Ebook: Linear Integral Equations

This book resulted from the author's fascination with the mathematical beauty of integral equations. It is an attempt to combine theory, applications, and numerical methods, and cover each of these fields with the same weight. In order to make the book accessible to mathematicians, physicists, and engineers, the author has made the work as self-contained as possible, by requiring only a solid foundation in differential and integral calculus. The functional analysis which is necessary for an adequate treatment of the theory and the numerical solution of integral equations is developed within the book. Problems are included at the end of each chapter. For the second edition, in addition to corrections and adjustments throughout the text, as well as an updated reference section, new topics have been added.

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Content:
Front Matter....Pages i-xiv
Normed Spaces....Pages 1-14
Bounded and Compact Operators....Pages 15-27
Riesz Theory....Pages 28-38
Dual Systems and Fredholm Alternative....Pages 39-54
Regularization in Dual Systems....Pages 55-66
Potential Theory....Pages 67-93
Singular Integral Equations....Pages 94-124
Sobolev Spaces....Pages 125-151
The Heat Equation....Pages 152-162
Operator Approximations....Pages 163-176
Degenerate Kernel Approximation....Pages 177-196
Quadrature Methods....Pages 197-217
Projection Methods....Pages 218-246
Iterative Solution and Stability....Pages 247-264
Equations of the First Kind....Pages 265-289
Tikhonov Regularization....Pages 290-307
Regularization by Discretization....Pages 308-319
Inverse Boundary Value Problems....Pages 320-346
Back Matter....Pages 347-367

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Content:
Front Matter....Pages i-xiv
Normed Spaces....Pages 1-14
Bounded and Compact Operators....Pages 15-27
Riesz Theory....Pages 28-38
Dual Systems and Fredholm Alternative....Pages 39-54
Regularization in Dual Systems....Pages 55-66
Potential Theory....Pages 67-93
Singular Integral Equations....Pages 94-124
Sobolev Spaces....Pages 125-151
The Heat Equation....Pages 152-162
Operator Approximations....Pages 163-176
Degenerate Kernel Approximation....Pages 177-196
Quadrature Methods....Pages 197-217
Projection Methods....Pages 218-246
Iterative Solution and Stability....Pages 247-264
Equations of the First Kind....Pages 265-289
Tikhonov Regularization....Pages 290-307
Regularization by Discretization....Pages 308-319
Inverse Boundary Value Problems....Pages 320-346
Back Matter....Pages 347-367
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