INTEGRAL
EQUATIONS
Theory of Fredholm and Volterra integral
equations on the space of continuous functions. Qualitative theory of integral
equations, which derive from general fixed point theorems. Solution of integral
equations, systems of integral equations and integro-differential equations of
Volterra type and of convolution type via the Laplcace transform. Methods of
solutions of Fredholm integral equations of 2nd type (method of
recursive kernels, Fredholm's method). Characteristic numbers and
eigenfunctions of Fredholm integral equations (degenerate kernels, kernels
which are Green functions of a homogeneous Sturm-Liouville problem). Fredholms'
theorems. Hilbert-Schmidt Theorem (symmetric kernels). Applications (transformation
of initial value problems to Volterra integral equations, transformation of
boundary value problems to Fredholm integral equations).