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

A Syntax-Oriented Translator

1st Edition
May 12, 2014
Peter Zilahy Ingerman
English
eBook
9 7 8 1 4 8 3 2 6 1 3 5 5

A Syntax-Oriented Translator focuses on the field of programming and the characteristics and functions of compilers and translators. The book first offers information on the metasyntactic language and the details of a parsing processor. Discussions focus on processing, recovery, and output sections, detailed flow-chart of the parsing processor, parsing form of a grammar, canonical ordering, and the metasyntactic language in general. The text then elaborates on some extensions to the metasyntactic language and metasemantic and metapragmatic language, including punctuation marks and format control, metasemantic and metapragmatic functions, basic form of the construct, and substitution MSF. The publication examines the details of an unparsing processor, as well as lists used in unparsing, subroutines, and the unparsing processor itself. The book is a dependable source of information for home compiler-writers who are interested in the use of a syntax-oriented translator.

Distributions and the Boundary Values of Analytic Functions

1st Edition
May 12, 2014
E. J. Beltrami + 1 more
English
eBook
9 7 8 1 4 8 3 2 6 8 1 0 1

Distributions and the Boundary Values of Analytic Functions focuses on the tools and techniques of distribution theory and the distributional boundary behavior of analytic functions and their applications. The publication first offers information on distributions, including spaces of testing functions, distributions of finite order, convolution and regularization, and testing functions of rapid decay and distributions of slow growth. The text then examines Laplace transform, as well as Laplace transforms of distributions with arbitrary support. The manuscript ponders on distributional boundary values of analytic functions, including causal and passive operators, analytic continuation and uniqueness, boundary value theorems and generalized Hilbert transforms, and representation theorems for half-plane holomorphic functions with S' boundary behavior. The publication is a valuable source of data for researchers interested in distributions and the boundary values of analytic functions.

Elementary Differential Geometry

1st Edition
May 12, 2014
Barrett O'Neill
English
eBook
9 7 8 1 4 8 3 2 6 8 1 1 8

Elementary Differential Geometry focuses on the elementary account of the geometry of curves and surfaces. The book first offers information on calculus on Euclidean space and frame fields. Topics include structural equations, connection forms, frame fields, covariant derivatives, Frenet formulas, curves, mappings, tangent vectors, and differential forms. The publication then examines Euclidean geometry and calculus on a surface. Discussions focus on topological properties of surfaces, differential forms on a surface, integration of forms, differentiable functions and tangent vectors, congruence of curves, derivative map of an isometry, and Euclidean geometry. The manuscript takes a look at shape operators, geometry of surfaces in E, and Riemannian geometry. Concerns include geometric surfaces, covariant derivative, curvature and conjugate points, Gauss-Bonnet theorem, fundamental equations, global theorems, isometries and local isometries, orthogonal coordinates, and integration and orientation. The text is a valuable reference for students interested in elementary differential geometry.

Entire Functions

1st Edition
May 12, 2014
A. I. Markushevich
English
eBook
9 7 8 1 4 8 3 2 7 4 9 0 4

Entire Functions focuses on complex numbers and the algebraic operations on them and the basic principles of mathematical analysis. The book first elaborates on the concept of an entire function, including the natural generalization of the concept of a polynomial and power series. The text then takes a look at the maximum absolute value and the order of an entire function, as well as calculations for the coefficients of power series representing a given function, use of integrals, and complex numbers. The publication elaborates on the zeros of an entire function and the fundamental theorem of algebra and Picard’s little theorem. Calculations for the zeros of an entire function and numerical representations of Liouville's theorem and Picard’s little theorem are presented. The book also examines algebraic relationships and addition theorems, including an explanation of Weierstrass' theorem and Picard’s little theorem. The manuscript is a vital reference for students interested in the numerical approaches involved in entire functions.

Functional Analysis and Numerical Mathematics

1st Edition
May 12, 2014
Lothar Collatz
English
eBook
9 7 8 1 4 8 3 2 6 4 0 0 4

Functional Analysis and Numerical Mathematics focuses on the structural changes which numerical analysis has undergone, including iterative methods, vectors, integral equations, matrices, and boundary value problems. The publication first examines the foundations of functional analysis and applications, including various types of spaces, convergence and completeness, operators in Hilbert spaces, vector and matrix norms, eigenvalue problems, and operators in pseudometric and other special spaces. The text then elaborates on iterative methods. Topics include the fixed-point theorem for a general iterative method in pseudometric spaces; special cases of the fixed-point theorem and change of operator; iterative methods for differential and integral equations; and systems of equations and difference methods. The manuscript takes a look at monotonicity, inequalities, and other topics, including monotone operators, applications of Schauder's theorem, matrices and boundary value problems of monotone kind, discrete Chebyshev approximation and exchange methods, and approximation of functions. The publication is a valuable source of data for mathematicians and researchers interested in functional analysis and numerical mathematics.

