Skip to main content
Elsevier
View Cart

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.

  • Algebra of Proofs

    • 1st Edition
    • M. E. Szabo
    • K. J. Barwise + 2 more
    • English
    Algebra of Proofs deals with algebraic properties of the proof theory of intuitionist first-order logic in a categorical setting. The presentation is based on the confluence of ideas and techniques from proof theory, category theory, and combinatory logic. The conceptual basis for the text is the Lindenbaum-Tarski algebras of formulas taken as categories. The formal proofs of the associated deductive systems determine structured categories as their canonical algebras (which are of the same type as the Lindenbaum-Tarski algebras of the formulas of underlying languages). Gentzen's theorem, which asserts that provable formulas code their own proofs, links the algebras of formulas and the corresponding algebras of formal proofs. The book utilizes the Gentzen's theorem and the reducibility relations with the Church-Rosser property as syntactic tools. The text explains two main types of theories with varying linguistic complexity and deductive strength: the monoidal type and the Cartesian type. It also shows that quantifiers fit smoothly into the calculus of adjoints and describe the topos-theoretical setting in which the proof theory of intuitionist first-order logic possesses a natural semantics. The text can benefit mathematicians, students, or professors of algebra and advanced mathematics.

  • Topological Vector Spaces, Distributions and Kernels

    Pure and Applied Mathematics, Vol. 25
    • 1st Edition
    • François Treves
    • Paul A. Smith + 1 more
    • English
    Topological Vector Spaces, Distributions and Kernels discusses partial differential equations involving spaces of functions and space distributions. The book reviews the definitions of a vector space, of a topological space, and of the completion of a topological vector space. The text gives examples of Frechet spaces, Normable spaces, Banach spaces, or Hilbert spaces. The theory of Hilbert space is similar to finite dimensional Euclidean spaces in which they are complete and carry an inner product that can determine their properties. The text also explains the Hahn-Banach theorem, as well as the applications of the Banach-Steinhaus theorem and the Hilbert spaces. The book discusses topologies compatible with a duality, the theorem of Mackey, and reflexivity. The text describes nuclear spaces, the Kernels theorem and the nuclear operators in Hilbert spaces. Kernels and topological tensor products theory can be applied to linear partial differential equations where kernels, in this connection, as inverses (or as approximations of inverses), of differential operators. The book is suitable for vector mathematicians, for students in advanced mathematics and physics.

  • Solution of Equations and Systems of Equations

    Pure and Applied Mathematics: A Series of Monographs and Textbooks, Vol. 9
    • 2nd Edition
    • A. M. Ostrowski
    • Paul A. Smith + 1 more
    • English
    Solution of Equations and Systems of Equations, Second Edition deals with the Laguerre iteration, interpolating polynomials, method of steepest descent, and the theory of divided differences. The book reviews the formula for confluent divided differences, Newton's interpolation formula, general interpolation problems, and the triangular schemes for computing divided differences. The text explains the method of False Position (Regula Falsi) and cites examples of computation using the Regula Falsi. The book discusses iterations by monotonic iterating functions and analyzes the connection of the Regula Falsi with the theory of iteration. The text also explains the idea of the Newton-Raphson method and compares it with the Regula Falsi. The book also cites asymptotic behavior of errors in the Regula Falsi iteration, as well as the theorem on the error of the Taylor approximation to the root. The method of steepest descent or gradient method proposed by Cauchy ensures "global convergence" in very general conditions. This book is suitable for mathematicians, students, and professor of calculus, and advanced mathematics.

  • Structural Design and Analysis

    Composite Materials, Vol. 8
    • 1st Edition
    • C. C. Chamis
    • English
    Composite Materials, Volume 8: Structural Design and Analysis, Part II covers the methods of structural design and analysis. The book discusses the discrete element analysis of composite structures; the concepts of probabilistic design and reliability as it pertains to composites; and the experimental methods for characterizing composites and composite components. The text also describes the state-of-the-art of the analysis of discontinuities, edge effects, and joints in composites; as well as the methodology for designing composite structural components. Materials scientists, materials engineers, and researchers of fiber composites will find the book invaluable.

