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.

Books Journals

2721-2730 of 3351 results in All results

Tables of Lommel's Functions of Two Pure Imaginary Variables

1st Edition
January 1, 1965
L. S. Bark + 1 more
English
eBook
9 7 8 - 1 - 4 8 3 1 - 6 4 9 6 - 0

Tables of Lommel's Functions of Two Pure Imaginary Variables provide tables on cylinder functions of two pure imaginary variables. These tables are computed on the "Strela" electronic computer and are checked and prepared in the Analytic Machine Department. The introductory part describes some properties of the Lommel's functions. This part also contains the integral forms and asymptotic expansions. Lommel's functions of two pure imaginary arguments are defined by the Neumann series. This text is of value to researchers and students.

Computing Methods

1st Edition
January 1, 1965
I. S. Berezin + 1 more
English
eBook
9 7 8 - 1 - 4 8 3 1 - 5 2 2 9 - 5

Computing Methods, Volume 2 is a five-chapter text that presents the numerical methods of solving sets of several mathematical equations. This volume includes computation sets of linear algebraic equations, high degree equations and transcendental equations, numerical methods of finding eigenvalues, and approximate methods of solving ordinary differential equations, partial differential equations and integral equations. The book is intended as a text-book for students in mechanical mathematical and physics-mathematical faculties specializing in computer mathematics and persons interested in the theory and practice of numerical methods.

A Collection of Problems on a Course of Mathematical Analysis

1st Edition
January 1, 1965
G. N. Berman
I. N. Sneddon + 2 more
English
eBook
9 7 8 - 1 - 4 8 3 1 - 8 4 8 4 - 5

Collection of Problems on a Course of Mathematical Analysis contains selected problems and exercises on the main branches of a Technical College course of mathematical analysis. This book covers the topics of functions, limits, derivatives, differential calculus, curves, definite integral, integral calculus, methods of evaluating definite integrals, and their applications. Other topics explored include numerical problems related to series and the functions of several variables in differential calculus, as well as their applications. The remaining chapters examine the principles of multiple, line, and surface integrals, the trigonometric series, and the elements of the theory of fields. This book is intended for students studying mathematical analysis within the framework of a technical college course.

The Fundamentals of Mathematical Analysis

1st Edition
January 1, 1965
G. M. Fikhtengol'ts
I. N. Sneddon + 2 more
English

The Fundamentals of Mathematical Analysis, Volume I is a translation from Russian and used as a textbook that provides a systematic and serious discussion of the fundamentals of mathematical analysis. Differential and integral calculus, which were established in the 17th century; the theory of limits as the foundation of mathematical analysis; and the concept of real numbers as justifying the theory of limits are discussed in the early part of the volume. The concept of the limit of a function related to the concept of continuity of a function as explained by Bolzano and Cauchy is discussed. Fermat's theorem and Taylor's formula in understanding differential calculus are then presented. The book also investigates the value of the function when several independent variables occur, by considering the values of all the independent variables simultaneously. The concept of a primitive function and of an indefinite integral used in science and engineering is noted. Integral calculus, as found in geometric and mechanical applications, and differential calculus, as significant in some geometric application, are then examined. In the last part, the text discusses the works of Newton and Leibniz. The book will serve as a guide and reference for mathematicians, students, and professors of calculus and advanced mathematics.

The Fundamentals of Mathematical Analysis

1st Edition
January 1, 1965
G. M. Fikhtengol'ts
I. N. Sneddon + 2 more
English
eBook
9 7 8 - 1 - 4 8 3 1 - 5 4 1 3 - 8

The Fundamentals of Mathematical Analysis, Volume 2 is a continuation of the discussion of the fundamentals of mathematical analysis, specifically on the subject of curvilinear and surface integrals, with emphasis on the difference between the curvilinear and surface ""integrals of first kind"" and ""integrals of second kind."" The discussions in the book start with an introduction to the elementary concepts of series of numbers, infinite sequences and their limits, and the continuity of the sum of a series. The definition of improper integrals of unbounded functions and that of uniform convergence of integrals are explained. Curvilinear integrals of the first and second kinds are analyzed mathematically. The book then notes the application of surface integrals, through a parametric representation of a surface, and the calculation of the mass of a solid. The text also highlights that Green's formula, which connects a double integral over a plane domain with curvilinear integral along the contour of the domain, has an analogue in Ostrogradski's formula. The periodic values and harmonic analysis such as that found in the operation of a steam engine are analyzed. The volume ends with a note of further developments in mathematical analysis, which is a chronological presentation of important milestones in the history of analysis. The book is an ideal reference for mathematicians, students, and professors of calculus and advanced mathematics.

Tables of the Function w (z)- e-z2 ? ex2 dx

1st Edition
January 1, 1965
K. A. Karpov
English
eBook
9 7 8 - 1 - 4 8 3 2 - 1 4 5 7 - 3

Tables of the Function w(z) = e-z2 z?0ex2dx in the Complex Domain contains tables of the function in connection with the problem of the radio wave propagation. These tables are compiled in the Experimental-Computing Laboratories of the Institute of Exact Mechanics and Computational Methods of the U.S.S.R. Academy of Sciences. The function w(z) is represented in the upper half-plane by the asymptotic series. Description of the tables and method of computation is provided. This book will prove useful to mathematicians and researchers.

