Analysis

Learn Integral Transforms

What a transform actually is, the region of convergence and Bromwich inversion, the heat semigroup, Poisson summation and Paley-Wiener, the radial family of Hankel, Abel and Radon, exact transforms over finite groups and finite fields, and the time-frequency distributions.

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

What you'll learn

30 lessons in Integral Transforms

What a transform isTwo-sided Laplace and the region of convergenceInverting Laplace: the Bromwich contourThe Gauss-Weierstrass transformThe Poisson summation formulaPaley-Wiener: support and analyticityThe Hankel transformThe Abel transformThe Radon transform and tomographyThe Riesz transformFourier analysis on finite abelian groupsThe number-theoretic transformThe Hartley transformChirp-z and Bluestein's algorithmThe fractional Fourier transformThe Wigner-Ville distributionThe cepstrumThe Stieltjes transformCausality and the Kramers–Kronig relationsThe Cauchy transform and the Plemelj formulasThe Wiener–Hopf techniqueFractional calculusOperational calculusNumerical inversion of the Laplace transformThe singular system and Picard's criterionTikhonov regularisationThe Fokas unified transformFourier–Bessel seriesThe Titchmarsh convolution theoremChoosing a transform
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 Integral Transforms exactly where it's useful.

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