Skip to main content
Elsevier

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.

  • Categorical Logic and Type Theory

    • 1st Edition
    • Volume 141
    • B. Jacobs
    • English
    This book is an attempt to give a systematic presentation of both logic and type theory from a categorical perspective, using the unifying concept of fibred category. Its intended audience consists of logicians, type theorists, category theorists and (theoretical) computer scientists.

  • A Course in Real Analysis

    • 1st Edition
    • John N. McDonald + 1 more
    • English
    A Course in Real Analysis provides a firm foundation in real analysis concepts and principles while presenting a broad range of topics in a clear and concise manner. This student-oriented text balances theory and applications, and contains a wealth of examples and exercises. Throughout the text, the authors adhere to the idea that most students learn more efficiently by progressing from the concrete to the abstract. McDonald and Weiss have also created real application chapters on probability theory, harmonic analysis, and dynamical systems theory. The text offers considerable flexibility in the choice of material to cover.

  • Recursive Algebra, Analysis and Combinatorics

    • 1st Edition
    • Volume 2
    • English

  • Recursive Model Theory

    • 1st Edition
    • Volume 1
    • English

  • Handbook of Coding Theory

    Part 2: Connections, Part 3: Applications
    • 1st Edition
    • Volume II
    • Bozzano G Luisa
    • English
    The second volume of this work contains Parts 2 and 3 of the "Handbook of Coding Theory". Part 2, "Connections", is devoted to connections between coding theory and other branches of mathematics and computer science. Part 3, "Applications", deals with a variety of applications for coding.

  • Projects for Calculus

    The Language of Change
    • 2nd Edition
    • Keith D. Stroyan
    • English
    Projects for Calculus is designed to add depth and meaning to any calculus course. The fifty-two projects presented in this text offer the opportunity to expand the use and understanding of mathematics. The wide range of topics will appeal to both instructors and students. Shorter, less demanding projects can be managed by the independent learner, while more involved, in-depth projects may be used for group learning. Each task draws on special mathematical topics and applications from subjects including medicine, engineering, economics, ecology, physics, and biology.

  • Handbook of Fourier Transform Raman and Infrared Spectra of Polymers

    • 1st Edition
    • Volume 45
    • A.H. Kuptsov + 1 more
    • English
    A collection of infrared and Raman spectra of 500 natural and synthetic polymers of industrial importance is presented in this book. A large variety of compounds are included, starting with linear polyolefins and finishing with complex biopolymers and related compounds. The spectra were registered using Infrared Fourier Transform Spectrometers in the laboratory of the All-Russia Institute of Forensic Sciences. The IR and Raman spectra are presented together on the same sheet. The accompanying data include general and structure formulae, CAS register numbers, and sample preparation conditions.Features of this book:• Continues the long tradition of publishing specific and standard data of new chemical compounds.• For low-molecular weight substances, complementary IR and Raman spectra are featured on the same sample and printed on the same page. This "fingerprint" data allows the substance of the sample to be identified without doubt.• An important feature of this unique collection of data is the increase in the identification precision of unknown substances.• Peak tables are available in digital (ASCII) format, on a diskette delivered with the book. This allows the user to search for unknowns.• All the spectra in the collection are base-line corrected.This book will be of interest to scientists involved in the synthesis of new polymeric materials, polymer identification, and quality control. Libraries of scientific institutes, research centers, and universities involved in vibrational spectroscopy will also find this collection invaluable.

  • Asymptotic Methods in Probability and Statistics

    A Volume in Honour of Miklós Csörgő
    • 1st Edition
    • B. Szyszkowicz
    • English
    One of the aims of the conference on which this book is based, was to provide a platform for the exchange of recent findings and new ideas inspired by the so-called Hungarian construction and other approximate methodologies. This volume of 55 papers is dedicated to Miklós Csörgő a co-founder of the Hungarian construction school by the invited speakers and contributors to ICAMPS'97.This excellent treatize reflects the many developments in this field, while pointing to new directions to be explored. An unequalled contribution to research in probability and statistics.

