Integral Equations and Transforms

Department: 
MATH
Course Number: 
6583
Hours - Lecture: 
3
Hours - Lab: 
0
Hours - Recitation: 
0
Hours - Total Credit: 
3
Typical Scheduling: 
Every odd summer

Volterra and Fredholm linear integral equations, relation to differential equations, solution methods, Fourier, Laplace and Mellin transforms, applications to boundary value problems and integral equations.

Prerequisites: 
Course Text: 

No text

Topic Outline: 
  • Hilbert spaces, Fredholm alternative
  • Fixed point theorems
  • Volterra equations of the first and second kind
  • Fredholm equations with L kernels
  • Compact operators
  • Integral operators with kernels of finite rank
  • Self-adjoint integral operators
  • Spectrum of positive definite integral operators
  • Applications to ordinary differential equations
  • Green's functions
  • Sturm-Liouville theory
  • Fourier transform
  • Laplace transform
  • Mellin transforms
  • Application to partial differential equations