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Books in Mathematics general

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821-830 of 853 results in All results

Elements of Probability Theory

  • 1st Edition
  • January 1, 1965
  • L. Z. Rumshiskii
  • English
  • eBook
    9 7 8 - 1 - 4 8 3 1 - 3 6 0 0 - 4
Elements of Probability Theory focuses on the basic ideas and methods of the theory of probability. The book first discusses events and probabilities, including the classical meaning of probability, fundamental properties of probabilities, and the primary rule for the multiplication of probabilities. The text also touches on random variables and probability distributions. Topics include discrete and random variables; functions of random variables; and binomial distributions. The selection also discusses the numerical characteristics of probability distributions; limit theorems and estimates of the mean; and the law of large numbers. The text also describes linear correlation, including conditional expectations and their properties, coefficient of correlation, and best linear approximation to the regression function. The book presents tables that show the values of the normal probability integral, Poisson distribution, and values of the normal probability density. The text is a good source of data for readers and students interested in probability theory.

Mathematical Analysis

  • 1st Edition
  • January 1, 1965
  • G. Ye. Shilov
  • I.N. Sneddon + 2 more
  • English
  • eBook
    9 7 8 - 1 - 4 8 3 1 - 3 9 1 3 - 5
Mathematical Analysis: A Special Course focuses on the study of mathematical analysis. The book first discusses set theory, including operations on sets, countable sets, equivalence of sets, and sets of the power of the continuum. The text also discusses the elements of the theory of metric and normed linear spaces. Topics include convergent sequences and closed sets; theorem of the fixed point; normed linear spaces; and continuous functions and compact spaces. The selection also discusses the calculus of variations; the theory of the integral; and geometry of Hilbert space. The text also covers differentiation and integration, including functions of bounded variation, derivative of a non-decreasing function, differentiation of functions of sets, and the Stieltjes integral. The book also looks at the Fourier transform. Topics include convergence of Fourier series; Laplace transform; Fourier transform in the case of various independent variables; and quasi-analytic classes of functions. The text is a valuable source of data for readers interested in the study of mathematical analysis.

Analogues for the Solution of Boundary-Value Problems

  • 1st Edition
  • January 1, 1965
  • B. A. Volynskii + 1 more
  • N. Metropolish + 2 more
  • English
  • eBook
    9 7 8 - 1 - 4 8 3 1 - 8 1 3 7 - 0
Analogues for the Solution of Boundary-Value Problems considers the simulation of integral methods of solving boundary-value problems. This book is organized into 11 chapters. After the introduction provided in Chapter I, the formulation of some important engineering problems that reduce to the solution of partial differential equations is reviewed in Chapter II. Chapter III covers the mathematical methods for the solution of problems, such as the thermal problem of electrode graphitization and underground coal gasification. The theory of the physical processes of electrical simulation and principles involved in the construction of analogues is elaborated in Chapter IV, while the measurements in electrical analogues is deliberated in Chapter V. Chapters VI to VIII describe the construction of network analyzers and star-integrating networks. The methods of physical simulation for the solution of certain boundary-value problems are analyzed in Chapter IX. Chapters X and XI are devoted to future improvements and developments in analogues for the solution of boundary-value problems. This publication is intended for college students and specialists engaged in solving boundary-value problems.

Representation Theory of Finite Groups

  • 1st Edition
  • January 1, 1965
  • Martin Burrow
  • English
  • eBook
    9 7 8 - 1 - 4 8 3 2 - 5 8 2 1 - 8
Representation Theory of Finite Groups is a five chapter text that covers the standard material of representation theory. This book starts with an overview of the basic concepts of the subject, including group characters, representation modules, and the rectangular representation. The succeeding chapters describe the features of representation theory of rings with identity and finite groups. These topics are followed by a discussion of some of the application of the theory of characters, along with some classical theorems. The last chapter deals with the construction of irreducible representations of groups. This book will be of great value to graduate students who wish to acquire some knowledge of representation theory.

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.