  • Fractional Differential Equations

    An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution and Some of Their Applications
    • 1st Edition
    • Volume 198
    • Igor Podlubny
    • English
    This book is a landmark title in the continuous move from integer to non-integer in mathematics: from integer numbers to real numbers, from factorials to the gamma function, from integer-order models to models of an arbitrary order. For historical reasons, the word 'fractional' is used instead of the word 'arbitrary'.This book is written for readers who are new to the fields of fractional derivatives and fractional-order mathematical models, and feel that they need them for developing more adequate mathematical models.In this book, not only applied scientists, but also pure mathematicians will find fresh motivation for developing new methods and approaches in their fields of research.A reader will find in this book everything necessary for the initial study and immediate application of fractional derivatives fractional differential equations, including several necessary special functions, basic theory of fractional differentiation, uniqueness and existence theorems, analytical numerical methods of solution of fractional differential equations, and many inspiring examples of applications.

  • Statistics with Mathematica

    • 1st Edition
    • Martha L. Abell + 2 more
    • English
    Mathematica's diverse capabilities make it particularly well suited to perform the many calculations encountered in statistics. This book introduces Mathematica for various types of statistical computations. It covers a broad range of topics, and should appeal to both students and professional statisticians.

  • The Nature of Mathematics and the Mathematics of Nature

    • 1st Edition
    • S. Andersson + 1 more
    • English
    Chemistry, physics and biology are by their nature genuinely difficult. Mathematics, however, is man-made, and therefore not as complicated. Two ideas form the basis for this book: 1) to use ordinary mathematics to describe the simplicity in the structure of mathematics and 2) to develop new branches of mathematics to describe natural sciences.Mathematics can be described as the addition, subtraction or multiplication of planes. Using the exponential scale the authors show that the addition of planes gives the polyhedra, or any solid. The substraction of planes gives saddles. The multiplication of planes gives the general saddle equations and the multispirals. The equation of symmetry is derived, which contains the exponential scale with its functions for solids, the complex exponentials with the nodal surfaces, and the GD (Gauss Distribution) mathematics with finite periodicity.Piece by piece, the authors have found mathematical functions for the geometrical descriptions of chemical structures and the structure building operations. Using the mathematics for dilatation; twins, trillings, fourlings and sixlings are made, and using GD mathematics these are made periodic. This description of a structure is the nature of mathematics itself. Crystal structures and 3D mathematics are synonyms. Mathematics are used to describe rod packings, Olympic rings and defects in solids. Giant molecules such as cubosomes, the DNA double helix, and certain building blocks in protein structures are also described mathematically.

  • Problems in Real Analysis

    • 2nd Edition
    • Charalambos D. Aliprantis + 1 more
    • English
    A collection of problems and solutions in real analysis based on the major textbook, Principles of Real Analysis (also by Aliprantis and Burkinshaw), Problems in Real Analysis is the ideal companion for senior science and engineering undergraduates and first-year graduate courses in real analysis. It is intended for use as an independent source, and is an invaluable tool for students who wish to develop a deep understanding and proficiency in the use of integration methods. Problems in Real Analysis teaches the basic methods of proof and problem-solving by presenting the complete solutions to over 600 problems that appear in Principles of Real Analysis, Third Edition. The problems are distributed in forty sections, and cover the entire spectrum of difficulty.

  • Time-Frequency/Time-Scale Analysis

    • 1st Edition
    • Volume 10
    • Patrick Flandrin
    • English
    This highly acclaimed work has so far been available only in French. It is a detailed survey of a variety of techniques for time-frequency/time-... analysis (the essence of "Wavelet Analysis"). This book has broad and comprehensive coverage of a topic of keen interest to a variety of engineers, especially those concerned with signal and image processing. Flandrin provides a discussion of numerous issues and problems that arise from a mixed description in time and frequency, as well as problems in interpretation inherent in signal theory.

  • Advanced Applied Finite Element Methods

    • 1st Edition
    • Carl T. F. Ross
    • English
    This book is aimed at senior undergraduates, graduates and engineers. It fills the gap between the numerous textbooks on traditional Applied Mechanics and postgraduate books on Finite Element Methods.

