Inverse Problems in the Mathematical Sciences

ISBN-13: 9783322992048 / Angielski / Miękka / 2014 / 154 str.

Charles W. Groetsch

Opis

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 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. An extensive annotated bibliography furnishes leads on the history of inverse problems and a guide to the frontiers of current research.

Spis treści

Contents: Introduction - 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 - An annotated bibliography on inverse problems.

O autorze

C. W. Groetsch ist Professor für Mathematik an der University of Cincinnati, USA.