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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.

  • Singular Optimal Control Problems

    • 1st Edition
    • Volume 117
    • October 29, 1975
    • 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.

  • II: Fourier Analysis, Self-Adjointness

    • 1st Edition
    • Volume 2
    • September 28, 1975
    • Michael Reed + 1 more
    • English
    This volume will serve several purposes: to provide an introduction for graduate students not previously acquainted with the material, to serve as a reference for mathematical physicists already working in the field, and to provide an introduction to various advanced topics which are difficult to understand in the literature. Not all the techniques and application are treated in the same depth. In general, we give a very thorough discussion of the mathematical techniques and applications in quatum mechanics, but provide only an introduction to the problems arising in quantum field theory, classical mechanics, and partial differential equations. Finally, some of the material developed in this volume will not find applications until Volume III. For all these reasons, this volume contains a great variety of subject matter. To help the reader select which material is important for him, we have provided a "Reader's Guide" at the end of each chapter.

  • An introduction to differentiable manifolds and Riemannian geometry

    • 1st Edition
    • Volume 63
    • August 22, 1975
    • English

  • Sobolev Spaces

    • 1st Edition
    • Volume 65
    • August 22, 1975
    • English

  • Basic Linear Partial Differential Equations

    • 1st Edition
    • August 8, 1975
    • François Treves
    • English

  • A First Course in Stochastic Processes

    • 2nd Edition
    • March 28, 1975
    • Samuel Karlin + 1 more
    • English
    The purpose, level, and style of this new edition conform to the tenets set forth in the original preface. The authors continue with their tack of developing simultaneously theory and applications, intertwined so that they refurbish and elucidate each other. The authors have made three main kinds of changes. First, they have enlarged on the topics treated in the first edition. Second, they have added many exercises and problems at the end of each chapter. Third, and most important, they have supplied, in new chapters, broad introductory discussions of several classes of stochastic processes not dealt with in the first edition, notably martingales, renewal and fluctuation phenomena associated with random sums, stationary stochastic processes, and diffusion theory.

  • General Systems Theory: Mathematical Foundations

    • 1st Edition
    • Volume 113
    • March 21, 1975
    • 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.

  • Hewitt-Nachbin Spaces

    • 1st Edition
    • Volume 17
    • January 1, 1975
    • English

  • Global Theory of a Second Order Linear Ordinary Differential Equation with a Polynomial Coefficient

    • 1st Edition
    • Volume 18
    • January 1, 1975
    • English

  • Localization of Nilpotent Groups and Spaces

    • 1st Edition
    • Volume 15
    • January 1, 1975
    • English

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