  • Practical Time-Frequency Analysis

    Gabor and Wavelet Transforms, with an Implementation in S
    • 1st Edition
    • Volume 9
    • Rene Carmona + 2 more
    • English
    Time frequency analysis has been the object of intense research activity in the last decade. This book gives a self-contained account of methods recently introduced to analyze mathematical functions and signals simultaneously in terms of time and frequency variables. The book gives a detailed presentation of the applications of these transforms to signal processing, emphasizing the continuous transforms and their applications to signal analysis problems, including estimation, denoising, detection, and synthesis. To help the reader perform these analyses, Practical Time-Frequency Analysis provides a set of useful tools in the form of a library of S functions, downloadable from the authors' Web sites in the United States and France.

  • Applications of Markov Chains in Chemical Engineering

    • 1st Edition
    • A. Tamir
    • English
    Markov chains make it possible to predict the future state of a system from its present state ignoring its past history. Surprisingly, despite the widespread use of Markov chains in many areas of science and technology, their applications in chemical engineering have been relatively meager. A possible reason for this phenomenon might be that books containing material on this subject have been written in such a way that the simplicity of Markov chains has been shadowed by the tedious mathematical derivations. Thus, the major objective of writing this book has been to try to change this situation.There are many advantages, detailed in Chapter 1, of using the discrete Markov-chain model in chemical engineering. Probably, the most important advantage is that physical models can be presented in a unified description via state vector and a one-step transition probability matrix. Consequently, a process is demonstrated solely by the probability of a system to occupy or not occupy a state.The book has been written in an easy and understandable form, where complex mathematical derivations are abandoned. The fundamentals of Markov chains are presented in Chapter 2 with examples from the bible, art and real life problems. An extremely wide collection is given of examples viz., reactions, reactors, reactions and reactors as well as combined processes, including their solution and a graphical presentation of it, all of which demonstrates the usefulness of applying Markov chains in chemical engineering.

  • Principles of Real Analysis

    • 3rd Edition
    • Charalambos D. Aliprantis
    • Owen Burkinshaw
    • English
    With the success of its previous editions, Principles of Real Analysis, Third Edition, continues to introduce students to the fundamentals of the theory of measure and functional analysis. In this thorough update, the authors have included a new chapter on Hilbert spaces as well as integrating over 150 new exercises throughout. The new edition covers the basic theory of integration in a clear, well-organized manner, using an imaginative and highly practical synthesis of the "Daniell Method" and the measure theoretic approach. Students will be challenged by the more than 600 exercises contained in the book. Topics are illustrated by many varied examples, and they provide clear connections between real analysis and functional analysis.

  • Wavelets in a Box

    • 1st Edition
    • Andrew K. Chan + 1 more
    • English
    Wavelets are considered by many to be the most powerful mathematical tool for signal and image processing. This unique CD-ROM boxed set contains three useful items: a copy of the text An Introduction to Wavelets by Charles Chui, a CD containing well-designed wavelets and signal processing software by computer scientist Steve Liu, and a booklet that serves both as the manual for the software and a quick reference guide to wavelet basics by electrical engineer Andrew Chan. The software supports all essential wavelets and allows users to put in additional wavelets of their choice and delete the ones they don't need. It also includes custom computation routines (in C-language) for wavelet signal processing. A flexible programming interface through the DLL standard allows the user to plug in new and original processing routines easily. This self-learning package provides the tools for the user to compare short time fourier transform and wavelet transform as well as the trade-off between time/spatial and frequency domain signal analysis.

