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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.

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2381-2390 of 2429 results in All results

A theory of sets

  • 1st Edition
  • Volume 18
  • January 1, 1965
  • Anthony P. Morse
  • English
  • eBook
    9 7 8 - 0 - 0 8 - 0 8 7 3 3 0 - 5

Theory of Categories

  • 1st Edition
  • Volume 17
  • January 1, 1965
  • Barry Mitchell
  • English
  • eBook
    9 7 8 - 0 - 0 8 - 0 8 7 3 2 9 - 9

Random Processes in Nonlinear Control Systems by A A Pervozvanskii

  • 1st Edition
  • Volume 15
  • January 1, 1965
  • A. A. Pervozvanskii
  • English
  • eBook
    9 7 8 - 0 - 0 8 - 0 9 5 5 2 1 - 6
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.

Intermediate Algebra & Analytic Geometry

  • 1st Edition
  • January 1, 1965
  • William R. Gondin + 1 more
  • English
  • eBook
    9 7 8 - 1 - 4 8 3 2 - 7 8 2 0 - 9
Intermediate Algebra & Analytic Geometry Made Simple focuses on the principles, processes, calculations, and methodologies involved in intermediate algebra and analytic geometry. The publication first offers information on linear equations in two unknowns and variables, functions, and graphs. Discussions focus on graphic interpretations, explicit and implicit functions, first quadrant graphs, variables and functions, determinate and indeterminate systems, independent and dependent equations, and defective and redundant systems. The text then examines quadratic equations in one variable, systems involving quadratics, and determinants. Topics include determinants of higher order, application of Cramer's rule, second-order determinants, systems linear in quadratic terms, systems treatable by substitution, systems with a linear equation, and other systems treated by comparison. The manuscript ponders on trigonometric functions and equations, straight lines, and points, distances, and slopes, including intersection points of lines, perpendicular distances, angles between lines, positions of points, inverse trigonometric functions, and trigonometric equations. The publication is a valuable source of data for readers interested in intermediate algebra and analytic geometry.

Tables of the Principal Unitary Representations of Fedorov Groups

  • 1st Edition
  • January 1, 1964
  • D. K. Faddeyev
  • English
  • eBook
    9 7 8 - 1 - 4 8 3 1 - 5 4 7 1 - 8
Tables of the Principal Unitary Representations of Fedorov Groups contains tables of all the principal representations of Fedorov groups from which all irreducible unitary representations can be obtained with the help of some standard operations. The work originated at a seminar on mathematical crystallography held in 1952-1953 at the Faculty of Mathematics and Mechanics of the Leningrad State University. The book is divided into two parts. The first part discusses the relation between the theory of representations and the generalized Fedorov groups in Shubnikov's sense. It shows that all unidimensional representations of Fedorov groups are basic, and hence are given in the tables. In particular, all representations defining generalized Fedorov groups are given in the tables. However, it should be noted that the same generalized Fedorov group may correspond to different representations, if the latter cross each other in certain automorphisms of the Fedorov group to be represented. The second part contains the tables of the principal unitary representations of Fedorov groups.

Periodic Differential Equations

  • 1st Edition
  • January 1, 1964
  • F. M. Arscott
  • I. N. Sneddon + 2 more
  • English
  • eBook
    9 7 8 - 1 - 4 8 3 1 - 6 4 8 8 - 5
Periodic Differential Equations: An Introduction to Mathieu, Lamé, and Allied Functions covers the fundamental problems and techniques of solution of periodic differential equations. This book is composed of 10 chapters that present important equations and the special functions they generate, ranging from Mathieu's equation to the intractable ellipsoidal wave equation. This book starts with a survey of the main problems related to the formation of periodic differential equations. The subsequent chapters deal with the general theory of Mathieu's equation, Mathieu functions of integral order, and the principles of asymptotic expansions. These topics are followed by discussions of the stable and unstable solutions of Mathieu's general equation; general properties and characteristic exponent of Hill's equation; and the general nature and solutions of the spheroidal wave equation. The concluding chapters explore the polynomials, orthogonality properties, and integral relations of Lamé's equation. These chapters also describe the wave functions and solutions of the ellipsoidal wave equation. This book will prove useful to pure and applied mathematicians and functional analysis.

