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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.

  • Geometric Measure Theory

    A Beginner's Guide
    • 3rd Edition
    • Frank Morgan
    • English
    Geometric measure theory has become increasingly essential to geometry as well as numerous and varied physical applications. The third edition of this leading text/reference introduces the theory, the framework for the study of crystal growth, clusters of soap bubbles, and similar structures involving minimization of energy. Over the past thirty years, this theory has contributed to major advances in geometry and analysis including, for example, the original proof of the positive mass conjecture in cosmology.This third edition of Geometric Measure Theory: A Beginner's Guide presents, for the first time in print, the proofs of the double bubble and the hexagonal honeycomb conjectures. Four new chapters lead the reader through treatments of the Weaire-Phelan counterexample of Kelvin's conjecture, Almgren's optimal isoperimetric inequality, and immiscible fluids and crystals. The abundant illustrations, examples, exercises, and solutions in this book will enhance its reputation as the most accessible introduction to the subject.

  • Power Geometry in Algebraic and Differential Equations

    • 1st Edition
    • Volume 57
    • A.D. Bruno
    • English
    The geometry of power exponents includes the Newton polyhedron, normal cones of its faces, power and logarithmic transformations. On the basis of the geometry universal algorithms for simplifications of systems of nonlinear equations (algebraic, ordinary differential and partial differential) were developed.The algorithms form a new calculus which allows to make local and asymptotical analysis of solutions to those systems.The efficiency of the calculus is demonstrated with regard to several complicated problems from Robotics, Celestial Mechanics, Hydrodynamics and Thermodynamics. The calculus also gives classical results obtained earlier intuitively and is an alternative to Algebraic Geometry, Differential Algebra, Lie group Analysis and Nonstandard Analysis.

  • Mathematics Mechanization and Applications

    • 1st Edition
    • Dongming Wang + 1 more
    • English
    Mathematics Mechanization and Applications provides a uniform presentation of major developments, carried out mostly in Wu's extended Chinese group, on algorithms and software tools for mechanizing algebraic equations solving and geometric theorem proving together with their applications to problems in science and engineering. It is distinguished by its uniform presentation with all-Chinese contributors and a 40-page list of references. There are 20 chapters written by experienced researchers. The book is divided into four parts: polynomial system solving, automated geometric reasoning, algebraic computation, and implementations and applications. Each chapter is devoted to surveying and expounding the main results achieved from one selected subject. The book contains surveys for diverse applications of the theories and methods to real world problems, ranging from the analysis of robotics and mechanisms to nonlinear programming and chemical equilibrium computation. Part of the theoretical and practical work reviewed in the book has been either unpublished or published only in Chinese journals or even only in the Chinese language. This book therefore provides Western readers working in symbolic and algebraic computation, geometric reasoning and modeling, algorithmic mathematics, robotics, CAGD, and other relevant areas with an easily accessible source of references for what the Chinese researchers have been doing under the banner of mathematics mechanization.

  • Computable Structures and the Hyperarithmetical Hierarchy

    • 1st Edition
    • Volume 144
    • C.J. Ash + 1 more
    • English
    This book describes a program of research in computable structure theory. The goal is to find definability conditions corresponding to bounds on complexity which persist under isomorphism. The results apply to familiar kinds of structures (groups, fields, vector spaces, linear orderings Boolean algebras, Abelian p-groups, models of arithmetic). There are many interesting results already, but there are also many natural questions still to be answered. The book is self-contained in that it includes necessary background material from recursion theory (ordinal notations, the hyperarithmetical hierarchy) and model theory (infinitary formulas, consistency properties).

  • Introductory Analysis

    A Deeper View of Calculus
    • 1st Edition
    • Richard J. Bagby
    • English
    Introductory Analysis addresses the needs of students taking a course in analysis after completing a semester or two of calculus, and offers an alternative to texts that assume that math majors are their only audience. By using a conversational style that does not compromise mathematical precision, the author explains the material in terms that help the reader gain a firmer grasp of calculus concepts.

  • Linear Algebra and Linear Operators in Engineering

    With Applications in Mathematica®
    • 1st Edition
    • Volume 3
    • H. Ted Davis + 1 more
    • English
    Designed for advanced engineering, physical science, and applied mathematics students, this innovative textbook is an introduction to both the theory and practical application of linear algebra and functional analysis. The book is self-contained, beginning with elementary principles, basic concepts, and definitions. The important theorems of the subject are covered and effective application tools are developed, working up to a thorough treatment of eigenanalysis and the spectral resolution theorem. Building on a fundamental understanding of finite vector spaces, infinite dimensional Hilbert spaces are introduced from analogy. Wherever possible, theorems and definitions from matrix theory are called upon to drive the analogy home. The result is a clear and intuitive segue to functional analysis, culminating in a practical introduction to the functional theory of integral and differential operators. Numerous examples, problems, and illustrations highlight applications from all over engineering and the physical sciences. Also included are several numerical applications, complete with Mathematica solutions and code, giving the student a "hands-on" introduction to numerical analysis. Linear Algebra and Linear Operators in Engineering is ideally suited as the main text of an introductory graduate course, and is a fine instrument for self-study or as a general reference for those applying mathematics.

