Applied Mathematics

Learn Mathematical Physics

The mathematical machinery of physics: Lagrangian and Hamiltonian mechanics, least action, Maxwell's equations, special relativity, the linear algebra of quantum mechanics, Noether's theorem, tensors, and normal modes.

Free to start · adaptive placement finds your level · reviews timed to your own forgetting.

What you'll learn

30 lessons in Mathematical Physics

Lagrangian mechanicsHamiltonian mechanicsThe principle of least actionVector calculus & Maxwell's equationsSpecial relativity: the mathThe mathematics of quantum mechanicsSymmetry & Noether's theoremTensors & index notationNormal modes & coupled oscillatorsDimensional analysis & scalingClassical field theoryGauge invarianceScattering & cross sectionsPartition functionsGreen's functions & propagatorsCurved spacetime & the metricRepresentations & angular momentumPerturbation theoryThe Legendre transformPoisson bracketsLiouville's theoremSymplectic integratorsAction-angle variables & adiabatic invariantsConstraints & Lagrange multipliersDistributions & the delta functionSelf-adjointness & boundary conditionsDifferential forms & MaxwellSU(2), SO(3) & the double coverThe Riemann tensor & curvatureThe path integral
How Erudia teaches

Built to be understood — and remembered.

Every idea is taught with motivation and a worked example before the drills, and an FSRS spaced-repetition engine schedules each review for the day its model predicts you would forget it. A short placement check finds what you already know, so you start Mathematical Physics exactly where it's useful.

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