Tables of the Velocity of Sound in Sea Water

  • 1st Edition
  • January 1, 1964
  • L. S. Bark + 2 more
  • English
  • eBook
    9 7 8 - 1 - 4 8 3 1 - 6 4 9 5 - 3
Tables of the Velocity of Sound in Sea Water contains tables of the velocity of sound in sea water computed on a "Strela-3" high-speed electronic computer and a T-5 tabulator at the Computational Center of the Academy of Sciences. Knowledge of the precise velocity of sound in sea water is of great importance when investigating sound propagations in the ocean and when solving practical problems involving the use of hydro-acoustic devices. This book demonstrates the computations made for the velocity of sound in sea water, which can be found in two ways: by direct measurement with the aid of suitable equipment, and by calculation from formula expressing the dependence of the velocity on the temperature and salinity of the water. This book will be of great value to researchers and students.

A Course of Higher Mathematics

  • 1st Edition
  • January 1, 1964
  • V. I. Smirnov
  • A. J. Lohwater
  • English
  • eBook
    9 7 8 - 1 - 4 8 3 1 - 5 6 3 6 - 1
A Course of Higher Mathematics, I: Elementary Calculus is a five-volume course of higher mathematics used by mathematicians, physicists, and engineers in the U.S.S.R. This volume deals with calculus and principles of mathematical analysis including topics on functions of single and multiple variables. The functional relationships, theory of limits, and the concept of differentiation, whether as theories and applications, are discussed. This book also examines the applications of differential calculus to geometry. For example, the equations to determine the differential of arc or the parameters of a curve are shown. This text then notes the basic problems involving integral calculus, particularly regarding indefinite integrals and their properties. The application of definite integrals in the calculation of area of a sector, the length of arc, and the calculation of the volumes of solids of a given cross-section are explained. This book further discusses the basic theory of infinite series, applications to approximate evaluations, Taylor's formula, and its extension. Finally, the geometrical approach to the concept of a number is reviewed. This text is suitable for physicists, engineers, mathematicians, and students in higher mathematics.

Tables of The Legendre Functions P—½+it(x)

  • 1st Edition
  • January 1, 1964
  • M. I. Zhurina + 1 more
  • English
  • eBook
    9 7 8 - 1 - 4 8 3 1 - 4 8 2 5 - 0
Tables of the Legendre Functions P–½+iτ (X), Part I tabulates in detail the Legendre spherical functions of the first kind Pv(x) with complex index v = – ½ + iτ and real values of X > – 1. P–½+iτ (X) plays an important role in mathematical physics and are used in solving boundary value problems in potential theory for domains bounded by cones, hyperboloids of revolution, two intersecting spheres, or other second order surfaces. These Legendre functions are also of theoretical interest in connection with the Meler-Fok integral expansion. This book is devoted to the tables of P–½+iτ (X) and coefficients in the asymptotic formula. Some properties of the functions P–½+iτ (X) and description of the tables are also discussed. This publication is a good source for mathematical physicists and students conducting work on Legendre functions P–½+iτ (X).

Non-Linear Differential Equations

  • 1st Edition
  • January 1, 1964
  • G. Sansone + 1 more
  • I. N. Sneddon + 2 more
  • English
  • eBook
    9 7 8 - 1 - 4 8 3 1 - 3 5 9 6 - 0
International Series of Monographs in Pure and Applied Mathematics, Volume 67: Non-Linear Differential Equations, Revised Edition focuses on the analysis of the phase portrait of two-dimensional autonomous systems; qualitative methods used in finding periodic solutions in periodic systems; and study of asymptotic properties. The book first discusses general theorems about solutions of differential systems. Periodic solutions, autonomous systems, and integral curves are explained. The text explains the singularities of Briot-Bouquet theory. The selection takes a look at plane autonomous systems. Topics include limiting sets, plane cycles, isolated singular points, index, and the torus as phase space. The text also examines autonomous plane systems with perturbations and autonomous and non-autonomous systems with one degree of freedom. The book also tackles linear systems. Reducible systems, periodic solutions, and linear periodic systems are considered. The book is a vital source of information for readers interested in applied mathematics.

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