  • Chaos and Fractals

    A Computer Graphical Journey
    • 1st Edition
    • C.A. Pickover
    • English
    These days computer-generated fractal patterns are everywhere, from squiggly designs on computer art posters to illustrations in the most serious of physics journals. Interest continues to grow among scientists and, rather surprisingly, artists and designers. This book provides visual demonstrations of complicated and beautiful structures that can arise in systems, based on simple rules. It also presents papers on seemingly paradoxical combinations of randomness and structure in systems of mathematical, physical, biological, electrical, chemical, and artistic interest. Topics include: iteration, cellular automata, bifurcation maps, fractals, dynamical systems, patterns of nature created through simple rules, and aesthetic graphics drawn from the universe of mathematics and art.Chaos and Fractals is divided into six parts: Geometry and Nature; Attractors; Cellular Automata, Gaskets, and Koch Curves; Mandelbrot, Julia and Other Complex Maps; Iterated Function Systems; and Computer Art.Additionally, information on the latest practical applications of fractals and on the use of fractals in commercial products such as the antennas and reaction vessels is presented. In short, fractals are increasingly finding application in practical products where computer graphics and simulations are integral to the design process. Each of the six sections has an introduction by the editor including the latest research, references, and updates in the field. This book is enhanced with numerous color illustrations, a comprehensive index, and the many computer program examples encourage reader involvement.

  • Handbook of Proof Theory

    • 1st Edition
    • Volume 137
    • S.R. Buss
    • English
    This volume contains articles covering a broad spectrum of proof theory, with an emphasis on its mathematical aspects. The articles should not only be interesting to specialists of proof theory, but should also be accessible to a diverse audience, including logicians, mathematicians, computer scientists and philosophers. Many of the central topics of proof theory have been included in a self-contained expository of articles, covered in great detail and depth.The chapters are arranged so that the two introductory articles come first; these are then followed by articles from core classical areas of proof theory; the handbook concludes with articles that deal with topics closely related to computer science.

  • Regression Analysis for Social Sciences

    • 1st Edition
    • Alexander von Eye + 1 more
    • English
    Regression Analysis for Social Sciences presents methods of regression analysis in an accessible way, with each method having illustrations and examples. A broad spectrum of methods are included: multiple categorical predictors, methods for curvilinear regression, and methods for symmetric regression. This book can be used for courses in regression analysis at the advanced undergraduate and beginning graduate level in the social and behavioral sciences. Most of the techniques are explained step-by-step enabling students and researchers to analyze their own data. Examples include data from the social and behavioral sciences as well as biology, making the book useful for readers with biological and biometrical backgrounds. Sample command and result files for SYSTAT are included in the text.

  • Vector Calculus

    • 1st Edition
    • William Cox
    • English
    Building on previous texts in the Modular Mathematics series, in particular 'Vectors in Two or Three Dimensions' and 'Calculus and ODEs', this book introduces the student to the concept of vector calculus. It provides an overview of some of the key techniques as well as examining functions of more than one variable, including partial differentiation and multiple integration.Undergra... who already have a basic understanding of calculus and vectors, will find this text provides tools with which to progress onto further studies; scientists who need an overview of higher order differential equations will find it a useful introduction and basic reference.

  • Partial Differential Equations & Boundary Value Problems with Maple V

    • 1st Edition
    • George A. Articolo
    • English
    George Articulo covers all the material found in traditional partial differentiation equations and boundary value courses in this textbook. Its unique approach allows students to learn the mathematics first, then use Maple graphics capabilities to visualize both static and animated behavior of the solution. The book provides many example problems using commands that render two- or three-dimensional animated graphics. The author focuses on the natural union between partial differential equations and a powerful computational language such as Maple.

  • Stream Ciphers and Number Theory

    • 1st Edition
    • Volume 55
    • T.W. Cusick + 2 more
    • English
    This book is almost entirely concerned with stream ciphers, concentrating on a particular mathematical model for such ciphers which are called additive natural stream ciphers. These ciphers use a natural sequence generator to produce a periodic keystream. Full definitions of these concepts are given in Chapter 2.This book focuses on keystream sequences which can be analysed using number theory. It turns out that a great deal of information can be deducted about the cryptographic properties of many classes of sequences by applying the terminology and theorems of number theory. These connections can be explicitly made by describing three kinds of bridges between stream ciphering problems and number theory problems. A detailed summary of these ideas is given in the introductory Chapter 1.Many results in the book are new, and over seventy percent of these results described in this book are based on recent research results.

