Research Catalog

Title

Inverse problems : mathematical and analytical techniques with applications to engineering / Alexander G. Ramm.

Author

Ramm, A. G. (Alexander G.)

Publication

New York : Springer, 2004.

Items in the Library & Off-site

Holdings

Details

Description

xx, 442 pages; 25 cm.

Summary

"Inverse problems are problems that consist of finding an unknown property of an object or medium through the observation of a response from this object or medium to a probing signal. Thus, the theory of inverse problems yields a theoretical basis for remote sensing and non-destructive evaluation. For example, if an acoustic plane wave is scattered by an obstacle, and one observes the scattered field from the obstacle, or in some exterior region, then the inverse problem is to find the shape and material properties of the obstacle. Such problems are important in the identification of flying objects (airplanes, missiles etc.), objects immersed in water (submarines, fish), and in many other situations." "This book presents the theory of inverse spectral and scattering problems and of many other inverse problems for differential equations in an essentially self-contained way. An outline of the theory of ill-posed problems is given because inverse problems are often ill-posed. There are many novel features in this book. The concept of property C, introduced by the author, is developed and used as the basic tool for a study of a wide variety of one- and multi-dimensional inverse problems, making the theory easier and shorter."--BOOK JACKET.

Series Statement

Mathematical and analytical techniques with applications to engineering

Uniform Title

Mathematical and analytical techniques with applications to engineering.

Subjects

• Engineering mathematics
• Inverse problems (Differential equations)

Bibliography (note)

• Includes bibliographical references and index.

Contents

1. Introduction -- 2. Methods of solving ill-posed problems -- 3. One-dimensional inverse scattering and spectral problems -- 4. Inverse obstacle scattering -- 5. Stability of the solutions to 3D inverse scattering problems with fixed-energy data -- 6. Non-uniqueness and uniqueness results -- 7. Inverse problems of potential theory and other inverse source problems -- 8. Non-overdetermined inverse problems -- 9. Low-frequency inversion -- 10. Wave scattering by small bodies of arbitrary shapes -- 11. The Pompeiu problem.

ISBN

0387231951

LCCN

2004057800

OCLC

• 506127682
• ocn506127682
• SCSB-5203829

Owning Institutions

Columbia University Libraries