# An Introduction To Inverse Scattering And Inverse Spectral Problems (monographs On Mathematical Modeling And Computation)

by David Colton /
1987 / English / PDF

16.9 MB Download

Here is a clearly written introduction to three central areas of
inverse problems: inverse problems in electromagnetic scattering
theory, inverse spectral theory, and inverse problems in quantum
scattering theory. Inverse problems, one of the most attractive
parts of applied mathematics, attempt to obtain information about
structures by nondestructive measurements. Based on a series of
lectures presented by three of the authors, all experts in the
field, the book provides a quick and easy way for readers to become
familiar with the area through a survey of recent developments in
inverse spectral and inverse scattering problems. In the opening
chapter, Paivarinta collects the mathematical tools needed in the
subsequent chapters and gives references for further study.
Colton's chapter focuses on electromagnetic scattering problems. As
an application he considers the problem of detecting and monitoring
leukemia. Rundell's chapter deals with inverse spectral problems.
He describes several exact and algorithmic methods for
reconstructing an unknown function from the spectral data. Chadan
provides an introduction to quantum mechanical inverse scattering
problems. As an application he explains the celebrated method of
Gardner, Greene, Kruskal, and Miura for solving nonlinear evolution
equations such as the Korteweg_de Vries equation. Each chapter
provides full references for further study.

Here is a clearly written introduction to three central areas of
inverse problems: inverse problems in electromagnetic scattering
theory, inverse spectral theory, and inverse problems in quantum
scattering theory. Inverse problems, one of the most attractive
parts of applied mathematics, attempt to obtain information about
structures by nondestructive measurements. Based on a series of
lectures presented by three of the authors, all experts in the
field, the book provides a quick and easy way for readers to become
familiar with the area through a survey of recent developments in
inverse spectral and inverse scattering problems. In the opening
chapter, Paivarinta collects the mathematical tools needed in the
subsequent chapters and gives references for further study.
Colton's chapter focuses on electromagnetic scattering problems. As
an application he considers the problem of detecting and monitoring
leukemia. Rundell's chapter deals with inverse spectral problems.
He describes several exact and algorithmic methods for
reconstructing an unknown function from the spectral data. Chadan
provides an introduction to quantum mechanical inverse scattering
problems. As an application he explains the celebrated method of
Gardner, Greene, Kruskal, and Miura for solving nonlinear evolution
equations such as the Korteweg_de Vries equation. Each chapter
provides full references for further study.