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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.

  • Computational Models for the Human Body: Special Volume

    • 1st Edition
    • Volume 12
    • Nicholas Philippe Ayache
    • English
    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.

  • Handbook of Differential Equations: Stationary Partial Differential Equations

    • 1st Edition
    • Michel Chipot + 1 more
    • English
    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.

  • Stochastic Processes

    Estimation, Optimisation and Analysis
    • 1st Edition
    • Kaddour Najim + 2 more
    • English
    A ‘stochastic’ process is a ‘random’ or ‘conjectural’ process, and this book is concerned with applied probability and statistics. Whilst maintaining the mathematical rigour this subject requires, it addresses topics of interest to engineers, such as problems in modelling, control, reliability maintenance, data analysis and engineering involvement with insurance.This book deals with the tools and techniques used in the stochastic process – estimation, optimisation and recursive logarithms – in a form accessible to engineers and which can also be applied to Matlab. Amongst the themes covered in the chapters are mathematical expectation arising from increasing information patterns, the estimation of probability distribution, the treatment of distribution of real random phenomena (in engineering, economics, biology and medicine etc), and expectation maximisation. The latter part of the book considers optimization algorithms, which can be used, for example, to help in the better utilization of resources, and stochastic approximation algorithms, which can provide prototype models in many practical applications.

  • Principles of Mathematical Modeling

    • 2nd Edition
    • Clive Dym
    • English
    Science and engineering students depend heavily on concepts of mathematical modeling. In an age where almost everything is done on a computer, author Clive Dym believes that students need to understand and "own" the underlying mathematics that computers are doing on their behalf. His goal for Principles of Mathematical Modeling, Second Edition, is to engage the student reader in developing a foundational understanding of the subject that will serve them well into their careers. The first half of the book begins with a clearly defined set of modeling principles, and then introduces a set of foundational tools including dimensional analysis, scaling techniques, and approximation and validation techniques. The second half demonstrates the latest applications for these tools to a broad variety of subjects, including exponential growth and decay in fields ranging from biology to economics, traffic flow, free and forced vibration of mechanical and other systems, and optimization problems in biology, structures, and social decision making. Prospective students should have already completed courses in elementary algebra, trigonometry, and first-year calculus and have some familiarity with differential equations and basic physics.

  • Nonmeasurable Sets and Functions

    • 1st Edition
    • Volume 195
    • Alexander Kharazishvili
    • English
    The book is devoted to various constructions of sets which are nonmeasurable with respect to invariant (more generally, quasi-invariant) measures. Our starting point is the classical Vitali theorem stating the existence of subsets of the real line which are not measurable in the Lebesgue sense. This theorem stimulated the development of the following interesting topics in mathematics:1. Paradoxical decompositions of sets in finite-dimensional Euclidean spaces;2. The theory of non-real-valued-meas... cardinals;3. The theory of invariant (quasi-invariant)ext... of invariant (quasi-invariant) measures.These topics are under consideration in the book. The role of nonmeasurable sets (functions) in point set theory and real analysis is underlined and various classes of such sets (functions) are investigated . Among them there are: Vitali sets, Bernstein sets, Sierpinski sets, nontrivial solutions of the Cauchy functional equation, absolutely nonmeasurable sets in uncountable groups, absolutely nonmeasurable additive functions, thick uniform subsets of the plane, small nonmeasurable sets, absolutely negligible sets, etc. The importance of properties of nonmeasurable sets for various aspects of the measure extension problem is shown. It is also demonstrated that there are close relationships between the existence of nonmeasurable sets and some deep questions of axiomatic set theory, infinite combinatorics, set-theoretical topology, general theory of commutative groups. Many open attractive problems are formulated concerning nonmeasurable sets and functions.

  • Advances in Computers

    Architectural Issues
    • 1st Edition
    • Volume 61
    • Marvin Zelkowitz
    • English
    Advances in Computers covers new developments in computer technology. Most chapters present an overview of a current subfield within computer science, with many citations, and often include new developments in the field by the authors of the individual chapters. Topics include hardware, software, theoretical underpinnings of computing, and novel applications of computers. This current volume emphasizes architectural issues in the design of new hardware and software system. An architectural design evaluation process is described that allows developers to make sure that their source programs adhere to the architectural design of the specifications. This greatly aids in the maintenance of the system. Telecommunications issues are covered from the impact of new technology to security of wireless systems. Quantum computing, an exciting development that may greatly increase the speed of present computers, is described. The book series is a valuable addition to university courses that emphasize the topics under discussion in that particular volume as well as belonging on the bookshelf of industrial practitioners who need to implement many of the technologies that are described.

  • Parallel Computational Fluid Dynamics 2003

    Advanced Numerical Methods, Software and Applications
    • 1st Edition
    • Boris Chetverushkin + 3 more
    • English
    The book is devoted to using of parallel multiprocessor computer systems for numerical simulation of the problems which can be described by the equations of continuum mechanics. Parallel algorithms and software, the problems of meta-computing are discussed in details, some results of high performance simulation of modern gas dynamic problems, combustion phenomena, plasma physics etc are presented.

  • Infinitesimal Methods of Mathematical Analysis

    • 1st Edition
    • J S Pinto
    • English
    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.

  • Advances in Computers

    Information Security
    • 1st Edition
    • Volume 60
    • Marvin Zelkowitz
    • English
    Advances in Computers covers new developments in computer technology. Most chapters present an overview of a current subfield within computers, with many citations, and often include new developments in the field by the authors of the individual chapters. Topics include hardware, software, theoretical underpinnings of computing, and novel applications of computers. This current volume emphasizes information security issues and includes topics like certifying computer professionals, non-invasive attacks ("cognitive hacking"), computer files as legal evidence ("computer forensics") and the use of processors on plastic ("smartcards"). The book series is a valuable addition to university courses that emphasize the topics under discussion in that particular volume as well as belonging on the bookshelf of industrial practitioners who need to implement many of the technologies that are described.

  • Mathematics of Optimization: Smooth and Nonsmooth Case

    • 1st Edition
    • Giorgio Giorgi + 2 more
    • English
    The book is intended for people (graduates, researchers, but also undergraduates with a good mathematical background) involved in the study of (static) optimization problems (in finite-dimensional spaces). It contains a lot of material, from basic tools of convex analysis to optimality conditions for smooth optimization problems, for non smooth optimization problems and for vector optimization problems.The development of the subjects are self-contained and the bibliographical references are usually treated in different books (only a few books on optimization theory deal also with vector problems), so the book can be a starting point for further readings in a more specialized literature.Assuming only a good (even if not advanced) knowledge of mathematical analysis and linear algebra, this book presents various aspects of the mathematical theory in optimization problems. The treatment is performed in finite-dimensional spaces and with no regard to algorithmic questions. After two chapters concerning, respectively, introductory subjects and basic tools and concepts of convex analysis, the book treats extensively mathematical programming problems in the smmoth case, in the nonsmooth case and finally vector optimization problems.

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