This book gives a rigorous and practical treatment of integral equations and 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 that arise, particularly in numerical analysis and fluid mechanics. Because it is not always possible to find explicit solutions to the problems posed, much attention is devoted to obtaining qualitative information and approximations and the associated error estimates.
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"...Porter and Stirling provide a precise and practical methodology for solving integral equations." Directions
"This book may be successfully used by graduate students and by any person working in the field of applied mathematics; it gives a very good treatment of all the subjects involved." A. Corduneanu, Mathematical Reviews
"...this is not a treatise but an excellent book from which to learn the subject, and therefore at least as valuable for the undergraduate library. Its level is just right for the beginning graduate student or the highly motivated senior." Choice
"...a very good book for students who want to become familiar with the basic theory of linear integral equations." Harry Hochstadt, SIAM Review
"...an excellent way to gain acquaintance with integral equations... Jet Wimp, The Mathematical Intelligencer
"This book may be successfully used by graduate students and by any person working in the field of applied mathematics; it gives a very good treatment of all the subjects involved." A. Corduneanu, Mathematical Reviews
"...this is not a treatise but an excellent book from which to learn the subject, and therefore at least as valuable for the undergraduate library. Its level is just right for the beginning graduate student or the highly motivated senior." Choice
"...a very good book for students who want to become familiar with the basic theory of linear integral equations." Harry Hochstadt, SIAM Review
"...an excellent way to gain acquaintance with integral equations... Jet Wimp, The Mathematical Intelligencer
Book Description
Blending abstract structural results and more direct, practical mathematics, this exacting study provides a thorough account of many types of integral equations, particularly in numerical analysis and fluid mechanics.
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Inside This Book
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First Sentence:
The mechanics problem of calculating the time a particle takes to slide under gravity down a given smooth curve, from any point on the curve to its lower end, leads to an exercise in integration. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
simplifying operator, dual extremum principles, constant test functions, complete orthonormal sequence, bounded linear map, hermitian kernel, many negative eigenvalues, second kind equation, stationary principle, corresponding integral operator, first kind equation, one positive eigenvalue, degenerate kernel, eigenvalue sequence, positive operator, spectral theorem, singular kernels, corresponding homogeneous equation, operator arising, spectral expansion, unique continuous solution, integrable solution, many eigenvalues, negative operator, compact operator Key Phrases - Capitalized Phrases (CAPs): (learn more)
Fredholm Alternative, Mercer's Theorem, Proof Let, Dini's Theorem, Fubini's Theorem, Proof Suppose, Proof Choose, Proof First New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
The mechanics problem of calculating the time a particle takes to slide under gravity down a given smooth curve, from any point on the curve to its lower end, leads to an exercise in integration. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
simplifying operator, dual extremum principles, constant test functions, complete orthonormal sequence, bounded linear map, hermitian kernel, many negative eigenvalues, second kind equation, stationary principle, corresponding integral operator, first kind equation, one positive eigenvalue, degenerate kernel, eigenvalue sequence, positive operator, spectral theorem, singular kernels, corresponding homogeneous equation, operator arising, spectral expansion, unique continuous solution, integrable solution, many eigenvalues, negative operator, compact operator Key Phrases - Capitalized Phrases (CAPs): (learn more)
Fredholm Alternative, Mercer's Theorem, Proof Let, Dini's Theorem, Fubini's Theorem, Proof Suppose, Proof Choose, Proof First New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 5
books:
3
books
cite this book:
- Integral Equations (Wiley Classics Library) by Harry Hochstadt in Front Matter
- Integral Equations (Cambridge Tracts in Mathematics) by F. Smithies in Front Matter
- An Introduction to Hilbert Space (Cambridge Mathematical Textbooks) by N. Young in Back Matter
- Singular Integral Equations by N.I. Muskhelishvili on page 345
- Introduction to Classical Real Analysis (Wadsworth & Brooks/Cole Mathematics Series) by Karl R. Stromberg in Back Matter
- Handbook of Integral Equations by Andrei D. Polyanin in Back Matter
- The Numerical Solution of Integral Equations of the Second Kind (Cambridge Monographs on Applied and Computational Mathematics) by Kendall E. Atkinson in Back Matter
- Solitons, Nonlinear Evolution Equations and Inverse Scattering (London Mathematical Society Lecture Note Series) by M. A. Ablowitz in Back Matter
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