Integral Equations By Md Raisinghania Pdf Free Download
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Integral Equations and Boundary Value Problems by M.D.Raisinghania: A Review
Integral equations and boundary value problems are two important topics in mathematics that have applications in various fields of science and engineering. In this article, we will review a book that covers these topics in a comprehensive and rigorous manner. The book is Integral Equations and Boundary Value Problems by M.D.Raisinghania, published by S. Chand Publishing in 2007[^1^].
The book is divided into 14 chapters, each covering a different aspect of integral equations and boundary value problems. The chapters are as follows:
Introduction to Integral Equations
Linear Integral Equations of the First Kind
Linear Integral Equations of the Second Kind
Nonlinear Integral Equations
Boundary Value Problems for Ordinary Differential Equations
Boundary Value Problems for Partial Differential Equations
Fredholm Theory of Integral Equations
Hilbert-Schmidt Theory of Integral Equations
Singular Integral Equations
Integral Equations with Separable Kernels
Volterra Integral Equations
The book is written in a clear and concise style, with plenty of examples and exercises to illustrate the concepts and methods. The book also provides solutions to some of the exercises at the end of each chapter. The book is suitable for undergraduate and postgraduate students of mathematics, as well as for various engineering and professional examinations such as GATE, CSIR NET/JRF, SLET, etc[^1^]. The book is also useful for researchers and practitioners who want to learn more about integral equations and boundary value problems.
The book can be downloaded as a PDF file from various online sources[^2^] [^3^] [^4^], or purchased as an eBook or a print copy from the publisher's website[^1^]. The book has received positive reviews from the readers, who have praised its coverage, clarity, and usefulness[^1^]. The book is one of the best books on integral equations and boundary value problems available in the market.Some of the topics that the book covers in detail are:
The classification and properties of linear and nonlinear integral equations of the first and second kind, and the methods of solving them using direct and indirect techniques.
The definition and properties of integral transforms such as Laplace, Fourier, Mellin, Hankel, and Legendre transforms, and their applications in solving integral equations and boundary value problems.
The concept and construction of Green's functions for various types of differential equations, and their use in solving boundary value problems using the method of variation of parameters.
The formulation and solution of boundary value problems for ordinary and partial differential equations using various methods such as separation of variables, eigenfunction expansion, Sturm-Liouville theory, Fourier series, and finite difference methods.
The theory and applications of Fredholm and Hilbert-Schmidt integral equations, including the existence and uniqueness of solutions, the Fredholm alternative theorem, the Fredholm resolvent kernel, the Hilbert-Schmidt theorem, and the eigenvalue problems.
The definition and properties of singular integral equations, and the methods of solving them using Cauchy principal value integrals, Cauchy type integrals, Hilbert transforms, Riemann-Hilbert problems, and Carleman's method.
The definition and properties of integral equations with separable kernels, and the methods of solving them using Neumann series, Liouville-Neumann series, resolvent kernels, degenerate kernels, and Fredholm determinants.
The definition and properties of Volterra integral equations of the first and second kind, and the methods of solving them using successive approximation, Picard's method, Taylor's series method, Laplace transform method, Abel's integral equation method, and convolution method.
The book also contains a large number of miscellaneous problems that test the reader's understanding and application of the concepts and methods learned in the book. The book is a comprehensive and rigorous treatment of integral equations and boundary value problems that will benefit anyone who wants to learn more about these topics. 061ffe29dd