  • Difference Equations

    An Introduction with Applications
    • 2nd Edition
    • Walter G. Kelley + 1 more
    • English
    Difference Equations, Second Edition, presents a practical introduction to this important field of solutions for engineering and the physical sciences. Topic coverage includes numerical analysis, numerical methods, differential equations, combinatorics and discrete modeling. A hallmark of this revision is the diverse application to many subfields of mathematics.

  • Handbook of Applied Multivariate Statistics and Mathematical Modeling

    • 1st Edition
    • Howard E.A. Tinsley + 1 more
    • English
    Multivariate statistics and mathematical models provide flexible and powerful tools essential in most disciplines. Nevertheless, many practicing researchers lack an adequate knowledge of these techniques, or did once know the techniques, but have not been able to keep abreast of new developments. The Handbook of Applied Multivariate Statistics and Mathematical Modeling explains the appropriate uses of multivariate procedures and mathematical modeling techniques, and prescribe practices that enable applied researchers to use these procedures effectively without needing to concern themselves with the mathematical basis. The Handbook emphasizes using models and statistics as tools. The objective of the book is to inform readers about which tool to use to accomplish which task. Each chapter begins with a discussion of what kinds of questions a particular technique can and cannot answer. As multivariate statistics and modeling techniques are useful across disciplines, these examples include issues of concern in biological and social sciences as well as the humanities.

  • Continuation of the Notas de Matemàtica

    • 1st Edition
    • Volume 177
    • Demeter Krupka
    • English
    This book provides a comprehensive introduction to modern global variational theory on fibred spaces. It is based on differentiation and integration theory of differential forms on smooth manifolds, and on the concepts of global analysis and geometry such as jet prolongations of manifolds, mappings, and Lie groups. The book will be invaluable for researchers and PhD students in differential geometry, global analysis, differential equations on manifolds, and mathematical physics, and for the readers who wish to undertake further rigorous study in this broad interdisciplinary field. Featured topics- Analysis on manifolds- Differential forms on jet spaces - Global variational functionals- Euler-Lagrange mapping - Helmholtz form and the inverse problem- Symmetries and the Noether’s theory of conservation laws- Regularity and the Hamilton theory- Variational sequences - Differential invariants and natural variational principles

  • Provability, Computability and Reflection

    • 1st Edition
    • Volume 25
    • Lev D. Beklemishev
    • English

  • Augmented Lagrangian Methods

    Applications to the Numerical Solution of Boundary-Value Problems
    • 1st Edition
    • Volume 15
    • M. Fortin + 1 more
    • English
    The purpose of this volume is to present the principles of the Augmented Lagrangian Method, together with numerous applications of this method to the numerical solution of boundary-value problems for partial differential equations or inequalities arising in Mathematical Physics, in the Mechanics of Continuous Media and in the Engineering Sciences.

  • Mathematical and Conceptual Foundations of 20th-Century Physics

    • 1st Edition
    • Volume 100
    • G.G. Emch
    • English
    This book is primarily intended for Mathematicians, but students in the physical sciences will find here information not usually available in physics texts.The main aim of this book is to provide a unified mathematical account of the conceptual foundations of 20th-Century Physics, in a form suitable for a one-year survey course in Mathematics or Mathematical Physics. Emphasis is laid on the interlocked historical development of mathematical and physical ideas.

  • Discrete Optimization I

    • 1st Edition
    • Volume 4
    • English

  • Functional Analysis: Surveys and Recent Results III

    • 1st Edition
    • Volume 90
    • K.-D. Bierstedt + 1 more
    • English
    This volume contains 22 articles on topics of current interest in functional analysis, operator theory and related areas. Some of the papers have connections with complex function theory in one and several variables, probability theory and mathematical physics.Surveys of some areas of recent progress in functional analysis are given and related new results are presented. The topics covered in this volume supplement the discussion of modern functional analysis in the previous Proceedings volumes. Together with the previous volumes, the reader obtains a good impression of many aspects of present-day functional analysis and its applications. Parts of this volume can be used profitably in advanced seminars and courses in functional analysis.

