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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.
- Sales Rank: #1896250 in Books
- Brand: Brand: Cmbrdgr U P
- Published on: 1990-09-28
- Original language: English
- Number of items: 1
- Dimensions: 8.98" h x .87" w x 5.98" l, 1.12 pounds
- Binding: Paperback
- 388 pages
- Used Book in Good Condition
Review
"...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
About the Author
Previous books by this editor: Acta Numerica 1992 - 2003 (Vols 1 - 12); as author: First Course in the Numerical Analysis of Differential Equations (0521 553768), Approximation Theory and Optimization (0521 581907).
Most helpful customer reviews
0 of 0 people found the following review helpful.
Excellent
By Rellek
Lots of exposition in this book. The beginning 3 chapters are very nice and clearly written, although it seems like the techniques of chapters 2 and 3 are essentially nulled after the introduction to the Spectral Theorem. At that point, he goes on to derive the general solution of any self-adjoint kernel in about half a page and give a general form to the Fredholm alternative as well.
After that, the book applies the techniques of spectral analysis for a huge host of applications. Another thing I enjoyed was some of the bonus information contained in the exercises. Although it is cumbersome to do every possible exercise (and unrealistic) I still suggest reading through all of the exercises. A lot of them will bring up pretty interesting applications in areas such and fluid dynamics and elastic theory. Initially I was weary to buy this book because there were no reviews up at the time, but I am very happy I ended up buying this book.
One more thing I would add is that the book technically does not require too much functional analysis, but I imagine that it would be incredibly tiring and possibly overwhelming to read through the wall of definitions introduced to try to get as much Hilbert space theory out there as possible. Integral equations are difficult on their own, but having to wrap your head around the definitions and theorems of Hilbert spaces would be a distraction from the material the author really wants to get across.
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