Math. Physics·Course
Mathematical Physics Equations
Equations of mathematical physics: heat, wave, Laplace equations, Fourier method, and Green's functions
Part of the Mathematics track — finish it for a verifiable diploma →
§ 01 — Orientation
New here?
What you'll be able to do, who this is for, how long it takes, and where to begin.
By the end, you will be able to
- 01Classify the PDEs of physics.
- 02Solve them by separation of variables.
- 03Work with potential theory.
- 04Model wave phenomena.
- 05Connect the math to physical intuition.
Who this is for
How long it takes
- Quick orientationSkim the opening module and the cheatsheet to get the shape of it.~2 h
- Full read-throughRead every article once, in order.~2 h
- Mastery pathRead, take the quizzes, and space out your reviews.~2 weeks
- APA
Stoa. (2026). Mathematical Physics Equations [Online course]. Stoa. https://stoa.school/course/math-physics
- MLA
Stoa. “Mathematical Physics Equations.” Stoa, 2026, https://stoa.school/course/math-physics.
- Chicago
Stoa. “Mathematical Physics Equations.” Stoa. Accessed September 1, 2026. https://stoa.school/course/math-physics.
§ 02 — Curriculum
5 modules.
Each module is a small unit. Most read in sequence — but a determined reader can begin anywhere.
- M IClassical Mechanics and Variational PrinciplesLagrangian and Hamiltonian mechanics, principle of least action3 articles
18 minBegin → - M IIElectromagnetism and Maxwell’s EquationsDifferential form of Maxwell’s equations, electromagnetic waves, and geometry3 articles
18 minBegin → - M IIIQuantum Mechanics: Formalism and ApplicationsSchrödinger equation, operators of observables, and exact solutions3 articles
18 minBegin → - M IVStatistical MechanicsEnsembles, distribution functions, phase transitions, and statistical physics3 articles
18 minBegin → - M VMathematical Methods of PhysicsGreen’s functions, integral equations, and methods of complex analysis3 articles
18 minBegin →
§ 03 — Learning outcomes
4 outcomes.
Classify second-order partial differential equations
Solve Sturm–Liouville problems and apply Fourier methods
Solve Laplace’s equation and understand Green’s functions
Analyze wave phenomena and the heat equation
§ 04 — Practices