  • Parallel Computational Fluid Dynamics '97

    Recent Developments and Advances Using Parallel Computers
    • 1st Edition
    • D. Emerson + 4 more
    • English
    Computational Fluid Dynamics (CFD) is a discipline that has always been in the vanguard of the exploitation of emerging and developing technologies. Advances in both algorithms and computers have rapidly been absorbed by the CFD community in its quest for more accurate simulations and reductions in the time to solution. Within this context, parallel computing has played an increasingly important role. Moreover, the uptake of parallel computing has brought the CFD community into ever-closer contact with hardware vendors and computer scientists. The multidisciplinary subject of parallel CFD and its rapidly evolving nature, in terms of hardware and software, requires a regular international meeting of this nature to keep abreast of the most recent developments.Paralle... CFD '97 is part of an annual conference series dedicated to the discussion of recent developments and applications of parallel computing in the field of CFD and related disciplines. This was the 9th in the series, and since the inaugural conference in 1989, many new developments and technologies have emerged. The intervening years have also proved to be extremely volatile for many hardware vendors and a number of companies appeared and then disappeared. However, the belief that parallel computing is the only way forward has remained undiminished. Moreover, the increasing reliability and acceptance of parallel computers has seen many commercial companies now offering parallel versions of their codes, many developed within the EC funded EUROPORT activity, but generally for more modest numbers of processors. It is clear that industry has not moved to large scale parallel systems but it has shown a keen interest in more modest parallel systems recognising that parallel computing will play an important role in the future. This book forms the proceedings of the CFD '97 conference, which was organised by the the Computational Engineering Group at Daresbury Laboratory and held in Manchester, England, on May 19-21 1997. The sessions involved papers on many diverse subjects including turbulence, reactive flows, adaptive schemes, unsteady flows, unstructured mesh applications, industrial applications, developments in software tools and environments, climate modelling, parallel algorithms, evaluation of computer architectures and a special session devoted to parallel CFD at the AEREA research centres. This year's conference, like its predecessors, saw a continued improvement in both the quantity and quality of contributed papers.Since the conference series began many significant milestones have been acheived. For example in 1994, Massively Parallel Processing (MPP) became a reality with the advent of Cray T3D. This, of course, has brought with it the new challenge of scalability for both algorithms and architectures. In the 12 months since the 1996 conference, two more major milestones were achieved: microprocessors with a peak performance of a Gflop/s became available and the world's first Tflop/s calculation was performed. In the 1991 proceedings, the editors indicated that a Tflop/s computer was likely to be available in the latter half of this decade. On December 4th 1996, Intel achieved this breakthrough on the Linpack benchmark using 7,264 (200MHz) Pentium Pro microprocessors as part of the ASCI Red project. With the developments in MPP, the rapid rise of SMP architectures and advances in PC technology, the future for parallel CFD looks both promising and challenging.

  • Precise Numerical Methods Using C++

    • 1st Edition
    • Oliver Aberth
    • English
    This book explains how precise numerical analysis is constructed with C++. Included is a CD-ROM which contains executable Windows 95 programs for the PC and which demonstrates how these programs can be used to solvetypical problems of elementary numerical analysis with precision. The book also provides exercises which illustrate points from the text and references for the methods presented.

  • Visualization of Categorical Data

    • 1st Edition
    • Jörg Blasius + 1 more
    • English
    A unique and timely monograph, Visualization of Categorical Data contains a useful balance of theoretical and practical material on this important new area. Top researchers in the field present the books four main topics: visualization, correspondence analysis, biplots and multidimensional scaling, and contingency table models.This volume discusses how surveys, which are employed in many different research areas, generate categorical data. It will be of great interest to anyone involved in collecting or analyzing categorical data.

  • Handbook of Differential Equations (CD-ROM Version 1 only)

    • 3rd Edition
    • Daniel Zwillinger
    • English
    This book and CD-ROM compile the most widely applicable methods for solving and approximating differential equations. The CD-ROM provides convenient access to these methods through electronic search capabilities, andtogether the book and CD-ROM contain numerous examples showing the methods use. Topics include ordinary differential equations, symplectic integration of differential equations, and the use of wavelets when numerically solving differential equations.

  • Experimental Design Techniques in Statistical Practice

    A Practical Software-Based Approach
    • 1st Edition
    • William P Gardiner + 1 more
    • English
    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.

