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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.

  • Introduction to Abstract Algebra

    • 6th Edition
    • Neil McCoy + 1 more
    • English
    A revision of McCoy's classic text, Introductory Abstract Algebra, Sixth Edition, retains the goals of earlier editions by providing the key information for a first course in abstract algebra in an easily understood, digestible manner. The material in the sixth edition is kept at approximately the same level as that in the previous editions with a number of comments, remarks, and exercises that point students toward more advanced topics. Rings are presented before groups because the ring of integers is already known to students and easily serves as a source of examples.

  • Rudiments of Calculus

    • 1st Edition
    • Volume 146
    • A. Arnold + 1 more
    • English
    This book presents what in our opinion constitutes the basis of the theory of the mu-calculus, considered as an algebraic system rather than a logic. We have wished to present the subject in a unified way, and in a form as general as possible. Therefore, our emphasis is on the generality of the fixed-point notation, and on the connections between mu-calculus, games, and automata, which we also explain in an algebraic way. This book should be accessible for graduate or advanced undergraduate students both in mathematics and computer science. We have designed this book especially for researchers and students interested in logic in computer science, comuter aided verification, and general aspects of automata theory. We have aimed at gathering in a single place the fundamental results of the theory, that are currently very scattered in the literature, and often hardly accessible for interested readers. The presentation is self-contained, except for the proof of the Mc-Naughton's Determinization Theorem (see, e.g., [97]. However, we suppose that the reader is already familiar with some basic automata theory and universal algebra. The references, credits, and suggestions for further reading are given at the end of each chapter.

  • Mathematical Methods for Physicists

    • 5th Edition
    • George B. Arfken + 1 more
    • English
    Through four editions, Arfken and Weber's best-selling Mathematical Methods for Physicists has provided upper-level undergraduate and graduate students with the paramount coverage of the mathematics necessary for advanced study in physics and engineering. It provides the essential mathematical methods that aspiring physicists are likely to encounter as students or beginning researchers. Appropriate for a physics service course, as well as for more advanced coursework, this is the book of choice in the field.

  • The Theory of Fractional Powers of Operators

    • 1st Edition
    • Volume 187
    • C. Martinez + 1 more
    • English
    This book makes available to researchers and advanced graduates a simple and direct presentation of the fundamental aspects of the theory of fractional powers of non-negative operators, which have important links with partial differential equations and harmonic analysis. For the first time ever, a book deals with this subject monographically, despite the large number of papers written on it during the second half of the century. The first chapters are concerned with the construction of a basic theory of fractional powers and study the classic questions in that respect. A new and distinct feature is that the approach adopted has allowed the extension of this theory to locally convex spaces, thereby including certain differential operators, which appear naturally in distribution spaces. The bulk of the second part of the book is dedicated to powers with pure imaginary exponents, which have been the focus of research in recent years, ever since the publication in 1987 of the now classic paper by G.Dore and A.Venni. Special care has been taken to give versions of the results with more accurate hypotheses, particularly with respect to the density of the domain or the range of the operator. The authors have made a point of making the text clear and self-contained. Accordingly, an extensive appendix contains the material on real and functional analysis used and, at the end of each chapter there are detailed historical and bibliographical notes in order to understand the development and current state of research into the questions dealt with.

  • Geometry with Trigonometry

    • 1st Edition
    • Patrick D Barry
    • English
    This book addresses a neglected mathematical area where basic geometry underpins undergraduate and graduate courses. Its interdisciplinary portfolio of applications includes computational geometry, differential geometry, mathematical modelling, computer science, computer-aided design of systems in mechanical, structural and other engineering, and architecture. Professor Barry, from his long experience of teaching and research, here delivers a modern and coherent exposition of this subject area for varying levels in mathematics, applied mathematics, engineering mathematics and other areas of application. Euclidean geometry is neglected in university courses or scattered over a number of them. This text emphasises a systematic and complete build-up of material, moving from pure geometrical reasoning aided by algebra to a blend of analytic geometry and vector methods with trigonometry, always with a view to efficiency. The text starts with a selection of material from the essentials of Euclidean geometry at A level, and ends with an introduction to trigonometric functions in calculus.Very many geometric diagrams are provided for a clear understanding of the text, with abundant Problem Exercises for each chapter. Students, researchers and industrial practitioners would benefit from this sustained mathematisation of shapes and magnitude from the real world of science which can raise and help their mathematical awareness and ability.

  • Introduction to Feedback Control

    • 1st Edition
    • Kirsten A. Morris
    • English
    What is often referred to as industrial mathematics is becoming a more important focus of applied mathematics. An increased interest in undergraduate control theory courses for mathematics students is part of this trend. This is due to the fact that control theory is both quite mathematical and very important in applications. Introduction to Feedback Control provides a rigorous introduction to input/output, controller design for linear systems to junior/senior level engineering and mathematics students. All explanations and most examples are single-input, single-output for ease of exposition. The student is assumed to have knowledge of linear ordinary differential equations and complex variables.

