Fredholm theory, Hilbert-Schmidt theory, Schmidt’s solution of non-homogeneous integral equations
Course Material
- Integral equation: definition and basics: Book
- classification of integral equations
- formulation of boundary value problems and initial value problems from integral equations and converse
- Leibnitz formula of differencitation
- Conversion of multiple integrals into single integrals, Relationship between differential equation and Volterra integral equation
- Kinds of Volterra intrgral equations
- Kinds of Fredholm intrgral equations
- Solution of Volterra intrgral equation of second kind
- Mid Term Exam
- Solution of Volterra intrgral equation of first kind, Neumann series
- Greens function construction, Eigenvalues and eigenvectors
- Variations of parameter
- Orthogonal series representation of Green’s function
- Fredholm Integreal equations with degenerate kernels
- Fredholm theory, Hilbert-Schmidt theory, Schmidt’s solution of non-homogeneous integral equations
- Iterated functions: Quadrature methods and Least square methods
- Regularization and filtering techniques
- Final Term Exam
- Chapters 18
- Department Mathematics(SCB)
- Teacher
Ms. Ammara Nazar
