Course Details

Classification of Integral Equations, various examples, Abel's problem, 2nd order ordinary differential equations and Integral Equations, Initial and boundary value problems, singular boundary value problems.
Integral Equations of second kind: degenerate kernels, Neumann series.
Compact self-adjoint operators: Structure theorem, spectrum, Applications to integral equations, positive operators and Integral equations arising from Sturm-Liouville theory.
Approximate methods for eigenvalues and eigenvectors of self-adjoint operators, Approximation of integral equations based on variational principles.
Singular integral equations: introduction, solution methods, applications.

Course References:

David Porter & David S.G. Stirling, Integral Equations: A Practical Treatment, from Spectral Theory to Applications, Cambridge texts in Applied Mathematics, 1990.