Books in Mathematics

The Mathematics collection presents a range of foundational and advanced research content across applied and discrete mathematics, including fields such as Computational Mathematics; Differential Equations; Linear Algebra; Modelling & Simulation; Numerical Analysis; Probability & Statistics.

Books Journals

Experimental Design Techniques in Statistical Practice

1st Edition
January 1, 1998
William P Gardiner + 1 more
English
eBook
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Provides an introduction to the diverse subject area of experimental design, with many practical and applicable exercises to help the reader understand, present and analyse the data. The pragmatic approach offers technical training for use of designs and teaches statistical and non-statistical skills in design and analysis of project studies throughout science and industry.

Linear Algebra, Rational Approximation and Orthogonal Polynomials

1st Edition
Volume 6
November 17, 1997
A. Bultheel + 1 more
English
eBook
9 7 8 0 0 8 0 5 3 5 5 2 4

Evolving from an elementary discussion, this book develops the Euclidean algorithm to a very powerful tool to deal with general continued fractions, non-normal Padé tables, look-ahead algorithms for Hankel and Toeplitz matrices, and for Krylov subspace methods. It introduces the basics of fast algorithms for structured problems and shows how they deal with singular situations.Links are made with more applied subjects such as linear system theory and signal processing, and with more advanced topics and recent results such as general bi-orthogonal polynomials, minimal Padé approximation, polynomial root location problems in the complex plane, very general rational interpolation problems, and the lifting scheme for wavelet transform computation. The text serves as a supplement to existing books on structured linear algebra problems, rational approximation and orthogonal polynomials.Features of this book:• provides a unifying approach to linear algebra, rational approximation and orthogonal polynomials• requires an elementary knowledge of calculus and linear algebra yet introduces advanced topics.The book will be of interest to applied mathematicians and engineers and to students and researchers.

Inequalities for Differential and Integral Equations

1st Edition
Volume 197
November 12, 1997
William F. Ames + 1 more
English
eBook
9 7 8 0 0 8 0 5 3 4 6 4 0

Inequalities for Differential and Integral Equations has long been needed; it contains material which is hard to find in other books. Written by a major contributor to the field, this comprehensive resource contains many inequalities which have only recently appeared in the literature and which can be used as powerful tools in the development of applications in the theory of new classes of differential and integral equations. For researchers working in this area, it will be a valuable source of reference and inspiration. It could also be used as the text for an advanced graduate course.

Lie Algebras, Part 2

1st Edition
Volume 7
October 30, 1997
E.A. de Kerf + 2 more
English
eBook
9 7 8 0 0 8 0 5 3 5 4 6 3

This is the long awaited follow-up to Lie Algebras, Part I which covered a major part of the theory of Kac-Moody algebras, stressing primarily their mathematical structure. Part II deals mainly with the representations and applications of Lie Algebras and contains many cross references to Part I.The theoretical part largely deals with the representation theory of Lie algebras with a triangular decomposition, of which Kac-Moody algebras and the Virasoro algebra are prime examples. After setting up the general framework of highest weight representations, the book continues to treat topics as the Casimir operator and the Weyl-Kac character formula, which are specific for Kac-Moody algebras.The applications have a wide range. First, the book contains an exposition on the role of finite-dimensional semisimple Lie algebras and their representations in the standard and grand unified models of elementary particle physics. A second application is in the realm of soliton equations and their infinite-dimensional symmetry groups and algebras. The book concludes with a chapter on conformal field theory and the importance of the Virasoro and Kac-Moody algebras therein.

Signal and Image Representation in Combined Spaces

1st Edition
Volume 7
October 9, 1997
Yehoshua Zeevi + 1 more
English
Hardback
9 7 8 0 1 2 7 7 7 8 3 0 3
eBook
9 7 8 0 0 8 0 5 4 1 1 7 4

This volume explains how the recent advances in wavelet analysis provide new means for multiresolution analysis and describes its wide array of powerful tools. The book covers variations of the windowed Fourier transform, constructions of special waveforms suitable for specific tasks, the use of redundant representations in reconstruction and enhancement, applications of efficient numerical compression as a tool for fast numerical analysis, and approximation properties of various waveforms in different contexts.

