhomogeneous equations, chaos and bifurcations, linearization, conserved quantities.
• Part III: Power-series methods, Euler's method, Runge–Kutta.
• Part IV: Introduction to PDEs, separation of variables, Fourier series.
• Part V: Fourier transform, Gaussians, convolution, wave equation.

Optional appendices (integrating factors, Laplace transform, Picard iteration, etc.) are not covered in depth here.

## Sources

• Stanford Math 53 textbook (local markdown, 2026 edition).
• Math 53 Spring 2026 syllabus and schedule (web.stanford.edu/class/math53).
• Practice exams #1 and #2 released by the course, used to calibrate problem style and difficulty.

## How to use it

• Browse the sidebar by Part and Chapter.
• Each concept page has: intro, definitions / theorems, worked sections, inline diagrams where helpful, and 3–5 practice problems with hints and solutions.
• Math is rendered with KaTeX. Diagrams are SVGs — click to expand.

## Building locally

`` cd ~/.tuft/projects/math53-review python3 build.py # serve python3 -m http.server --directory site 8000 ``

## Deploy (Cloudflare Pages)

`` wrangler pages deploy site --project-name math53-review ``

## Caveats

• Written quickly. Problems and derivations should be double-checked against the textbook before use in exam prep.
• Anything flagged needs a look before trusting.
• Convention disputes (signs, factors of \(2\pi\) in Fourier transform, etc.) follow the Stanford Math 53 textbook.