The bookUnit 3 · Linear Integral Equations67 / 83

Separable kernels and resolvent kernels

Why this is asked: Separable kernels turn integral equations into matrix problems. The resolvent kernel sums the Neumann series and gives the solution in closed form.

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Separable kernels turn an integral equation into linear algebrainteractive

A degenerate kernel reduces the whole problem to a finite system — worked.

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The eigenvalue $\lambda$ for which $y(x) = \lambda\int_{0}^{1} x t y(t)$ dt has a non-trivial solution is

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Open this in the full syllabus view · Unit 3