Inverse Problems
Mathematical and Analytical Techniques with Applications to Engineering
Published on 19. November 2010
Book
Paperback/Softback
XX, 442 pages
978-1-4419-3585-4 (ISBN)
Description
Inverse Problems is a monograph which contains a self-contained presentation of the theory of several major inverse problems and the closely related results from the theory of ill-posed problems. The book is aimed at a large audience which include graduate students and researchers in mathematical, physical, and engineering sciences and in the area of numerical analysis.
Reviews / Votes
From the reviews of the first edition:"The author's attention is addressed . to inverse problems for scattering theory . . the reviewer emphasizes the author's effort of simplifying both the results in the mathematical literature and his own ones as well as the effort of unifying the theory of the inverse problems illustrated. Moreover, the proofs of the various propositions are almost always inserted in the book so that we can say the volume is friendly to readers . . Finally, the proofs are well written . ." (Alfredo Lorenzi, Zentralblatt MATH, Vol. 1083, 2006)"This book is devoted to the investigation of inverse problems for PDEs, in particular, to the theory of inverse spectral problems and inverse scattering problems. . Graduate students and researchers will find in this work extensive reference material including a collection of relevant classical results as well as several new developments in the area of inverse and ill-posed problems." (Antonio C. G. Leitão, Mathematical Reviews, Issue 2012 k)More details
Series
Edition
Softcover of orig. ed. 2005
Language
English
Place of publication
New York
United States
Target group
Professional and scholarly
Research
Illustrations
XX, 442 p.
Dimensions
Height: 235 mm
Width: 155 mm
Thickness: 25 mm
Weight
698 gr
ISBN-13
978-1-4419-3585-4 (9781441935854)
DOI
10.1007/b100958
Schweitzer Classification
Other editions
Additional editions
Alexander G. Ramm
Inverse Problems
Mathematical and Analytical Techniques with Applications to Engineering
Book
12/2004
Springer
€160.49
Shipment within 5-7 days
Person
Alexander G. Ramm, Ph.D., was born in Russia, immigrated to the U.S. in 1979, and is a U.S. citizen. He is Professor of Mathematics with broad interests in analysis, scattering theory, inverse problems, theoretical physics, engineering, signal estimation, tomography, theoretical numerical analysis, and applied mathematics. He is an author of 690 research papers, 16 monographs, and an editor of 3 books. He has lectured in many universities throughout the world, presented approximately 150 invited and plenary talks at various conferences, and has supervised 11 Ph.D. students. He was Fulbright Research Professor in Israel and in Ukraine, distinguished visiting professor in Mexico and Egypt, Mercator professor, invited plenary speaker at the 7th PACOM, won the Khwarizmi international award, and received other honors. Recently he solved inverse scattering problems with non-over-determined data and the many-body wave-scattering problem when the scatterers are small particles of an arbitraryshape; Dr. Ramm used this theory to give a recipe for creating materials with a desired refraction coefficient, gave a solution to the refined Pompeiu problem and proved the refined Schiffers conjecture.
Content
Methods of Solving Ill-Posed Problems.- One-Dimensional Inverse Scattering and Spectral Problems.- Inverse Obstacle Scattering.- Stability of the Solutions to 3D Inverse Scattering Problems with Fixed-Energy Data.- Non-Uniqueness and Uniqueness Results.- Inverse Problems of Potential Theory and Other Inverse Source Problems.- Non-Overdetermined Inverse Problems.- Low-Frequency Inversion.- Wave Scattering by Small Bodies of Arbitrary Shapes.- The Pompeiu Problem.