Finding a formula is only part of solving an integral equation. You also need to know whether a solution exists, whether it's unique and how much you can trust a numerical approximation.Integral Equations: An Interactive Course in Theory, Methods, and Computation by Gaurav Tiwari connects those questions throughout the course. You begin with accumulation and simple feedback, then work toward spectral theory and the recovery of signals from blurred, noisy data. The same 6 benchmark problems return throughout the book, so each new method meets an equation you've already learned to recognize.Inside the book: Fredholm and Volterra equations, with a decision map for choosing a method.Separable kernels, successive approximations, resolvent kernels and transform methods.Green's functions, the Fredholm alternative and the spectral theory of symmetric kernels.Abel equations, nonlinear integral equations and Cauchy principal values.Numerical quadrature, collocation, Galerkin methods and regularization, with attention to error and stability.24 chapters and 321 exercises, with a hint or answer for every exercise and selected full solutions in this volume.The larger worked examples follow a practical sequence: predict what should happen, work through the calculation, check it in the original equation and change an assumption to see what survives. Optional Python examples connect the analysis to computation. Full solutions to every exercise belong to the companion volume.This course suits undergraduate study or self-study after calculus, ordinary differential equations and basic linear algebra. It introduces the functional analysis as needed, so you don't need a prior course in it. Programming is optional for the core text.