Six-Figure Tables of Trigonometric Functions

1st Edition
January 1, 1965
L. S. Khrenov
English
eBook
9 7 8 - 1 - 4 8 3 1 - 8 4 9 2 - 0

THE PRESENT six-figure trigonometric tables complete the series of tables of the natural values of the trigonometric functions published by Fizmatgiz. Now that small computers have become very widely available, almost all computations are carried out by machine, and the majority of computational schemes arc suited to this purpose. The situation calls urgently for the availability of tables containing the natural values of all six trigonometric functions. The following special factor emerges here. In logarithmic computations the same relative accuracy is guaranteed more or less automatically for all values of the argument: the number of correct significant figures in the result is either equal to or (in rare cases) one less than, the number of significant figures in the mantissa of the logarithm. In computations with natural values of the functions the same relative accuracy is guaranteed in practice for all arguments only by having a constant nmber of significant figures throughout the tables. Until recently however, tables of the natural values of the trigonometric functions have been compiled both in Russia and abroad with the same number of places after the decimal point, which leads to a loss of accuracy when computing with functions of small angles. In view of this there is an urgent need for tables of the natural values of the trigonometric functions with a constant number of significant figures which substantially guarantees roughly the- same relative accuracy for all angles. The present tables, together with the following, already published by Fizmatgiz: Fil'e-figure Tables (L. S. Khrenov~ 1954), Five-.figure Tables l~,ith the Argument in Time (L. S. Khrenov, 1954), Seven-figure Tables(L. S. Khrenov, 1956) and Six-figure Tables with the Argunlent in Time (S. A. Angelov, 1957), form a complete series ~ith the same number of significant figures, satisfying the main requirements of a wide variety of computers. When compiling the present tables, use was made for purposes of collation of the following tables of the natural values of the trigonometric functions: The I)-figure Table..' of H. Andoyer, (Paris, 1915-1918), the Eight-figure Table of J. Peters (Berlin) J939), the Seven-figure Table of °L.S. Khrenov (2nd. ed., Gostekhizdat, 1956), the Seven-figure Table of H. C. Ives, and the Eight-figure Tables oj' the Logarith,l1.ft of NumberaV and oJ the Trigonometric functions of J. Bauschin.e;er and J. Peters (Geodezizdat, 1942 and 1944).

Ten-Decimal Tables of the Logarithms of Complex Numbers and for the Transformation from Cartesian to Polar Coordinates

1st Edition
January 1, 1965
L. A. Lyusternik
English
eBook
9 7 8 - 1 - 4 8 3 1 - 8 4 9 7 - 5

Ten-Decimal Tables of the Logarithms of Complex Numbers and for the Transformation from Cartesian to Polar Coordinates contains Tables of mathematical functions up to ten-decimal value. These tables are compiled in the Department for Approximate Computations of the Institute of Exact Mechanics and Computational Methods of the U.S.S.R. Academy of Sciences. The computations are carried out by this department in conjunction with the Computational-Experimental Laboratory of the Institute. This book will be of value to mathematicians and researchers.

Tables of Generalized Airy Functions for the Asymptotic Solution of the Differential Equation

1st Edition
January 1, 1965
L. N. Nosova + 1 more
English
eBook
9 7 8 - 1 - 4 8 3 1 - 8 4 9 9 - 9

Tables of Generalized Airy Functions for the Asymptotic Solution of the Differential Equations contains tables of the special functions, namely, the generalized Airy functions, and their first derivatives, for real and pure imaginary values. The tables are useful for calculations on toroidal shells, laminae, rode, and for the solution of certain other problems of mathematical physics. The values of the functions were computed on the "Strela" highspeed electronic computer. This book will be of great value to mathematicians, researchers, and students.

Lectures in General Algebra

1st Edition
January 1, 1965
A. G. Kurosh
I. N. Sneddon + 2 more
English
eBook
9 7 8 - 1 - 4 8 3 1 - 4 9 5 7 - 8

Lectures in General Algebra is a translation from the Russian and is based on lectures on specialized courses in general algebra at Moscow University. The book starts with the basics of algebra. The text briefly describes the theory of sets, binary relations, equivalence relations, partial ordering, minimum condition, and theorems equivalent to the axiom of choice. The text gives the definition of binary algebraic operation and the concepts of groups, groupoids, and semigroups. The book examines the parallelism between the theory of groups and the theory of rings; such examinations show the convenience of constructing a single theory from the results of group experiments and ring experiments which are known to follow simple corollaries. The text also presents algebraic structures that are not of binary nature. From this parallelism arise other concepts, such as that of the lattices, complete lattices, and modular lattices. The book then proves the Schmidt-Ore theorem, and also describes linear algebra, as well as the Birkhoff-Witt theorem on Lie algebras. The text also addresses ordered groups, the Archimedean groups and rings, and Albert's theorem on normed algebras. This book can prove useful for algebra students and for professors of algebra and advanced mathematicians.