UID:
almafu_9960119323802883
Umfang:
1 online resource (xi, 372 pages) :
,
digital, PDF file(s).
Ausgabe:
1st ed.
ISBN:
1-139-17202-6
Serie:
Cambridge texts in applied mathematics ; 5
Inhalt:
This book gives a rigorous and practical treatment of integral equations. These are significant because they occur in many problems in mathematics, physics and engineering and they offer a powerful (sometimes the only) technique for solving these problems. The book aims to tackle the solution of integral equations using a blend of abstract 'structural' results and more direct, down-to-earth mathematics. The interplay between these two approaches is a central feature of the text and it allows a thorough account to be given of many of the types of integral equation which arise in application areas. Since it is not always possible to find explicit solutions of the problems posed, much attention is devoted to obtaining qualitative information and approximations to the solutions, with the associated error estimates. This treatment is intended for final year mathematics undergraduates, postgraduates and research workers in application areas such as numerical analysis and fluid mechanics.
Anmerkung:
Title from publisher's bibliographic system (viewed on 05 Oct 2015).
,
Cover -- Frontmatter -- Contents -- Preface -- Classification and examples of integral equations -- 1.1 Introduction -- 1.2 Classification of integral equations -- 1.3 A collection of examples -- Problems -- Second order ordinary differential equations and integral equations -- 2.1 Introduction -- 2.2 Differential equation theory -- 2.3 Initial value problems -- 2.4 Boundary value problems -- 2.5 Singular boundary value problems -- Problems -- Integral equations of the second kind -- 3.1 Introduction -- 3.2 Degenerate kernels -- 3.3 A different approach -- 3.4 Operators -- 3.5 The Neumann series -- Problems -- Compact operators -- 4.1 Introduction -- 4.2 General properties -- 4.3 Adjoint operators -- 4.4 The Spectral Theorem -- 4.5 Applications to integral equations -- Problems -- The spectrum of a compact self-adjoint operator -- 5.1 Introduction -- 5.2 The Rayleigh quotient -- 5.3 Eigenvalue inequalities -- Problems -- Positive operators -- 6.1 Introduction -- 6.2 General properties -- 6.3 The Sturm-Liouville problem revisited -- Problems -- Approximation methods for eigenvalues and eigenvectors of self-adjoint operators -- 7.1 Introduction -- 7.2 Variational principles -- 7.3 Kellogg's method -- 7.4 The trace method -- 7.5 Comparison and related methods -- Problems -- Approximation methods for inhomogeneous integral equations -- 8.1 Introduction -- 8.2 Well-posed problems -- 8.3 Methods based on variational principles -- 8.4 Galerkin's method and related topics -- Problems -- Some singular integral equations -- 9.1 Introduction -- 9.2 Volterra operators with weakly singular kernels -- 9.3 First kind Fredholm equations -- 9.4 Fourier transforms and the Hilbert transform -- 9.5 Equations with Cauchy singular kernels -- 9.6 Fourier transform methods -- 9.7 An example -- Problems -- Appendix A: Functional analysis.
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Appendix B: Measure theory and integration -- Appendix C: Miscellaneous results -- Notation Index -- Index.
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English
Weitere Ausg.:
ISBN 0-521-33742-9
Weitere Ausg.:
ISBN 0-521-33151-X
Sprache:
Englisch
URL:
https://doi.org/10.1017/CBO9781139172028
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