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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.

BooksJournals

    • Handbook of Differential Equations

      • 3rd Edition
      • October 29, 1997
      • Daniel Zwillinger
      • English
      • Hardback
        9 7 8 0 1 2 7 8 4 3 9 6 4
      • eBook
        9 7 8 0 0 8 0 5 7 2 7 4 1
      Handbook of Differential Equations, Third Edition compiles the most widely applicable methods for solving and approximating differential equations, also providing numerous examples that show methods being used. Topics include ordinary differential equations, symplectic integration of differential equations, and the use of wavelets when numerically solving differential equations.

    • Lie Algebras, Part 2

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

    • Multiscale Wavelet Methods for Partial Differential Equations

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

    • Linear Differential and Difference Equations

      • 1st Edition
      • June 1, 1997
      • R. M. Johnson
      • English
      • Paperback
        9 7 8 1 8 9 8 5 6 3 1 2 9
      • eBook
        9 7 8 0 8 5 7 0 9 9 8 0 8
      This text for advanced undergraduates and graduates reading applied mathematics, electrical, mechanical, or control engineering, employs block diagram notation to highlight comparable features of linear differential and difference equations, a unique feature found in no other book. The treatment of transform theory (Laplace transforms and z-transforms) encourages readers to think in terms of transfer functions, i.e. algebra rather than calculus. This contrives short-cuts whereby steady-state and transient solutions are determined from simple operations on the transfer functions.

    • Covering Codes

      • 1st Edition
      • Volume 54
      • April 14, 1997
      • G. Cohen + 3 more
      • English
      • Paperback
        9 7 8 0 4 4 4 5 5 2 1 6 7
      • Hardback
        9 7 8 0 4 4 4 8 2 5 1 1 7
      • eBook
        9 7 8 0 0 8 0 5 3 0 0 7 9
      The problems of constructing covering codes and of estimating their parameters are the main concern of this book. It provides a unified account of the most recent theory of covering codes and shows how a number of mathematical and engineering issues are related to covering problems.Scientists involved in discrete mathematics, combinatorics, computer science, information theory, geometry, algebra or number theory will find the book of particular significance. It is designed both as an introductory textbook for the beginner and as a reference book for the expert mathematician and engineer.A number of unsolved problems suitable for research projects are also discussed.

    • Non-Standard and Improperly Posed Problems

      • 1st Edition
      • Volume 194
      • July 7, 1997
      • William F. Ames + 1 more
      • English
      • Hardback
        9 7 8 0 1 2 0 5 6 7 4 5 4
      • 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.

    • Submodular Functions and Electrical Networks

      • 1st Edition
      • Volume 54
      • May 1, 1997
      • H. Narayanan
      • English
      • eBook
        9 7 8 0 0 8 0 8 6 7 9 4 6
      There is a strong case for electrical network topologists and submodular function theorists being aware of each other's fields.Presenting a topological approach to electrical network theory, this book demonstrates the strong links that exist between submodular functions and electrical networks.The book contains:• a detailed discussion of graphs, matroids, vector spaces and the algebra of generalized minors, relevant to network analysis (particularly to the construction of efficient circuit simulators)• a detailed discussion of submodular function theory in its own right; topics covered include, various operations, dualization, convolution and Dilworth truncation as well as the related notions of prinicpal partition and principal lattice of partitions.In order to make the book useful to a wide audience, the material on electrical networks and that on submodular functions is presented independently of each other. The hybrid rank problem, the bridge between (topological) electrical network theory and submodular functions, is covered in the final chapter.The emphasis in the book is on low complexity algorithms, particularly based on bipartite graphs.The book is intended for self-study and is recommended to designers of VLSI algorithms. More than 300 problems, almost all of them with solutions, are included at the end of each chapter.

    • 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
      • eBook
        9 7 8 0 0 8 0 9 1 7 2 3 8
      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.

    • 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.

Related subjects

Mathematics and applied mathematics

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