Analysis

Learn Numerical methods

Computing math approximately, for when symbolic answers don't exist or aren't enough.

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

What you'll learn

39 lessons in Numerical methods

Newton's method for rootsBisection: the reliable root-finderNumerical integrationFloating point & errorLinear systems numericsInterpolationStability vs accuracyIterative linear solversEigenvalue algorithmsFast Fourier Transform (FFT)Sparse matrix methodsKrylov subspace methodsMultigrid methodsFinite element method (FEM)Monte Carlo methodsProof: bisection convergesProof: Newton converges quadraticallyFloating point: machine epsilonStiff ODE solversNumerical optimizationGaussian quadratureRunge–Kutta methods & order of accuracyConditioning & the condition numberFixed-point iteration & contractionCubic spline interpolationNumerical differentiation & finite differencesRichardson extrapolationLeast squares & the normal equationsSingular value decomposition & low-rankAutomatic differentiationSpectral & pseudospectral methodsAdaptive quadrature & step controlPreconditioning for iterative solversCancellation & stable summationRunge's phenomenon & node choiceMethod of lines for PDEsNewton's method for systemsBoundary value problems: shooting & finite differencesComputing the matrix exponential
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 Numerical methods exactly where it's useful.

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