  • Introduction to Holomorphy

    • 1st Edition
    • Volume 106
    • J.A. Barroso
    • English
    This book presents a set of basic properties of holomorphic mappings between complex normed spaces and between complex locally convex spaces. These properties have already achieved an almost definitive form and should be known to all those interested in the study of infinite dimensional Holomorphy and its applications.The author also makes ``incursions'' into the study of the topological properties of the spaces of holomorphic mappings between spaces of infinite dimension. An attempt is then made to show some of the several topologies that can naturally be considered in these spaces.Infinite dimensional Holomorphy appears as a theory rich in fascinating problems and rich in applications to other branches of Mathematics and Mathematical Physics.

  • Differential Equations

    • 1st Edition
    • Volume 92
    • I.W. Knowles + 1 more
    • English
    This volume forms a record of the lectures given at this International Conference. Under the general heading of the equations of mathematical physics, contributions are included on a broad range of topics in the theory and applications of ordinary and partial differential equations, including both linear and non-linear equations. The topics cover a wide variety of methods (spectral, theoretical, variational, topological, semi-group), and a equally wide variety of equations including the Laplace equation, Navier-Stokes equations, Boltzmann's equation, reaction-diffusion equations, Schroedinger equations and certain non-linear wave equations. A number of papers are devoted to multi-particle scattering theory, and to inverse theory. In addition, many of the plenary lectures contain a significant amount of survey material on a wide variety of these topics.

  • An Algebraic Approach to Non-Classical Logics

    • 1st Edition
    • Volume 78
    • Lev D. Beklemishev
    • English

  • Provability, Computability and Reflection

    • 1st Edition
    • Volume 23
    • Lev D. Beklemishev
    • English

  • Intuitionism An Introduction

    • 1st Edition
    • Volume 41
    • Lev D. Beklemishev
    • English

  • Comparison and Oscillation Theory of Linear Differential Equations by C A Swanson

    • 1st Edition
    • Volume 48
    • English
    In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; andmethods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory.As a result, the book represents a blend of new methods in general computational analysis,and specific, but also generic, techniques for study of systems theory ant its particularbranches, such as optimal filtering and information compression.

  • Provability, Computability and Reflection

    • 1st Edition
    • Volume 29
    • Lev D. Beklemishev
    • English

  • Introduction to Global Variational Geometry

    • 1st Edition
    • Volume 183
    • Demeter Krupka
    • English
    This book provides a comprehensive introduction to modern global variational theory on fibred spaces. It is based on differentiation and integration theory of differential forms on smooth manifolds, and on the concepts of global analysis and geometry such as jet prolongations of manifolds, mappings, and Lie groups. The book will be invaluable for researchers and PhD students in differential geometry, global analysis, differential equations on manifolds, and mathematical physics, and for the readers who wish to undertake further rigorous study in this broad interdisciplinary field. Featured topics- Analysis on manifolds- Differential forms on jet spaces - Global variational functionals- Euler-Lagrange mapping - Helmholtz form and the inverse problem- Symmetries and the Noether’s theory of conservation laws- Regularity and the Hamilton theory- Variational sequences - Differential invariants and natural variational principles

  • Logic Colloquium '77

    • 1st Edition
    • Volume 96
    • Lev D. Beklemishev
    • English

  • Introduction to Global Variational Geometry

    • 1st Edition
    • Volume 17
    • Demeter Krupka
    • English
    This book provides a comprehensive introduction to modern global variational theory on fibred spaces. It is based on differentiation and integration theory of differential forms on smooth manifolds, and on the concepts of global analysis and geometry such as jet prolongations of manifolds, mappings, and Lie groups. The book will be invaluable for researchers and PhD students in differential geometry, global analysis, differential equations on manifolds, and mathematical physics, and for the readers who wish to undertake further rigorous study in this broad interdisciplinary field. Featured topics- Analysis on manifolds- Differential forms on jet spaces - Global variational functionals- Euler-Lagrange mapping - Helmholtz form and the inverse problem- Symmetries and the Noether’s theory of conservation laws- Regularity and the Hamilton theory- Variational sequences - Differential invariants and natural variational principles

  • Introduction to Global Variational Geometry

    • 1st Edition
    • Volume 16
    • Demeter Krupka
    • English
    This book provides a comprehensive introduction to modern global variational theory on fibred spaces. It is based on differentiation and integration theory of differential forms on smooth manifolds, and on the concepts of global analysis and geometry such as jet prolongations of manifolds, mappings, and Lie groups. The book will be invaluable for researchers and PhD students in differential geometry, global analysis, differential equations on manifolds, and mathematical physics, and for the readers who wish to undertake further rigorous study in this broad interdisciplinary field. Featured topics- Analysis on manifolds- Differential forms on jet spaces - Global variational functionals- Euler-Lagrange mapping - Helmholtz form and the inverse problem- Symmetries and the Noether’s theory of conservation laws- Regularity and the Hamilton theory- Variational sequences - Differential invariants and natural variational principles

  • Concepts from Tensor Analysis and Differential Geometry by Tracy Y Thomas

    • 1st Edition
    • Volume 1
    • English
    In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; andmethods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory.As a result, the book represents a blend of new methods in general computational analysis,and specific, but also generic, techniques for study of systems theory ant its particularbranches, such as optimal filtering and information compression.

