Analysis

Learn Differential equations

Equations involving derivatives: the language of change.

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

What you'll learn

39 lessons in Differential equations

First-order ODEsSecond-order linear ODEsModeling with ODEsSystems & phase portraitsLaplace transform introNumerical ODE solversExact equations & integrating factorsMethod of undetermined coefficientsVariation of parametersPower series solutionsBernoulli equationsAutonomous equations & equilibriaFourier series for PDEsSturm-Liouville theoryPicard's existence theoremProof: superposition for linear homogeneous ODEsProof: Picard-Lindelöf via Banach fixed pointEnergy methodsStability analysisPDEs intro: heat, wave, LaplaceMethod of characteristicsSobolev spaces & weak solutionsGreen's functions & fundamental solutionsClairaut's equation & singular solutionsThe differential operator DEuler–Cauchy equidimensional equationsRiccati equationsOrthogonal trajectoriesReduction of orderSimultaneous linear ODEsPfaffian (total) differential equationsLyapunov stability theoryBifurcation theoryLimit cycles & Poincaré–BendixsonHamiltonian & Lagrangian dynamicsPerturbation & asymptotic methodsCalculus of variationsIntegral equationsConservation laws & shocks
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 Differential equations exactly where it's useful.

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Related Analysis subjects
CalculusMultivariable calculusPartial Differential EquationsDynamical Systems & ChaosReal analysisFourier & Harmonic Analysis