Mathematical Tools for Applied Multivariate Analysis

1st Edition
September 30, 1997
J. Douglas Carroll + 1 more
Anil Chaturvedi
English
Paperback
9 7 8 0 1 2 1 6 0 9 5 5 9

This revised edition presents the relevant aspects of transformational geometry, matrix algebra, and calculus to those who may be lacking the necessary mathematical foundations of applied multivariate analysis. It brings up-to-date many definitions of mathematical concepts and their operations. It also clearly defines the relevance of the exercises to concerns within the business community and the social and behavioral sciences. Readers gain a technical background for tackling applications-oriente... multivariate texts and receive a geometric perspective for understanding multivariate methods."Mathematica... Tools for Applied Multivariate Analysis, Revised Edition illustrates major concepts in matrix algebra, linear structures, and eigenstructures geometrically, numerically, and algebraically. The authors emphasize the applications of these techniques by discussing potential solutions to problems outlined early in the book. They also present small numerical examples of the various concepts.

Numbers and Proofs

1st Edition
September 26, 1997
Reg Allenby
English
Paperback
9 7 8 0 3 4 0 6 7 6 5 3 0
eBook
9 7 8 0 0 8 0 9 2 8 7 7 7

'Numbers and Proofs' presents a gentle introduction to the notion of proof to give the reader an understanding of how to decipher others' proofs as well as construct their own. Useful methods of proof are illustrated in the context of studying problems concerning mainly numbers (real, rational, complex and integers). An indispensable guide to all students of mathematics. Each proof is preceded by a discussion which is intended to show the reader the kind of thoughts they might have before any attempt proof is made. Established proofs which the student is in a better position to follow then follow.Presented in the author's entertaining and informal style, and written to reflect the changing profile of students entering universities, this book will prove essential reading for all seeking an introduction to the notion of proof as well as giving a definitive guide to the more common forms. Stressing the importance of backing up "truths" found through experimentation, with logically sound and watertight arguments, it provides an ideal bridge to more complex undergraduate maths.

Advances in Computers

1st Edition
Volume 45
August 19, 1997
Marvin Zelkowitz
English
eBook
9 7 8 0 0 8 0 5 6 6 7 7 1

Since its first volume in 1960, Advances in Computers has presented detailed coverage of innovations in hardware and software and in computer theory, design, and applications. It has also provided contributorswith a medium in which they can examine their subjects in greater depth and breadth than that allowed by standard journal articles. As a result, many articles have become standard references that continue to be of significant, lasting value despite the rapid growth taking place in the field.

Multiscale Wavelet Methods for Partial Differential Equations

1st Edition
Volume 6
August 4, 1997
Wolfgang Dahmen + 2 more
English
eBook
9 7 8 0 0 8 0 5 3 7 1 4 6

This latest volume in the Wavelets Analysis and Its Applications Series provides significant and up-to-date insights into recent developments in the field of wavelet constructions in connection with partial differential equations. Specialists in numerical applications and engineers in a variety of fields will find Multiscale Wavelet for Partial Differential Equations to be a valuable resource.

Non-Standard and Improperly Posed Problems

1st Edition
Volume 194
July 7, 1997
William F. Ames + 1 more
William F. Ames
English
eBook
9 7 8 0 0 8 0 5 3 7 7 4 0

Written by two international experts in the field, this book is the first unified survey of the advances made in the last 15 years on key non-standard and improperly posed problems for partial differential equations.This reference for mathematicians, scientists, and engineers provides an overview of the methodology typically used to study improperly posed problems. It focuses on structural stability--the continuous dependence of solutions on the initial conditions and the modeling equations--and on problems for which data are only prescribed on part of the boundary. The book addresses continuous dependence on initial-time and spatial geometry and on modeling backward and forward in time. It covers non-standard or non-characteristic problems, such as the sideways problem for a heat or hyberbolic equation and the Cauchy problem for the Laplace equation and other elliptic equations. The text also presents other relevant improperly posed problems, including the uniqueness and continuous dependence for singular equations, the spatial decay in improperly posed parabolicproblems, the uniqueness for the backward in time Navier-Stokes equations on an unbounded domain, the improperly posed problems for dusty gases, the linear thermoelasticity, and the overcoming Holder continuity and image restoration.

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