Linear Integral Equations

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Springer Science & Business Media, Mar 26, 1999 - Mathematics - 367 pages
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In the ten years since the first edition of this book appeared, integral equations and integral operators have revealed more of their mathematical beauty and power to me. Therefore, I am pleased to have the opportunity to share some of these new insights with the readers of this book. As in the first edition, the main motivation is to present the fundamental theory of integral equations, some of their main applications, and the basic concepts of their numerical solution in a single volume. This is done from my own perspective of integral equations; I have made no attempt to include all of the recent developments. In addition to making corrections and adjustments throughout the text and updating the references, the following topics have been added: In Sec tion 4.3 the presentation of the Fredholm alternative in dual systems has been slightly simplified and in Section 5.3 the short presentation on the index of operators has been extended. The treatment of boundary value problems in potential theory now includes proofs of the jump relations for single-and double-layer potentials in Section 6.3 and the solution of the Dirichlet problem for the exterior of an arc in two dimensions (Section 7.6). The numerical analysis of the boundary integral equations in Sobolev space settings has been extended for both integral equations of the first kind in Section 13.4 and integral equations of the second kind in Section 12.4.
 

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Contents

III
1
IV
2
V
5
VI
6
VII
9
VIII
11
IX
13
X
15
LV
175
LVI
177
LVII
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LVIII
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LIX
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LX
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LXI
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LXII
195

XI
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XIII
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XXX
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XLI
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XLIV
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XLIX
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L
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LI
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LII
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LIII
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LIV
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LXIII
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LXIV
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LXV
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LXVI
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LXXX
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LXXXIV
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LXXXVI
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LXXXIX
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XC
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XCI
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XCII
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XCIV
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XCV
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XCVI
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XCVII
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XCVIII
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XCIX
328
C
333
CI
341
CII
345
CIII
347
CIV
361
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About the author (1999)

Rainer Kress is a Full Professor of Numerical and Applied Mathematics at the University of Gottingen. He has been a member of the Gottingen Academy of Sciences since 1995 and Professor Emeritus since 2010. He is the author or coauthor of five books.

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