  • Projection Methods for Systems of Equations

    • 1st Edition
    • Volume 7
    • C. Brezinski
    • English
    The solutions of systems of linear and nonlinear equations occurs in many situations and is therefore a question of major interest. Advances in computer technology has made it now possible to consider systems exceeding several hundred thousands of equations. However, there is a crucial need for more efficient algorithms.The main focus of this book (except the last chapter, which is devoted to systems of nonlinear equations) is the consideration of solving the problem of the linear equation Ax = b by an iterative method. Iterative methods for the solution of this question are described which are based on projections. Recently, such methods have received much attention from researchers in numerical linear algebra and have been applied to a wide range of problems.The book is intended for students and researchers in numerical analysis and for practitioners and engineers who require the most recent methods for solving their particular problem.

  • Linear Algebra, Rational Approximation and Orthogonal Polynomials

    • 1st Edition
    • Volume 6
    • A. Bultheel + 1 more
    • English
    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
    • English
    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

    Finite and Infinite Dimensional Lie Algebras and Applications in Physics
    • 1st Edition
    • Volume 7
    • E.A. de Kerf + 2 more
    • English
    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.

  • Handbook of Differential Equations

    • 3rd Edition
    • Daniel Zwillinger
    • English
    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.

  • Signal and Image Representation in Combined Spaces

    • 1st Edition
    • Volume 7
    • Yehoshua Zeevi + 1 more
    • English
    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
    • J. Douglas Carroll + 1 more
    • Anil Chaturvedi
    • English
    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
    • Reg Allenby
    • English
    '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.

  • Mathematical Tools for Applied Multivariate Analysis, Revised Edition

    • 1st Edition
    • J. Douglas Carroll + 1 more
    • Anil Chaturvedi
    • English
    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.Mathematical 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.

  • Advances in Computers

    • 1st Edition
    • Volume 45
    • English
    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
    • Wolfgang Dahmen + 2 more
    • English
    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.

  • Mathematical Elasticity

    Volume II: Theory of Plates
    • 1st Edition
    • Volume 27
    • English
    The objective of Volume II is to show how asymptotic methods, with the thickness as the small parameter, indeed provide a powerful means of justifying two-dimensional plate theories. More specifically, without any recourse to any a priori assumptions of a geometrical or mechanical nature, it is shown that in the linear case, the three-dimensional displacements, once properly scaled, converge in H1 towards a limit that satisfies the well-known two-dimensional equations of the linear Kirchhoff-Love theory; the convergence of stress is also established.In the nonlinear case, again after ad hoc scalings have been performed, it is shown that the leading term of a formal asymptotic expansion of the three-dimensional solution satisfies well-known two-dimensional equations, such as those of the nonlinear Kirchhoff-Love theory, or the von Kármán equations. Special attention is also given to the first convergence result obtained in this case, which leads to two-dimensional large deformation, frame-indifferent, nonlinear membrane theories. It is also demonstrated that asymptotic methods can likewise be used for justifying other lower-dimensional equations of elastic shallow shells, and the coupled pluri-dimensional equations of elastic multi-structures, i.e., structures with junctions. In each case, the existence, uniqueness or multiplicity, and regularity of solutions to the limit equations obtained in this fashion are also studied.

  • Non-Standard and Improperly Posed Problems

    • 1st Edition
    • Volume 194
    • William F. Ames + 1 more
    • English
    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.

  • Advances in Computers

    • 1st Edition
    • Volume 44
    • English
    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.

  • Linear Differential and Difference Equations

    A Systems Approach for Mathematicians and Engineers
    • 1st Edition
    • R. M. Johnson
    • English
    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.

  • Submodular Functions and Electrical Networks

    • 1st Edition
    • Volume 54
    • H. Narayanan
    • English
    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.

  • Covering Codes

    • 1st Edition
    • Volume 54
    • G. Cohen + 3 more
    • English
    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.