  • Interpolation and Extrapolation

    • 1st Edition
    • Volume 2
    • C. Brezinski
    • English
    /homepage/sac/cam/na... Set now available at special set price!This volume is dedicated to two closely related subjects: interpolation and extrapolation. The papers can be divided into three categories: historical papers, survey papers and papers presenting new developments.Interpo... is an old subject since, as noticed in the paper by M. Gasca and T. Sauer, the term was coined by John Wallis in 1655. Interpolation was the first technique for obtaining an approximation of a function. Polynomial interpolation was then used in quadrature methods and methods for the numerical solution of ordinary differential equations.Extrapolat... is based on interpolation. In fact, extrapolation consists of interpolation at a point outside the interval containing the interpolation points. Usually, this point is either zero or infinity. Extrapolation is used in numerical analysis to improve the accuracy of a process depending of a parameter or to accelerate the convergence of a sequence. The most well-known extrapolation processes are certainly Romberg's method for improving the convergence of the trapezoidal rule for the computation of a definite integral and Aiken's &Dgr;2 process which can be found in any textbook of numerical analysis.Obviously, all aspects of interpolation and extrapolation have not been treated in this volume. However, many important topics have been covered.

  • Homology

    The Hierarchical Basis of Comparative Biology
    • 1st Edition
    • Brian K. Hall
    • English
    The application of homology varies depending on the data being examined. This volume represents a state-of-the-art treatment of the different applications of this unifying concept. Chapters deal with homology on all levels, from molecules to behavior, and are authored by leading contributors to systematics, natural history, and evolutionary, developmental, and comparative biology. This paperback reprint of the original hardbound edition continues to commemorate the 150th anniversary of Sir Richard Owen's seminal paper distinguishing homology from analogy.

  • A Matlab Companion for Multivariable Calculus

    • 1st Edition
    • Jeffery Cooper
    • English
    Offering a concise collection of MatLab programs and exercises to accompany a third semester course in multivariable calculus, A MatLab Companion for Multivariable Calculus introduces simple numerical procedures such as numerical differentiation, numerical integration and Newton's method in several variables, thereby allowing students to tackle realistic problems. The many examples show students how to use MatLab effectively and easily in many contexts. Numerous exercises in mathematics and applications areas are presented, graded from routine to more demanding projects requiring some programming. Matlab M-files are provided on the Harcourt/Academic Press web site at http://www.harcourt-...

  • Theory of Relations

    • 1st Edition
    • Volume 145
    • R. Fraisse
    • English
    Relation theory originates with Hausdorff (Mengenlehre 1914) and Sierpinski (Nombres transfinis, 1928) with the study of order types, specially among chains = total orders = linear orders. One of its first important problems was partially solved by Dushnik, Miller 1940 who, starting from the chain of reals, obtained an infinite strictly decreasing sequence of chains (of continuum power) with respect to embeddability. In 1948 I conjectured that every strictly decreasing sequence of denumerable chains is finite. This was affirmatively proved by Laver (1968), in the more general case of denumerable unions of scattered chains (ie: which do not embed the chain Q of rationals), by using the barrier and the better orderin gof Nash-Williams (1965 to 68).Another important problem is the extension to posets of classical properties of chains. For instance one easily sees that a chain A is scattered if the chain of inclusion of its initial intervals is itself scattered (6.1.4). Let us again define a scattered poset A by the non-embedding of Q in A. We say that A is finitely free if every antichain restriction of A is finite (antichain = set of mutually incomparable elements of the base). In 1969 Bonnet and Pouzet proved that a poset A is finitely free and scattered iff the ordering of inclusion of initial intervals of A is scattered. In 1981 Pouzet proved the equivalence with the a priori stronger condition that A is topologically scattered: (see 6.7.4; a more general result is due to Mislove 1984); ie: every non-empty set of initial intervals contains an isolated elements for the simple convergence topology.In chapter 9 we begin the general theory of relations, with the notions of local isomorphism, free interpretability and free operator (9.1 to 9.3), which is the relationist version of a free logical formula. This is generalized by the back-and-forth notions in 10.10: the (k,p)-operator is the relationist version of the elementary formula (first order formula with equality).Chapter 12 connects relation theory with permutations: theorem of the increasing number of orbits (Livingstone, Wagner in 12.4). Also in this chapter homogeneity is introduced, then more deeply studied in the Appendix written by Norbert Saucer.Chapter 13 connects relation theory with finite permutation groups; the main notions and results are due to Frasnay. Also mention the extension to relations of adjacent elements, by Hodges, Lachlan, Shelah who by this mean give an exact calculus of the reduction threshold.The book covers almost all present knowledge in Relation Theory, from origins (Hausdorff 1914, Sierpinski 1928) to classical results (Frasnay 1965, Laver 1968, Pouzet 1981) until recent important publications (Abraham, Bonnet 1999).All results are exposed in axiomatic set theory. This allows us, for each statement, to specify if it is proved only from ZF axioms of choice, the continuum hypothesis or only the ultrafilter axiom or the axiom of dependent choice, for instance.

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