  • Provability, Computability and Reflection

    • 1st Edition
    • Volume 7
    • Lev D. Beklemishev
    • English

  • Provability, Computability and Reflection

    • 1st Edition
    • Volume 22
    • Lev D. Beklemishev
    • English

  • Unification of Finite Element Methods

    • 1st Edition
    • Volume 94
    • H. Kardestuncer
    • English

  • Provability, Computability and Reflection

    • 1st Edition
    • Volume 14
    • Lev D. Beklemishev
    • English

  • Functional Analysis, Holomorphy and Approximation Theory

    • 1st Edition
    • Volume 71
    • J.A. Barroso
    • English

  • Sets and Classes on The Work by Paul Bernays

    • 1st Edition
    • Volume 84
    • Lev D. Beklemishev
    • English

  • Provability, Computability and Reflection

    • 1st Edition
    • Volume 30
    • Lev D. Beklemishev
    • English

  • Word Problems

    • 1st Edition
    • Volume 71
    • Lev D. Beklemishev
    • English

  • Generalized Recursion Theory

    • 1st Edition
    • Volume 79
    • Lev D. Beklemishev
    • English

  • Problems in the Philosophy of Science

    • 1st Edition
    • Volume 49
    • Lev D. Beklemishev
    • English

  • Provability, Computability and Reflection

    • 1st Edition
    • Volume 16
    • Lev D. Beklemishev
    • English

  • Provability, Computability and Reflection

    • 1st Edition
    • Volume 24
    • Lev D. Beklemishev
    • English

  • Algebra of Proofs

    • 1st Edition
    • Volume 88
    • Lev D. Beklemishev
    • English

  • Non-Classical Logics, Model Theory, And Computability

    • 1st Edition
    • Volume 89
    • Lev D. Beklemishev
    • English

  • Model Theory For Infinitary Logic

    • 1st Edition
    • Volume 62
    • Lev D. Beklemishev
    • English

  • Mathematical Logic in Latin America, Proceedings of the IV Latin American Symposium on Mathematical Logic

    • 1st Edition
    • Volume 99
    • Lev D. Beklemishev
    • English

  • Families of Curves and the Origins of Partial Differentiation

    • 1st Edition
    • Volume 93
    • S.B. Engelsman
    • English
    This book provides a detailed description of the main episodes in the emergence of partial differentiation during the period 1690-1740. It argues that the development of this concept - to a considerable degree of perfection - took place almost exclusively in problems concerning families of curves. Thus, the book shows the origins of the ideas and techniques which paved the way for the sudden introduction of partial differential equations in 1750. The main methodological characteristic of the book is its emphasis on a full understanding of the motives, problems and goals of the mathematicians of that time.

  • Set Theory

    • 1st Edition
    • Volume 76
    • Lev D. Beklemishev
    • English

  • Computational Techniques for Differential Equations

    • 1st Edition
    • Volume 83
    • J. Noye
    • English

  • Provability, Computability and Reflection

    • 1st Edition
    • Volume 17
    • Lev D. Beklemishev
    • English

  • Logic Colloquium '87

    • 1st Edition
    • Volume 129
    • H.-D. Ebbinghaus + 4 more
    • English
    Fourteen papers presented at the 1987 European Summer Meeting of the Association for Symbolic Logic are collected in this volume.The main areas covered by the conference were Logic, Set Theory, Recursion Theory, Model Theory, Logic for Computer Science and Semantics of Natural Languages.

  • Computer Programming and Formal Systems

    • 1st Edition
    • Volume 35
    • Lev D. Beklemishev
    • English

  • Recent Topics in Nonlinear PDE IV

    • 1st Edition
    • Volume 160
    • M. Mimura + 1 more
    • English
    This fourth volume concerns the theory and applications of nonlinear PDEs in mathematical physics, reaction-diffusion theory, biomathematics, and in other applied sciences. Twelve papers present recent work in analysis, computational analysis of nonlinear PDEs and their applications.

  • Systems and Simulation by Dimitris N Chorafas

    • 1st Edition
    • Volume 14
    • English
    In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; andmethods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory.As a result, the book represents a blend of new methods in general computational analysis,and specific, but also generic, techniques for study of systems theory ant its particularbranches, such as optimal filtering and information compression.

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