Week  Topics  Study Materials  Materials 
1 
Integral Equation, Special Kinds of Kernels, Classification of Integral Equation, Iterated Kernels, Resolvent Kernel, Solution of an Integral Equation



2 
Method of Conversion of an Initial Value Problem to a Volterra Integral Equation, Boundary Value Problem and its Conversion to a Fredholm Integral Equation



3 
Eigenvalue and Eigenfunction, Solution of Homogeneous Fredholm Integral Equation of the Second Kind with Separable Kernel



4 
Orthogonality of Two Functions, Orthogonality of Eigenfunctions



5 
Solution of Fredholm Integral Equation of the Second Kind with Separable Kernel



6 
Solution of Fredholm Integral Equation of the Second Kind with Separable Kernel



7 
Symmetric Kernel, Regularity Condition, Inner Product of Two Functions, Orthogonal System of Functions



8 
Fundamental Properties of Eigenvalues and
Eigenfunctions of Symmetric Kernels, Hilbert–Schmidt Theorem, Schmidt’s Solution of Nonhomogeneous Fredholm Integral Equation of the Second Kind



9 
Solution of Fredholm Integral Equation of the Second Kind by Successive Substitutions, Solution of Volterra Integral Equation of the Second Kind by Successive Substitutions



10 
Solution of Fredholm Integral Equation of the Second Kind by Successive Approximations: Iterative Method, Solution of Volterra Integral Equation of the Second Kind by Successive Approximations: Iterative Method



11 
Fredholm’s First Theorem, Evaluating the Resolvent Kernel and Solution of Fredholm Integral Equation of the Second Kind by Using Fredholm’s First Theorem



12 
Fredholm’s Second Fundamental Theorem, Fredholm’s Third Theorem



13 
Singular Integral Equation, Some Important Properties of Laplace Transform, Integral Equations in Special Forms



14 
Application of Laplace Transform to Find the Solutions of Volterra Integral Equation, Fourier Transforms and Their Important Properties, Application of Fourier Transform to Determine the Solution of Singular Integral Equations


