# Partial Differential Equations

Canonical: https://manyspace.aporia.systems/subjects/mathematics/partial-differential-equations-43
Updated: 2026-10-13

Partial Differential Equations: about 55 hours. Each topic lists what you need first and what it unlocks.

## Classification & First-Order

- [Classification of PDEs](https://manyspace.aporia.systems/topics/classification-of-pdes-mth-pde-296)
- [First-Order PDEs](https://manyspace.aporia.systems/topics/first-order-pdes-mth-pde-297)

## Classical Equations

- [The Wave Equation](https://manyspace.aporia.systems/topics/the-wave-equation-mth-pde-298)
- [The Heat Equation](https://manyspace.aporia.systems/topics/the-heat-equation-mth-pde-299)
- [Laplace & Poisson Equations](https://manyspace.aporia.systems/topics/laplace-poisson-equations-mth-pde-300)
- [Separation of Variables](https://manyspace.aporia.systems/topics/separation-of-variables-mth-pde-301)

## Methods & Theory

- [Fourier Series & Transforms](https://manyspace.aporia.systems/topics/fourier-series-transforms-mth-pde-302)
- [Green's Functions](https://manyspace.aporia.systems/topics/green-s-functions-mth-pde-303)
- [Sturm-Liouville Theory](https://manyspace.aporia.systems/topics/sturm-liouville-theory-mth-pde-304)
- [Introduction to Nonlinear PDEs](https://manyspace.aporia.systems/topics/introduction-to-nonlinear-pdes-mth-pde-305)