  • Fractal Imaging

    • 1st Edition
    • Wei-Kao Lu
    • English
    Fractal image compression technology, one of the major digital image compression techniques, has been a well kept secret for many years. While there are many books written on other technologies, such as DCT/JPEG andwavelet theory, few books touch the subject of fractal image compression. Fractal Imaging presents the logic, technology, and various uses of fractal imaging by analyzing a complete, usable fractal image representation system. This detailed work will be a must for engineers interested in building fractal imaging systems. It will also be of interest to the general public, showing how mathematics once again plays a central role in our lives, where art and science intersect.

  • Handbook of Logic and Language

    • 1st Edition
    • J. van Benthem + 1 more
    • English
    This Handbook documents the main trends in current research between logic and language, including its broader influence in computer science, linguistic theory and cognitive science.The history of the combined study of Logic and Linguistics goes back a long way, at least to the work of the scholastic philosophers in the Middle Ages. At the beginning of this century, the subject was revitalized through the pioneering efforts of Gottlob Frege, Bertrand Russell, and Polish philosophical logicians such as Kazimierz Ajdukiewicz. Around 1970, the landmark achievements of Richard Montague established a junction between state-of-the-art mathematical logic and generative linguistic theory. Over the subsequent decades, this enterprise of Montague Grammar has flourished and diversified into a number of research programs with empirical and theoretical substance.This appears to be the first Handbook to bring logic-language interface to the fore. Both aspects of the interaction between logic and language are demonstrated in the book i.e. firstly, how logical systems are designed and modified in response to linguistic needs and secondly, how mathematical theory arises in this process and how it affects subsequent linguistic theory.The Handbook presents concise, impartial accounts of the topics covered. Where possible, an author and a commentator have cooperated to ensure the proper breadth and technical content of the papers.The Handbook is self-contained, and individual articles are of the highest quality.

  • The Language of Shape

    The Role of Curvature in Condensed Matter: Physics, Chemistry and Biology
    • 1st Edition
    • S. Hyde + 6 more
    • English
    This book develops the thesis that structure and function in a variety of condensed systems - from the atomic assemblies in inorganic frameworks and organic molecules, through molecular self-assemblies to proteins - can be unified when curvature and surface geometry are taken together with molecular shape and forces. An astonishing variety of synthetic and biological assemblies can be accurately modelled and understood in terms of hyperbolic surfaces, whose richness and beauty are only now being revealed by applied mathematicians, physicists, chemists and crystallographers. These surfaces, often close to periodic minimal surfaces, weave and twist through space, carving out interconnected labyrinths whose range of topologies and symmetries challenge the imaginative powers.The book offers an overview of these structures and structural transformations, convincingly demonstrating their ubiquity in covalent frameworks from zeolites used for cracking oil and pollution control to enzymes and structural proteins, thermotropic and lyotropic bicontinuous mesophases formed by surfactants, detergents and lipids, synthetic block copolymer and protein networks, as well as biological cell assemblies, from muscles to membranes in prokaryotic and eukaryotic cells. The relation between structure and function is analysed in terms of the previously neglected hidden variables of curvature and topology. Thus, the catalytic activity of zeolites and enzymes, the superior material properties of interpenetrating networks in microstructured polymer composites, the transport requirements in cells, the transmission of nerve signals and the folding of DNA can be more easily understood in the light of this.The text is liberally sprinkled with figures and colour plates, making it accessible to both the beginning graduate student and researchers in condensed matter physics and chemistry, mineralogists, crystallographers and biologists.

  • Fourier Analysis and Boundary Value Problems

    • 1st Edition
    • Enrique A. Gonzalez-Velasco
    • English
    Fourier Analysis and Boundary Value Problems provides a thorough examination of both the theory and applications of partial differential equations and the Fourier and Laplace methods for their solutions. Boundary value problems, including the heat and wave equations, are integrated throughout the book. Written from a historical perspective with extensive biographical coverage of pioneers in the field, the book emphasizes the important role played by partial differential equations in engineering and physics. In addition, the author demonstrates how efforts to deal with these problems have lead to wonderfully significant developments in mathematics. A clear and complete text with more than 500 exercises, Fourier Analysis and Boundary Value Problems is a good introduction and a valuable resource for those in the field.

Related subjects