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Elsevier

Books in Theory and mathematics

Our portfolio includes foundational theories, algorithms, formal methods, and computational complexity. Featuring rigorous research, mathematical frameworks, and practical applications, these titles support theorists, mathematicians, and computer scientists in advancing the theoretical underpinnings of computing. Addressing emerging areas like quantum algorithms and formal verification, the collection fuels innovation and scientific discovery.

  • Introduction to the Mathematical Theory of Control Processes: Nonlinear Processes v. 2

    • 1st Edition
    • Volume 40B
    • Bellman
    • English

  • Finite State Markovian Decision Processes

    • 1st Edition
    • Volume 67
    • Derman
    • English

  • The Computation and Theory of Optimal Control

    • 1st Edition
    • Volume 65
    • Dyer
    • English

  • Algorithms, Graphs, and Computers

    • 1st Edition
    • Volume 62
    • Bellman
    • English

  • An Algorithmic Approach to Nonlinear Analysis and Optimization

    • 1st Edition
    • Volume 63
    • Beltrami
    • English

  • Adaptive, Learning, and Pattern Recognition Systems; theory and applications

    • 1st Edition
    • Volume 66
    • Mendel
    • English

  • Special Functions and Their Approximations: v. 2

    • 1st Edition
    • Volume 53B
    • Yudell L. Luke
    • English

  • Functional Analysis and Time Optimal Control

    • 1st Edition
    • Volume 56
    • Hermes
    • English

  • Differential and integral inequalities; theory and applications PART B: Functional, partial, abstract, and complex differential equations

    • 1st Edition
    • Volume 55B
    • Lakshmikantham
    • English

  • Function Theoretic Methods in Partial Differential Equations

    • 1st Edition
    • Volume 54
    • Gilbert
    • English

  • The Special Functions and Their Approximations

    • 1st Edition
    • Volume 53A
    • Yudell L. Luke
    • English
    A detailed and self-contained and unified treatment of many mathematical functions which arise in applied problems, as well as the attendant mathematical theory for their approximations. many common features of the Bessel functions, Legendre functions, incomplete gamma functions, confluent hypergeometric functions, as well as of otherw, can be derived. Hitherto, many of the material upon which the volumes are based has been available only in papers scattered throughout the literature.

  • Differential and Integral Inequalities: Theory and Applications

    Volume I: Ordinary Differential Equations
    • 1st Edition
    • Volume 55A
    • V. Lakshmikantham + 1 more
    • English
    This volume constitutes the first part of a monograph on theory and applications of differential and integral inequalities. 'The entire work, as a whole, is intended to be a research monograph, a guide to the literature, and a textbook for advanced courses. The unifying theme of this treatment is a systematic development of the theory and applicationsof differential inequalities as well as Volterra integral inequalities. The main tools for applications are the norm and the Lyapunov functions. Familiarity with real and complex analysis, elements of general topology and functional analysis, and differential and integral equations is assumed.

  • Sequential Methods in Pattern Recognition and Machine Learning

    • 1st Edition
    • Volume 52
    • K.C. Fu
    • English

  • Nonlinear Ordinary Differential Equations in Transport Processes

    • 1st Edition
    • Volume 42
    • W. F. Ames
    • English

  • Quasilinearization and invariant imbedding, with applications to chemical engineering and adaptive control

    • 1st Edition
    • Volume 41
    • Lee
    • English

  • Introduction to Operations Research

    • 1st Edition
    • Volume 47
    • Faure
    • English

  • Variational Methods in Optimum Control Theory

    • 1st Edition
    • Volume 45
    • Petrov
    • English

  • Linear and Quasilinear Elliptic Equations

    • 1st Edition
    • Volume 46
    • Ladyzhenskaya
    • English

  • Nonlinear Two Point Boundary Value Problems

    • 1st Edition
    • Volume 44
    • Bailey
    • English

  • The Theory of Splines and Their Applications

    • 1st Edition
    • Volume 38
    • Ahlberg
    • English

  • Optimization of Stochastic Systems

    Topics in Discrete-time Systems
    • 1st Edition
    • Volume 32
    • Masanao Aoki
    • English
    Optimization of Stochastic Systems is an outgrowth of class notes of a graduate level seminar on optimization of stochastic systems. Most of the material in the book was taught for the first time during the 1965 Spring Semester while the author was visiting the Department of Electrical Engineering, University of California, Berkeley. The revised and expanded material was presented at the Department of Engineering, University of California, Los Angeles during the 1965 Fall Semester. The systems discussed in the book are mostly assumed to be of discrete-time type with continuous state variables taking values in some subsets of Euclidean spaces. There is another class of systems in which state variables are assumed to take on at most a denumerable number of values, i.e., these systems are of discrete-time discrete-space type. Although the problems associated with the latter class of systems are many and interesting, andalthough they are amenable to deep analysis on such topics as the limiting behaviors of state variables as time indexes increase to infinity, this class of systems is not included here, partly because there are many excellent books on the subjects and partly because inclusion of these materials would easily double the size of the book.