  • Treatise on Analysis

    • 1st Edition
    • J. Dieudonné
    • H. Bass + 2 more
    • English
    Treatise on Analysis, Volume 10–VIII provides information pertinent to the study of the most common boundary problems for partial differential equations. This book presents the study of Cauchy's problem in its most elementary form. Comprised of one chapter, this volume begins with an overview of Hilbert-von Neumann spectral theory and explores all possible boundary conditions related to spectral theory. This text then examines the link of Cauchy's problem with the behavior of the equation's characteristics. This book discusses as well the case of linear elliptic operators. The reader is also introduced to Sobolev spaces and some of their generalizations that provide an essential tool in the study of these elliptic problems, and their manipulation requires delicate upper bounds to obtain the best possible results. This book is a valuable resource for mathematicians.

  • Advanced Topics in the Theory of Dynamical Systems

    Notes and Reports in Mathematics in Science and Engineering, Vol. 6
    • 1st Edition
    • G. Fusco + 2 more
    • English
    Advanced Topics in the Theory of Dynamical Systems covers the proceedings of the international conference by the same title, held at Villa Madruzzo, Trento, Italy on June 1-6, 1987. The conference reviews research advances in the field of dynamical systems. This book is composed of 20 chapters that explore the theoretical aspects and problems arising from applications of these systems. Considerable chapters are devoted to finite dimensional systems, with special emphasis on the analysis of existence of periodic solutions to Hamiltonian systems. Other chapters deal with infinite dimensional systems and the developments of methods in the general approach to existence and qualitative analysis problems in the general theory, as well as in the study of particular systems concerning natural sciences. The final chapters discuss the properties of hyperbolic sets, equivalent period doubling, Cauchy problems, and quasiperiodic solitons for nonlinear Klein-Gordon equations. This book is of value to mathematicians, physicists, researchers, and advance students.

  • Semihypergroup Theory

    • 1st Edition
    • Bijan Davvaz
    • English
    Semihypergroup Theory is the first book devoted to the semihypergroup theory and it includes basic results concerning semigroup theory and algebraic hyperstructures, which represent the most general algebraic context in which reality can be modelled. Hyperstructures represent a natural extension of classical algebraic structures and they were introduced in 1934 by the French mathematician Marty. Since then, hundreds of papers have been published on this subject.

  • Theory and Methods of Statistics

    • 1st Edition
    • P.K. Bhattacharya + 1 more
    • English
    Theory and Methods of Statistics covers essential topics for advanced graduate students and professional research statisticians. This comprehensive resource covers many important areas in one manageable volume, including core subjects such as probability theory, mathematical statistics, and linear models, and various special topics, including nonparametrics, curve estimation, multivariate analysis, time series, and resampling. The book presents subjects such as "maximum likelihood and sufficiency," and is written with an intuitive, heuristic approach to build reader comprehension. It also includes many probability inequalities that are not only useful in the context of this text, but also as a resource for investigating convergence of statistical procedures.

  • Poincaré-Andronov-Melnikov Analysis for Non-Smooth Systems

    • 1st Edition
    • Michal Feckan + 1 more
    • English
    Poincaré-Andronov-Me... Analysis for Non-Smooth Systems is devoted to the study of bifurcations of periodic solutions for general n-dimensional discontinuous systems. The authors study these systems under assumptions of transversal intersections with discontinuity-switch... boundaries. Furthermore, bifurcations of periodic sliding solutions are studied from sliding periodic solutions of unperturbed discontinuous equations, and bifurcations of forced periodic solutions are also investigated for impact systems from single periodic solutions of unperturbed impact equations. In addition, the book presents studies for weakly coupled discontinuous systems, and also the local asymptotic properties of derived perturbed periodic solutions. The relationship between non-smooth systems and their continuous approximations is investigated as well. Examples of 2-, 3- and 4-dimensional discontinuous ordinary differential equations and impact systems are given to illustrate the theoretical results. The authors use so-called discontinuous Poincaré mapping which maps a point to its position after one period of the periodic solution. This approach is rather technical, but it does produce results for general dimensions of spatial variables and parameters as well as the asymptotical results such as stability, instability, and hyperbolicity.

  • Newnes Circuit Calculations Pocket Book

    with Computer Programs
    • 1st Edition
    • Thomas J. Davies
    • English
    Newnes Circuit Calculations Pocket Book: With Computer Programs presents equations, examples, and problems in circuit calculations. The text includes 300 computer programs that help solve the problems presented. The book is comprised of 20 chapters that tackle different aspects of circuit calculation. The coverage of the text includes dc voltage, dc circuits, and network theorems. The book also covers oscillators, phasors, and transformers. The text will be useful to electrical engineers and other professionals whose work involves electronic circuitry.

Related subjects