The importance of mathematics in the study of problems arising from
the real world, and the increasing success with which it has been
used to model situations ranging from the purely deterministic to
the stochastic, in all areas of today's Physical Sciences and
Engineering, is well established. The purpose of the sets of
volumes, the present one being the first in a planned series of
sequential sets, is to make available authoritative, up to date,
and self-contained accounts of some of the most important and
useful of these analytical approaches and techniques. Each volume
in each set will provide a detailed introduction to a specific
subject area of current importance, and then goes beyond this by
reviewing recent contributions, thereby serving as a valuable
reference source. The progress in applicable mathematics has been
brought about by the extension and development of many important
analytical approaches and techniques, in areas both old and new,
frequently aided by the use of computers without which the solution
of realistic problems in modern Physical Sciences and Engineering
would otherwise have been impossible.A case in point is the
analytical technique of singular perturbation theory (Volume 3),
which has a long history. In recent years it has been used in many
different ways, and its importance has been enhanced by its having
been used in various fields to derive sequences of asymptotic
approximations, each with a higher order of accuracy than its
predecessor. These approximations have, in turn, provided a better
understanding of the subject and stimulated the development of new
methods for the numerical solution of the higher order
approximations. A typical example of this type is to be found in
the general study of nonlinear wave propagation phenomena as
typified by the study of water waves. Elsewhere, as with the
identification and emergence of the study of inverse problems
(volumes 1 and 2), new analytical approaches have stimulated the
development of numerical techniques for the solution of this major
class of problems.Such work divides naturally into two parts, the
first being the identification and formulation of inverse problems,
the theory of ill-posed problems and the class of one-dimensional
inverse problems, and the second being the study and theory of
multidimensional inverse problems. Volume 1: Inverse Problems 1
Volume 2: Inverse Problems 2 Alexander G. Ramm, Author These
volumes present the theory of inverse spectral and scattering
problems and of many other inverse problems for differential
equations in an essentially self-contained way.Highlights of these
volumes include novel presentation of the classical theories
(Gel'fand-Levitan's and Marchenko's), analysis of the invertibility
of the inversion steps in these theories, study of some new inverse
problems in one-and multi-dimensional cases; I-function and
applications to classical and new inverse scattering and spectral
problems, study of inverse problems with incomplete data, study of
some new inverse problems for parabolic and hyperbolic equations,
discussion of some non-overdetermined inverse problems, a study of
inverse problems arising in the theory of ground-penetrating
radars, development of DSM (dynamical systems method) for solving
ill-posed nonlinear operator equations, comparison of the Ramm's
inversion method for solving fixed-energy inverse scattering
General
Is the information for this product incomplete, wrong or inappropriate?
Let us know about it.
Does this product have an incorrect or missing image?
Send us a new image.
Is this product missing categories?
Add more categories.
Review This Product
No reviews yet - be the first to create one!
Welcome to Loot.co.za!
Sign in / Register |Wishlists & Gift Vouchers |Help | Advanced search
