NEXT

• 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