Alexey N. Karapetyants is professor of the Institute of Mathematics, Mechanics and Computer Sciences and director of Regional Mathematical Center at the Southern Federal University, Rostov-on-Don, Russia. His research interests include operator theory, mathematical physics, harmonic analysis: real and complex variable methods, and functional analysis.Vladislav V. Kravchenko is a researcher in the Department of Mathematics of Center for Research and Advanced Studies of the National Polytechnic Institute, Campus Queretaro, Mexico. His research interests include mathematical physics, differential equations, complex and hypercomplex analysis, spectral theory, and inverse problems.

• Introduction.- Classification of PDEs.- Models of mathematical physics.- Boundary value problems.- Cauchy problem for hyperbolic equations.- Fourier method for the wave equation.- Sturm-Liouville problems.- Boundary value problems for the heat equation.- Harmonic functions and their properties.- Boundary value problems for the Laplace equation.- Potential theory.- Elements of theory of integral equations.- Solution of boundary value problems for the Laplace equation.- Helmholtz equation.- Method of non-orthogonal series.- Bergman kernel approach.- Bibliography.- Index.

Alexey N. Karapetyants is professor of the Institute of Mathematics, Mechanics and Computer Sciences and director of Regional Mathematical Center at the Southern Federal University, Rostov-on-Don, Russia. His research interests include operator theory, mathematical physics, harmonic analysis: real and complex variable methods, and functional analysis.Vladislav V. Kravchenko is a researcher in the Department of Mathematics of Center for Research and Advanced Studies of the National Polytechnic Institute, Campus Queretaro, Mexico. His research interests include mathematical physics, differential equations, complex and hypercomplex analysis, spectral theory, and inverse problems.

• Introduction.- Classification of PDEs.- Models of mathematical physics.- Boundary value problems.- Cauchy problem for hyperbolic equations.- Fourier method for the wave equation.- Sturm-Liouville problems.- Boundary value problems for the heat equation.- Harmonic functions and their properties.- Boundary value problems for the Laplace equation.- Potential theory.- Elements of theory of integral equations.- Solution of boundary value problems for the Laplace equation.- Helmholtz equation.- Method of non-orthogonal series.- Bergman kernel approach.- Bibliography.- Index.

Alexey N. Karapetyants is professor of the Institute of Mathematics, Mechanics and Computer Sciences and director of Regional Mathematical Center at the Southern Federal University, Rostov-on-Don, Russia. His research interests include operator theory, mathematical physics, harmonic analysis: real and complex variable methods, and functional analysis.Vladislav V. Kravchenko is a researcher in the Department of Mathematics of Center for Research and Advanced Studies of the National Polytechnic Institute, Campus Queretaro, Mexico. His research interests include mathematical physics, differential equations, complex and hypercomplex analysis, spectral theory, and inverse problems.

• Introduction.- Classification of PDEs.- Models of mathematical physics.- Boundary value problems.- Cauchy problem for hyperbolic equations.- Fourier method for the wave equation.- Sturm-Liouville problems.- Boundary value problems for the heat equation.- Harmonic functions and their properties.- Boundary value problems for the Laplace equation.- Potential theory.- Elements of theory of integral equations.- Solution of boundary value problems for the Laplace equation.- Helmholtz equation.- Method of non-orthogonal series.- Bergman kernel approach.- Bibliography.- Index.