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Inverse Problems in the Mathematical Sciences (Vieweg Mathematics for Scientists and Engineers) 🔍
Professor Charles W. Groetsch (auth.) Vieweg+Teubner Verlag : Imprint: Vieweg+Teubner Verlag, 1st ed. 1993, Wiesbaden, 1993
英语 [en] · PDF · 5.9MB · 1993 · 📘 非小说类图书 · 🚀/duxiu/lgli/lgrs/nexusstc/scihub/zlib · Save
描述
Classical applied mathematics is dominated by the Laplacian paradigm of known causes evolving continuously into uniquely determined effects. The classical direct problem is then to find the unique effect of a given cause by using the appropriate law of evolution. It is therefore no surprise that traditional teaching in mathema tics and the natural sciences emphasizes the point of view that problems have a solution, this solution is unique, and the solution is insensitive to small changes in the problem. Such problems are called well-posed and they typically arise from the so-called direct problems of natural science. The demands of science and technology have recently brought to the fore many problems that are inverse to the classical direct problems, that is, problems which may be interpreted as finding the cause of a given effect or finding the law of evolution given the cause and effect. Included among such problems are many questions of remote sensing or indirect measurement such as the determination of internal characteristics of an inaccessible region from measurements on its boundary, the determination of system parameters from input output measurements, and the reconstruction of past events from measurements of the present state. Inverse problems of this type are often ill-posed in the sense that distinct causes can account for the same effect and small changes in a perceived effect can correspond to very large changes in a given cause. Very frequently such inverse problems are modeled by integral equations of the first kind.
Erscheinungsdatum: 11.04.2014
备用文件名
lgrsnf/D:\HDD4\!genesis\SPR_NEW_2013-12\bok%3A978-3-322-99202-4.pdf
备用文件名
nexusstc/Inverse Problems in the Mathematical Sciences/e7f2d45de4232030faa69fd6a8320e5e.pdf
备用文件名
scihub/10.1007/978-3-322-99202-4.pdf
备用文件名
zlib/Mathematics/Professor Charles W. Groetsch (auth.)/Inverse Problems in the Mathematical Sciences_2301926.pdf
备选标题
Inverse Problems in the Mathematical Sciences (Theory & Practice of Applied Geophysics)
备选作者
Charles W. Groetsch, C. W. Groetsch
备选作者
Groetsch, Charles W.
备用出版商
Betriebswirtschaftlicher Verlag Dr. Th. Gabler. in Springer Fachmedien Wiesbaden GmbH
备用出版商
Vieweg & Teubner. in Springer Fachmedien Wiesbaden GmbH
备用出版商
Vieweg Verlag, Friedr, & Sohn Verlagsgesellschaft mbH
备用出版商
Informatica International, Inc.
备用出版商
Springer-Verlag GmbH
备用出版商
Springer Vieweg
备用版本
Vieweg mathematics for scientists and engineers, Wiesbaden (Alemania), 1993
备用版本
Vieweg mathematics for scientists and engineers, Braunschweig, ©1993
备用版本
Springer Nature, Wiesbaden, 2013
备用版本
Wiesbaden, post 2005], 1993
备用版本
Aufl. 1993, Wiesbaden, 2014
备用版本
Germany, Germany
备用版本
1993, US, 1993
备用版本
December 1993
备用版本
Dec 17, 2013
元数据中的注释
lg1133217
元数据中的注释
{"edition":"1","isbns":["3322992020","3322992047","3528065451","9783322992024","9783322992048","9783528065454"],"last_page":154,"publisher":"Springer Vieweg"}
备用描述
Aims To Remedy The Scant Attention Paid To Inverse Problems In University Curricula By Supplying An Accessible Introduction, At A Modest Mathematical Level, To The Alluring Field Of Inverse Problems. Many Models Of Inverse Problems From Science And Engineering Are Dealt With. Inverse Problems Are Immensely Important In Modern Science And Technology. However, The Broad Mathematical Issues Raised By Inverse Problems Receive Scant Attention In University Curricula. This Book Aims To Remedy This State Of Affairs By Supplying An Accessible Introduction, At A Modest Mathematical Level, To The Alluring Field Of Inverse Problems. Many Models Of Inverse Problems From Science And Engineering Are Dealt With And Nearly 100 Exercises, Or Varying Difficulty, Involving Mathematical Analysis, Numerical Treatment, Or Modelling Of Inverse Problems, Are Provided. The Main Themes Of The Books Are: Causation Problem Modeled As Integral Equations; Model Identification Problems Posed As Coefficient Determination Problems In Differential Equations; The Functional Analytic Framework For Inverse Problems; And A Survey Of The Principal Numerical Methods For Inverse Problems. Inverse Problems Modeled By Integral Equations Of The First Kind -- Causation-parameter Estimation In Differential Equations -- Model Identification -- Mathematical Background For Inverse Problems -- Some Methodology For Inverse Problems. Charles W. Groetsch. Vieweg Mathematics For Scientists And Engineers--cover. Includes Bibliographical References (p. 121-150) And Index.
备用描述
Inverse problems are immensely important in modern science and technology. However, the broad mathematical issues raised by inverse problems receive scant attention in the university curriculum. This book aims to remedy this state of affairs by supplying an accessible introduction, at a modest mathematical level, to the alluring field of inverse problems. Many models of inverse problems from science and engineering are dealt with and nearly a hundred exercises, of varying difficulty, involving mathematical analysis, numerical treatment, or modelling of inverse problems, are provided. The main themes of the book causation problem modeled as integral equations; model identification problems, posed as coefficient determination problems in differential equations; the functional analytic framework for inverse problems; and a survey of the principal numerical methods for inverse problems. An extensive annotated bibliography furnishes leads on the history of inverse problems and a guide to the frontiers of current research.
备用描述
Front Matter....Pages I-1
Introduction....Pages 2-4
Inverse Problems Modeled by Integral Equations of the First Kind: Causation....Pages 5-40
Parameter Estimation in Differential Equations: Model Identification....Pages 41-66
Mathematical Background for Inverse Problems....Pages 67-83
Some Methodology for Inverse Problems....Pages 84-120
An Annotated Bibliography on Inverse Problems....Pages 121-150
Back Matter....Pages 151-154
开源日期
2014-01-18
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