The Remarkable Sine Functions

1st Edition
May 12, 2014
A. I. Markushevich
English
eBook
9 7 8 1 4 8 3 2 7 5 2 1 5

The Remarkable Sine Functions focuses on the trigonometric functions of sine and cosine. The publication first offers information on the geometric definition of circular, hyperbolic, and lemniscate functions, generalized sines, and integration in the complex plane. Discussions focus on the properties and characteristics of circular, lemniscate, and hyperbolic functions, uniform approach to generalized sines, and the process of integration in complex variables. The text then elaborates on the use of Euler's method in deriving the addition theorems and study of complex values, including the employment of the relationship between the sine and cosine in rewriting addition theorems and formulas that can be used in the determination of real values. The manuscript ponders on zeros and poles, simple and double periodicity, and the concept of an elliptic function. Concerns include circular and hyperbolic functions, Jacobian functions, and the functions of sine and cosine. The book is a valuable reference for mathematicians and researchers interested in the functions of sine and cosine.

Theoretical Numerical Analysis

1st Edition
May 12, 2014
Burton Wendroff
English
eBook
9 7 8 1 4 8 3 2 7 5 2 2 2

Theoretical Numerical Analysis focuses on the presentation of numerical analysis as a legitimate branch of mathematics. The publication first elaborates on interpolation and quadrature and approximation. Discussions focus on the degree of approximation by polynomials, Chebyshev approximation, orthogonal polynomials and Gaussian quadrature, approximation by interpolation, nonanalytic interpolation and associated quadrature, and Hermite interpolation. The text then ponders on ordinary differential equations and solutions of equations. Topics include iterative methods for nonlinear systems, matrix eigenvalue problems, matrix inversion by triangular decomposition, homogeneous boundary value problems, and initial value problems. The publication takes a look at partial differential equations, including heat equation, stability, maximum principle, and first order systems. The manuscript is a vital source of data for mathematicians and researchers interested in theoretical numerical analysis.

How to Find Out in Mathematics

2nd Edition
May 15, 2014
John E. Pemberton
G. Chandler
English
eBook
9 7 8 1 4 8 3 1 3 8 6 4 0

How to Find Out in Mathematics: A Guide to Sources of Information, Second Revised Edition presents updated topics about probability and statistics, dictionaries and encyclopedias, computing, and mathematical education. The book discusses the modifications of the content of professional actuarial examinations; the assimilation of modern mathematics into the school curriculum; and the establishment of government departments to administer financial support for mathematical research. The text also describes the efforts to improve communication between mathematicians (i.e. the inception of the Mathematical Offprint Service and the publication of Contents of Contemporary Mathematical Journals by the American Mathematical Society). People who are studying, teaching, or applying mathematics will find the book helpful.

Tables of Racah Coefficients

1st Edition
May 23, 2014
A. F. Nikiforov + 2 more
English
eBook
9 7 8 1 4 8 3 1 4 9 9 2 9

Tables of Racah Coefficients presents a compilation of tables of Racah coefficients. Racah coefficients appear and are widely used in a number of problems in quantum mechanics; in the theory of spectra of complex atoms and nuclei; in the theory of angular distributions of nuclear reactions; in the theory of angular correlations of decay particles; and many other problems where the sums of products of three or more Clebsch-Gordan coefficients occur. In compiling tables of Racah coefficients certain conditions can be imposed on the indices, which follow from the symmetry relations. Only those coefficients are given which satisfy these conditions. The present tables consist of three parts. The first part gives Racah coefficients in which the first four indices are half-integers, and the other two integers. The second gives Racah coefficients with integer indices. The third gives Racah coefficients in which the three indices, a, c, e are half-integers, and the other three are integers.

Tables of Lommel's Functions of Two Pure Imaginary Variables

1st Edition
May 23, 2014
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.

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