Introduction to Integral Equations, classification: Volterra and Fredholm integral equations,
First kind, second kind, Relation between differential and integral equations, Conversion of initial and boundary value problems into integral equations

Fredholm Integral Equations, Fredholm equations of the second kind, terative method (successive approximations)
Volterra integral equations of the first and second kinds, Successive approximation and resolvent kernel for Volterra equations

Laplace transform: definition, properties, Inverse Laplace transform,
Applications to solving ordinary differential equations Convolution theorem, Integral equations solved by Laplace transforms

Fourier transform and its properties, Fourier sine and cosine transforms, Applications of Fourier transforms in solving PDEs and integral equations

Other Integral Transforms, Hankel Transform, Mellin Transform, Z-Transform (brief introduction), Applications to simple models in physics and engineering

Understand the formulation and classification of integral equations.

Learn methods to solve various types of integral equations.

Study important integral transforms (Fourier, Laplace, Z-Transform, Hankel, etc.) and their applications.

Apply transforms to solve differential and integral equations.

Classify and analyze different types of integral equations (Fredholm, Volterra, first kind, second kind, homogeneous, nonhomogeneous).

Demonstrate problem-solving skills in both theoretical and application-oriented contexts involving integral transforms and equations.

A.M. Davie, Integral Equations and Their Applications, Wit Press

Sneddon, The Use of Integral Transforms, McGraw-Hill Inc

A.J. Jerri, Introduction to Integral Equations with Applications, Wiley–Blackwell

Debnath and Bhatta , Integral Transforms and Their Applications, Chapman and Hall/CRC

SIAM Journal on Mathematical Analysis (Society for Industrial and Applied Mathematics)