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Applied Mathematical Sciences

An Introduction to the Mathematical Theory of Inverse Problems

Authors: Kirsch, Andreas

  • Offers a good mixture of general results and particular cases
  • Covers electrical impedance tomography and the Factorization Method
  • New edition features new chapters 
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  • ISBN 978-1-4419-8474-6
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Hardcover $99.00
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  • ISBN 978-1-4419-8473-9
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Softcover $99.00
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  • ISBN 978-1-4614-2851-0
  • Free shipping for individuals worldwide
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About this Textbook

This book introduces the reader to the area of inverse problems. The study of inverse problems is of vital interest to many areas of science and technology such as geophysical exploration, system identification, nondestructive testing and ultrasonic tomography.

 

The aim of this book is twofold: in the first part, the reader is exposed to the basic notions and difficulties encountered with ill-posed problems. Basic properties of regularization methods for linear ill-posed problems are studied by means of several simple analytical and numerical examples.

 

The second part of the book presents three special nonlinear inverse problems in detail - the inverse spectral problem, the inverse problem of electrical impedance tomography (EIT), and the inverse scattering problem.

The corresponding direct problems are studied with respect to existence, uniqueness and continuous dependence on parameters. Then some theoretical results as well as numerical procedures for the inverse problems are discussed.

 

In this new edition, the Factorization Method is included as one of the prominent members in this monograph. Since the Factorization Method is particularly simple for the problem of EIT and this field has attracted a lot of attention during the past decade a chapter on EIT has been added in this monograph.

 

The book is highly illustrated and contains many exercises. This together with the choice of material and its presentation in the book are new, thus making it particularly suitable for graduate students in mathematics and engineering.

About the authors

Andreas Kirsch is a Professor in the Department of Mathematics at Karlsruhe Institute of Technology.

Reviews

From the reviews of the second edition:

“Andreas Kirsch successfully wrote this book not only for mathematics students but also physics and engineering students. … I think that this book would work very nicely as a university textbook. … All sections of the books seemed sprinkled with the latest results, showing that there is a surprising amount of current research activity in this area. I recommend this book to anyone interested in inverse problems, and book’s index makes it a valuable reference volume for your book shelf.” (Collin Carbno, The Mathematical Association of America, January, 2012)


Table of contents (6 chapters)

  • Introduction and Basic Concepts

    Kirsch, Andreas

    Pages 1-21

  • Regularization Theory for Equations of the First Kind

    Kirsch, Andreas

    Pages 23-61

  • Regularization by Discretization

    Kirsch, Andreas

    Pages 63-119

  • Inverse Eigenvalue Problems

    Kirsch, Andreas

    Pages 121-165

  • An Inverse Problem in Electrical Impedance Tomography

    Kirsch, Andreas

    Pages 167-189

Buy this book

eBook $74.99
price for USA (gross)
  • ISBN 978-1-4419-8474-6
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $99.00
price for USA
  • ISBN 978-1-4419-8473-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $99.00
price for USA
  • ISBN 978-1-4614-2851-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the eBook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
An Introduction to the Mathematical Theory of Inverse Problems
Authors
Series Title
Applied Mathematical Sciences
Series Volume
120
Copyright
2011
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media, LLC
eBook ISBN
978-1-4419-8474-6
DOI
10.1007/978-1-4419-8474-6
Hardcover ISBN
978-1-4419-8473-9
Softcover ISBN
978-1-4614-2851-0
Series ISSN
0066-5452
Edition Number
2
Number of Pages
XIV, 310
Topics