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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

    • Introduction to Robust Estimation and Hypothesis Testing

      • 2nd Edition
      • December 22, 2004
      • Rand R. Wilcox
      • English
      • Hardback
        9 7 8 0 1 2 7 5 1 5 4 2 7
      • eBook
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      This revised book provides a thorough explanation of the foundation of robust methods, incorporating the latest updates on R and S-Plus, robust ANOVA (Analysis of Variance) and regression. It guides advanced students and other professionals through the basic strategies used for developing practical solutions to problems, and provides a brief background on the foundations of modern methods, placing the new methods in historical context. Author Rand Wilcox includes chapter exercises and many real-world examples that illustrate how various methods perform in different situations.Introduct... to Robust Estimation and Hypothesis Testing, Second Edition, focuses on the practical applications of modern, robust methods which can greatly enhance our chances of detecting true differences among groups and true associations among variables.

    • Handbook of Differential Equations: Ordinary Differential Equations

      • 1st Edition
      • Volume 1
      • August 1, 2004
      • A. Canada + 2 more
      • English
      • Hardback
        9 7 8 0 4 4 4 5 1 1 2 8 7
      • eBook
        9 7 8 0 0 8 0 5 3 2 8 2 0
      The book contains seven survey papers about ordinary differential equations.The common feature of all papers consists in the fact that nonlinear equations are focused on. This reflects the situation in modern mathematical modelling - nonlinear mathematical models are more realistic and describe the real world problems more accurately. The implications are that new methods and approaches have to be looked for, developed and adopted in order to understand and solve nonlinear ordinary differential equations.The purpose of this volume is to inform the mathematical community and also other scientists interested in and using the mathematical apparatus of ordinary differential equations, about some of these methods and possible applications.

    • Handbook of MRI Pulse Sequences

      • 1st Edition
      • September 7, 2004
      • Matt A. Bernstein + 2 more
      • English
      • Hardback
        9 7 8 0 1 2 0 9 2 8 6 1 3
      • eBook
        9 7 8 0 0 8 0 5 3 3 1 2 4
      Magnetic Resonance Imaging (MRI) is among the most important medical imaging techniques available today. There is an installed base of approximately 15,000 MRI scanners worldwide. Each of these scanners is capable of running many different "pulse sequences", which are governed by physics and engineering principles, and implemented by software programs that control the MRI hardware. To utilize an MRI scanner to the fullest extent, a conceptual understanding of its pulse sequences is crucial. Handbook of MRI Pulse Sequences offers a complete guide that can help the scientists, engineers, clinicians, and technologists in the field of MRI understand and better employ their scanner.

    • Krylov Solvers for Linear Algebraic Systems

      • 1st Edition
      • Volume 11
      • September 8, 2004
      • Charles George Broyden + 1 more
      • English
      • Paperback
        9 7 8 0 4 4 4 5 4 0 3 0 0
      • eBook
        9 7 8 0 0 8 0 4 7 8 8 7 6
      The first four chapters of this book give a comprehensive and unified theory of the Krylov methods. Many of these are shown to be particular examples ofthe block conjugate-gradient algorithm and it is this observation thatpermits the unification of the theory. The two major sub-classes of thosemethods, the Lanczos and the Hestenes-Stiefel, are developed in parallel asnatural generalisations of the Orthodir (GCR) and Orthomin algorithms. Theseare themselves based on Arnoldi's algorithm and a generalised Gram-Schmidtalgorith... and their properties, in particular their stability properties,are determined by the two matrices that define the block conjugate-gradiental... These are the matrix of coefficients and the preconditioningmatri... Chapter 5 the"transpose-free" algorithms based on the conjugate-gradient squared algorithm are presented while Chapter 6 examines the various ways in which the QMR technique has been exploited. Look-ahead methods and general block methods are dealt with in Chapters 7 and 8 while Chapter 9 is devoted to error analysis of two basic algorithms.In Chapter 10 the results of numerical testing of the more important algorithms in their basic forms (i.e. without look-ahead or preconditioning) are presented and these are related to the structure of the algorithms and the general theory. Graphs illustrating the performances of various algorithm/problem combinations are given via a CD-ROM.Chapter 11, by far the longest, gives a survey of preconditioning techniques. These range from the old idea of polynomial preconditioning via SOR and ILU preconditioning to methods like SpAI, AInv and the multigrid methods that were developed specifically for use with parallel computers. Chapter 12 is devoted to dual algorithms like Orthores and the reverse algorithms of Hegedus. Finally certain ancillary matters like reduction to Hessenberg form, Chebychev polynomials and the companion matrix are described in a series of appendices.

