Math. Physics·Course
Mathematical Physics Equations
Equations of mathematical physics: heat, wave, Laplace equations, Fourier method, and Green's functions
5
Modules
15
Articles
~2 h
Reading
IV
CLOs
§ 01 — 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 →
§ 02 — Learning outcomes
4 outcomes.
CLO I
Classification of PDEs
Classify second-order partial differential equations
CLO II
Separation of Variables
Solve Sturm–Liouville problems and apply Fourier methods
CLO III
Potential Theory
Solve Laplace’s equation and understand Green’s functions
CLO IV
Wave Processes
Analyze wave phenomena and the heat equation
§ 03 — Practices