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This comprehensive textbook on linear integral equations and integral transforms is aimed at senior undergraduate and graduate students of mathematics and physics. The book covers a range of topics including Volterra and Fredholm integral equations, the second kind of integral equations with symmetric kernels, eigenvalues and eigen functions, the Hilbert–Schmidt theorem, and the solution of Abel integral equations by using an elementary method. In addition, the book covers various integral transforms including Fourier, Laplace, Mellin, Hankel, and Z-transforms. One of the unique features of the book is a general method for the construction of various integral transforms and their inverses, which is based on the properties of delta function representation in terms of Green’s function of a Sturm–Liouville type ordinary differential equation and its applications to physical problems. The book is divided into two parts: integral equations and integral transforms. Each chapter is supplemented with numerous illustrative examples to aid in understanding. The clear and concise presentation of the topics covered makes this book an ideal resource for students, researchers, and professionals interested in the theory and application of linear integral equations and integral transforms.

Integral equations. --- Mathematical analysis. --- Integral Equations. --- Integral Transforms and Operational Calculus. --- Equacions integrals --- Transformacions integrals

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Numerical analysis. --- Integral equations. --- Equations, Integral --- Functional equations --- Functional analysis --- Mathematical analysis --- Equacions integrals --- Equacions funcionals --- Càlcul operacional --- Equacions de Fredholm --- Equacions de Volterra --- Equacions integrals estocàstiques --- Transformacions integrals --- Anàlisi funcional

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Boundary element methods --- Integral equations. --- Data processing. --- Equations, Integral --- Functional equations --- Functional analysis --- BEM (Engineering analysis) --- BIE analysis --- BIE methods --- Boundary element analysis --- Boundary elements methods --- Boundary integral equation analysis --- Boundary integral equation methods --- Boundary integral methods --- Numerical analysis --- Equacions integrals --- Equacions funcionals --- Càlcul operacional --- Equacions de Fredholm --- Equacions de Volterra --- Equacions integrals estocàstiques --- Transformacions integrals --- Anàlisi funcional

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Problemes de contorn --- Integrals singulars --- Operadors integrals --- Transformacions integrals --- Problemes de valor límit --- Equacions diferencials --- Física matemàtica --- Funcions de variables complexes --- Dispersió (Matemàtica) --- Equacions de Von Kármán --- Problema de Dirichlet --- Problema de Neumann --- Problemes de Riemann-Hilbert --- Problemes de valor inicial --- Boundary value problems. --- Singular integrals. --- Integrals, Singular --- Integral operators --- Integral transforms --- Boundary conditions (Differential equations) --- Differential equations --- Functions of complex variables --- Mathematical physics --- Initial value problems

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Boundary element methods. --- Integral equations. --- Equations, Integral --- Functional equations --- Functional analysis --- BEM (Engineering analysis) --- BIE analysis --- BIE methods --- Boundary element analysis --- Boundary elements methods --- Boundary integral equation analysis --- Boundary integral equation methods --- Boundary integral methods --- Numerical analysis --- Problemes de contorn --- Equacions integrals --- Equacions funcionals --- Càlcul operacional --- Equacions integrals estocàstiques --- Transformacions integrals --- Anàlisi funcional --- Problemes de valor límit --- Equacions diferencials --- Física matemàtica --- Funcions de variables complexes --- Dispersió (Matemàtica) --- Equacions de Von Karman --- Problema de Dirichlet --- Problema de Neumann --- Problemes de Riemann-Hilbert --- Problemes de valor inicial --- Equacions de Volterra --- Equacions de Fredholm --- Equacions de Von Kármán