    • Computational Models for the Human Body: Special Volume

      • 1st Edition
      • Volume 12
      • July 16, 2004
      • Nicholas Philippe Ayache
      • English
      • Hardback
        9 7 8 0 4 4 4 5 1 5 6 6 7
      Provides a better understanding of the physiological and mechanical behaviour of the human body and the design of tools for their realistic numerical simulations, including concrete examples of such computational models. This book covers a large range of methods and an illustrative set of applications.

    • Random Matrices

      • 3rd Edition
      • Volume 142
      • October 6, 2004
      • Madan Lal Mehta
      • English
      • Paperback
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      • Hardback
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      • eBook
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      Random Matrices gives a coherent and detailed description of analytical methods devised to study random matrices. These methods are critical to the understanding of various fields in in mathematics and mathematical physics, such as nuclear excitations, ultrasonic resonances of structural materials, chaotic systems, the zeros of the Riemann and other zeta functions. More generally they apply to the characteristic energies of any sufficiently complicated system and which have found, since the publication of the second edition, many new applications in active research areas such as quantum gravity, traffic and communications networks or stock movement in the financial markets. This revised and enlarged third edition reflects the latest developements in the field and convey a greater experience with results previously formulated. For example, the theory of skew-orthogoanl and bi-orthogonal polynomials, parallel to that of the widely known and used orthogonal polynomials, is explained here for the first time.

    • Infinitesimal Methods of Mathematical Analysis

      • 1st Edition
      • May 1, 2004
      • J S Pinto
      • English
      • Paperback
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      • eBook
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      This modern introduction to infinitesimal methods is a translation of the book Métodos Infinitesimais de Análise Matemática by José Sousa Pinto of the University of Aveiro, Portugal and is aimed at final year or graduate level students with a background in calculus. Surveying modern reformulations of the infinitesimal concept with a thoroughly comprehensive exposition of important and influential hyperreal numbers, the book includes previously unpublished material on the development of hyperfinite theory of Schwartz distributions and its application to generalised Fourier transforms and harmonic analysis. This translation by Roy Hoskins was also greatly assisted by the comments and constructive criticism of Professor Victor Neves, of the University of Aveiro.

    • Handbook of Differential Equations: Stationary Partial Differential Equations

      • 1st Edition
      • July 6, 2004
      • Michel Chipot + 1 more
      • English
      • Hardback
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      • eBook
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      The book could be a good companion for any graduate student in partial differential equations or in applied mathematics. Each chapter brings indeed new ideas and new techniques which can be used in these fields. The differents chapters can be read independently and are of great pedagogical value. The advanced researcher will find along the book the most recent achievements in various fields.

    • Control and Optimal Control Theories with Applications

      • 1st Edition
      • December 1, 2004
      • D N Burghes + 1 more
      • English
      • Paperback
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      • eBook
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      This sound introduction to classical and modern control theory concentrates on fundamental concepts. Employing the minimum of mathematical elaboration, it investigates the many applications of control theory to varied and important present-day problems, e.g. economic growth, resource depletion, disease epidemics, exploited population, and rocket trajectories. An original feature is the amount of space devoted to the important and fascinating subject of optimal control. The work is divided into two parts. Part one deals with the control of linear time-continuous systems, using both transfer function and state-space methods. The ideas of controllability, observability and minimality are discussed in comprehensible fashion. Part two introduces the calculus of variations, followed by analysis of continuous optimal control problems. Each topic is individually introduced and carefully explained with illustrative examples and exercises at the end of each chapter to help and test the reader’s understanding. Solutions are provided at the end of the book.

    • Differential Equations with Mathematica

      • 3rd Edition
      • February 2, 2004
      • Martha L. Abell + 1 more
      • English
      • Paperback
        9 7 8 0 1 2 0 4 1 5 6 2 5
      • eBook
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      The Third Edition of the Differential Equations with Mathematica integrates new applications from a variety of fields,especially biology, physics, and engineering. The new handbook is also completely compatible with recent versions of Mathematica and is a perfect introduction for Mathematica beginners.

Related subjects

Mathematics and applied mathematics

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