Analysis

Learn Multivariable calculus

Calculus with multiple inputs: partials, gradients, and multiple integrals.

Start Multivariable calculus free → Browse all subjects

Free to start · adaptive placement finds your level · reviews timed so it stays learned.

What you'll learn

35 lessons in Multivariable calculus

Partial derivativesGradients & directional derivativesMultiple integralsLine integralsGreen's & Stokes' theoremsGradient descentVector fields, curl & divergenceSurface integrals & fluxChange of variables / JacobianCylindrical & spherical coordsTangent planes & linear approximationsDivergence theoremConservative fields & potentialsDouble integrals in polarClairaut's theorem & proofGradient ⊥ level sets — proofLagrange multipliers proofTriple integral applicationsHessian & second-derivative testEuler's theorem on homogeneous functionsThe implicit function theoremTotal differential & the multivariable chain ruleTaylor's theorem in several variablesPlanes & lines in spaceQuadric surfacesSpace curves: arc length, curvature & the Frenet frameVector identities & the triple productsDifferential forms & generalized StokesConstrained optimization & the KKT conditionsTensors & index notationThe Laplacian & harmonic functionsVector calculus in curvilinear coordinatesThe Helmholtz decompositionThe Gaussian integralIndex of a vector field & Poincaré–Hopf
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 moment just before you'd forget it. A short placement check finds what you already know, so you start Multivariable calculus exactly where it's useful.

Start Multivariable calculus →
Related Analysis subjects
CalculusDifferential equationsPartial Differential EquationsDynamical Systems & ChaosReal analysisFourier & Harmonic Analysis