Inverse Problems for Partial Differential Equations (Applied Mathematical Sciences) [Hardcover]

Victor Isakov (Author)

Book Description

Publication Date: November 20, 1997 | ISBN-10: 0387982566 | ISBN-13: 978-0387982564 | Edition: 1

This book is a comprehensive description of the current theoretical and numerical aspects of inverse problems in partial differential equations. Applications include recovery of inclusions from anomalies of their gravity fields, reconstruction of the interior of the human body from exterior electrical, ultrasonic, and magnetic measurement. The reconstruction of the interior structural parameters of machines and of the underground are also discussed together with further scientific and engineering applications. By presenting this data in a readable and informative manner, the book introduces both scientific and engineering researchers and graduate students to significant work done in this area in recent years, relating it to broader themes in mathematical analysis.

Editorial Reviews

Review

From the reviews of the second edition: "The first edition of this excellent book appeared in 1998 and became a standard reference for everyone interested in analysis and numerics of inverse problems in partial differential equations. … The second edition is considerably expanded and reflects important recent developments in the field … . Some of the research problems from the first edition have been solved … ." (Johannes Elschner, Zentralblatt MATH, Vol. 1092 (18), 2006) --This text refers to an alternate Hardcover edition.

From the Back Cover

The topic of the inverse problems is of substantial and rapidly growing interest for many scientists and engineers. The second edition covers most important recent developments in the field of inverse problems, describing theoretical and computational methods, and emphasizing new ideas and techniques. It also reflects new changes since the first edition, including some corrections. This edition is considerably expanded, with some concepts such as pseudo-convexity, and proofs simplified. New material is added to reflect recent progress in theory of inverse problems. This book is intended for mathematicians working with partial differential equations and their applications, and physicists, geophysicists and engineers involved with experiments in nondestructive evaluation, seismic exploration, remote sensing and tomography. --This text refers to an alternate Hardcover edition.

Product Details

• Hardcover: 284 pages
• Publisher: Springer; 1 edition (November 20, 1997)
• Language: English
• ISBN-10: 0387982566
• ISBN-13: 978-0387982564
• Product Dimensions: 9.5 x 6.3 x 0.8 inches
• Shipping Weight: 1.2 pounds
• Average Customer Review: 3.0 out of 5 stars  See all reviews (2 customer reviews)
• Amazon Best Sellers Rank: #5,162,395 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

6 of 6 people found the following review helpful:

4.0 out of 5 stars finding interiors of objects, July 28, 2006

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W Boudville (Terra, Sol 3) - See all my reviews
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This review is from: Inverse Problems for Partial Differential Equations (Applied Mathematical Sciences) (Hardcover)

Isakov describes various ways to solve the inverse problem. In simplest form, one might have, say, Poisson's equation. But whereas the conventional problem is to find the potential, given the source, the inverse problem involves knowing the potential, or its gradient, and having to find the source.

The book draws together many results which thus far have mostly resided in maths journals. Isakov explains common themes to these research papers. Plus, and more importantly to some readers, he also gives the practical contexts in which the problems might arise. Such include determining the inside of a portion of a person's body, given various external measurements. Or finding structural data of a machine from external probes. The basic situation is that we are often outside something, and cannot physically go inside that object in a non-destructive manner.

The level of maths is broadly accessible to a reader with an undergrad major in maths or physics.

5 of 7 people found the following review helpful:

2.0 out of 5 stars Unreadable, April 20, 2007

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A Reader "MSA" (Los Angeles, CA, USA) - See all my reviews

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This review is from: Inverse Problems for Partial Differential Equations (Applied Mathematical Sciences) (Hardcover)

One would think that Springer-Verlag would be able to afford an editor

for the second edition of a book they charge $80 for. Apparently not.

This book is so full of typos, misspellings, and bad grammar that it is

essentially unreadable. The completely stochastic sprinkling of "the"'s

and "a"'s throughout the text (a particular grammar difficulty of native

Russian speakers) suggests that no editor has ever read this manuscript.

On the positive side, the mathematical expertise of the author in PDE

theory is not in question, and the book does contain useful technical

information on inverse problems once you strip away the typos and

decipher the grammar.