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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.

BooksJournals

    • Logic, Automata, and Algorithms

      • 1st Edition
      • Volume 79
      • July 1, 1971
      • English
      • eBook
        9 7 8 0 0 8 0 9 5 5 8 7 2
      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.

    • Introduction to Stochastic Control Theory

      • 1st Edition
      • Volume 70
      • November 28, 1970
      • English
      • eBook
        9 7 8 0 0 8 0 9 5 5 7 9 7
      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.

    • Dimension Theory

      • 1st Edition
      • Volume 37
      • May 31, 1970
      • English
      • eBook
        9 7 8 0 0 8 0 8 7 3 5 0 3

    • Methods of Nonlinear Analysis

      • 1st Edition
      • Volume 61A
      • April 1, 1970
      • Richard Bellman
      • English
      • eBook
        9 7 8 0 0 8 0 9 5 5 7 0 4
      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.

    • Stochastic Processes and Filtering Theory

      • 1st Edition
      • Volume 64
      • January 31, 1970
      • Andrew H. Jazwinski
      • English
      • Paperback
        9 7 8 0 1 2 4 1 5 7 4 3 9
      • eBook
        9 7 8 0 0 8 0 9 6 0 9 0 6
      This book presents a unified treatment of linear and nonlinear filtering theory for engineers, with sufficient emphasis on applications to enable the reader to use the theory. The need for this book is twofold. First, although linear estimation theory is relatively well known, it is largely scattered in the journal literature and has not been collected in a single source. Second, available literature on the continuous nonlinear theory is quite esoteric and controversial, and thus inaccessible to engineers uninitiated in measure theory and stochastic differential equations. Furthermore, it is not clear from the available literature whether the nonlinear theory can be applied to practical engineering problems. In attempting to fill the stated needs, the author has retained as much mathematical rigor as he felt was consistent with the prime objective—to explain the theory to engineers. Thus, the author has avoided measure theory in this book by using mean square convergence, on the premise that everyone knows how to average. As a result, the author only requires of the reader background in advanced calculus, theory of ordinary differential equations, and matrix analysis.

    • Theory of H[superscript p] spaces

      • 1st Edition
      • Volume 38
      • July 31, 1970
      • English
      • eBook
        9 7 8 0 0 8 0 8 7 3 5 1 0
      The theory of HP spaces has its origins in discoveries made forty or fifty years ago by such mathematicians as G. H. Hardy, J. E. Littlewood, I. I. Privalov, F. and M. Riesz, V. Smirnov, and G. Szego. Most of this early work is concerned with the properties of individual functions of class HP, and is classical in spirit. In recent years, the development of functional analysis has stimulated new interest in the HP classes as linear spaces. This point of viewhas suggested a variety of natural problems and has provided new methods of attack, leading to important advances in the theory. This book is an account of both aspects of the subject, the classical and the modern. It is intended to provide a convenient source for the older parts of the theory (the work of Hardy and Littlewood, for example), as well as to give a self-contained exposition of more recent developments such as Beurling’s theorem on invariant subspaces, the Macintyre-Rogosinski... theory of extremal problems, interpolation theory, the dual space structure of HP with p < 1, HP spaces over general domains, and Carleson’s proof of the corona theorem. Some of the older results are proved by modern methods. In fact, the dominant theme of the book is the interplay of “ hard” and “ soft” analysis, the blending of classical and modern techniques and viewpoints.

    • Cohomology of groups

      • 1st Edition
      • Volume 34
      • January 1, 1969
      • English
      • Hardback
        9 7 8 0 1 2 7 4 2 7 5 0 8
      • eBook
        9 7 8 0 0 8 0 8 7 3 4 6 6

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