  • Nonlinear Autonomous Oscillations: Analytical Theory

    • 1st Edition
    • Volume 34
    • Urabe
    • English
    Nonlinear Autonomous Oscillations presents a self-contained and readable account for mathematicians, physicists, and engineers. This monograph is mainly concerned with the analytical theory of nonlinear autonomous oscillations, with the approach based mostly on the author’s work. After some introductory material, in Chapter 5 a moving orthogonal coordinate system along a closed orbit is introduced. In the next four chapters, stability theory and perturbation theory are systematically discussed for general autonomous systems by means of a moving coordinate system. In Chapter 10, the two-dimensional autonomous system is discussed in detail on the basis of results obtained in the preceding chapters. In Chapter 11, a numerical method for determining a periodic solution of the general nonlinear autonomous system is described. To illustrate this, the periodic solutions of the autonomous van der Pol equation for various values of thedamping coefficient are computed. Chapter 12, which is based on the work of the author and Sibuya, discusses the center of higher dimension. Chapter 13 discusses a particular inverse problem connected with the period of periodicsolutions of one interesting equation. There are, of course, many other topics of importance in the theory of nonlinear autonomous oscillations. These are, however, omitted in the present monograph because they are mainly topological rather than analytical and in order to keep the book from growing inordinately long.

  • Graphs, Dynamic Programming and Finite Games

    • 1st Edition
    • Volume 36
    • Kaufmann
    • English

  • Introduction to the Mathematical Theory of Control Processes: Linear Equations and Quadratic Criteria v. 1

    • 1st Edition
    • Volume 40A
    • Bellman
    • English
    This work discusses the theory of control processes. The extremely rapid growth of the theory, associated intimately with the continuing trend toward automation, makes it imperative that the courses of this nature rest upon a broad basis. The work discusses the fundamentals of the calculus of variations, dynamic programming, discrete control processes, use of the digital computer, and functional analysis. Introductory courses in control theory are essential for training the modern graduate student in pure and applied mathematics, engineering, mathematical physics, economics, biology, operations research, and related fields. The work also describes the dual approaches of the calculus of variations and dynamic programming in the scalar case and illustrates ways to tackle the multidimensional optimization problems.

  • Lectures on Functional Equations and Their Applications

    • 1st Edition
    • Volume 19
    • J. Aczél
    • English
    Numerous detailed proofs highlight this treatment of functional equations. Starting with equations that can be solved by simple substitutions, the book then moves to equations with several unknown functions and methods of reduction to differential and integral equations. Also includes composite equations, equations with several unknown functions of several variables, vector and matrix equations, more. 1966 edition.

  • Time-Lag Control Systems

    • 1st Edition
    • Volume 24
    • Og?uzto?reli
    • English

  • Linear Systems of Ordinary Differential Equations, with Periodic and Quasi-Periodic Coefficients

    • 1st Edition
    • Volume 28
    • Erugin
    • English

  • Differential Equations

    Stability, Oscillations, Time Lags
    • 1st Edition
    • Volume 23
    • Halanay
    • English

  • Dynamic Programming and the Calculus of Variations

    • 1st Edition
    • Volume 21
    • Dreyfus
    • English

  • Mathematical Theory of Connecting Networks and Telephone Traffic

    • 1st Edition
    • Volume 17
    • V.E. Beneš
    • English

  • Stability of Nonlinear Control Systems

    • 1st Edition
    • Volume 13
    • Lefschetz
    • English

  • Discrete and Continuous Boundary Problems

    • 1st Edition
    • Volume 8
    • Atkinson
    • English

  • Optimization Techniques

    With Applications to Aerospace Systems
    • 1st Edition
    • Volume 5
    • George Leitmann
    • English
    During the past decade there has been a remarkable growth of interest in problems of systems optimization and of optimal control. And with this interest has come an increasing need for methods useful for rendering systems optimum. Rising to meet this challengc there have sprung up various “schools,” often championing onc method and regarding it superior to all others. Long experience has shown that life is not so simple, that the picture is not all white and black. In short, one may expect that a particular method is superior to others for the solution of some problems-rarely for all problems. Furthermore, since the basic mathematical formulation of optimization problems is often essentially the same in many approaches, it is not unreasonable to expect that there may be a great deal of similarity among various methods, a similarity - often, indeed, an identity-which is obscured by dissimilarities in language and notation. To help the uncommitted in his search for and rhoice of the optimum optimization technique is the fundamental aim of this volume. To accomplish this aim there are assembled in one book ten chapters dealing &h the various methods currently espoused for the solution of problems in systems optimization and optimal control. The choice of authors has been dictated solely by a consideration of an author’s interest and expertiless in a particular method. With the advantages of such an eclectic approach and the ensuing multiple authorship there comes some loss of smoothness of over - all presentation, for which the Editor must take the sole blame. On the one hand, correlation between the various chapters has been achieved by cross-referencing; on the other hand, each chapter can be read as a separate entity setting forth the technique championed by a particular “School.” While each of the ten chapters dealing with methods includes simple examples, primarily for didactic purposes, it has been thought useful to present four additional chapters dealing with applications alone. Of these, the first three, Chapters 11-13, cover specific optimization problems, and the final chapter contains a discussion of problems in the optimization of a complete system, in this case a nuclear propulsion system.

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