Skip to main content
View Cart

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.

  • Theory of Differential Equations

    • 1st Edition
    • I. M. Gel'fand + 1 more
    • English
    Generalized Functions, Volume 3: Theory of Differential Equations focuses on the application of generalized functions to problems of the theory of partial differential equations. This book discusses the problems of determining uniqueness and correctness classes for solutions of the Cauchy problem for systems with constant coefficients and eigenfunction expansions for self-adjoint differential operators. The topics covered include the bounded operators in spaces of type W, Cauchy problem in a topological vector space, and theorem of the Phragmén-Lindelöf type. The correctness classes for the Cauchy problem, systems that are Petrovski?-correct, and generalized eigenfunctions of self-adjoint operators are also reviewed. This text likewise covers the differentiation of functionals of strongly and weakly bounded variation. This volume is beneficial to students and researchers interested in the theory of differential equations.

  • Linear Algebra

    • 1st Edition
    • R. R. Stoll + 1 more
    • English
    Linear Algebra is intended to be used as a text for a one-semester course in linear algebra at the undergraduate level. The treatment of the subject will be both useful to students of mathematics and those interested primarily in applications of the theory. The major prerequisite for mastering the material is the readiness of the student to reason abstractly. Specifically, this calls for an understanding of the fact that axioms are assumptions and that theorems are logical consequences of one or more axioms. Familiarity with calculus and linear differential equations is required for understanding some of the examples and exercises. This book sets itself apart from other similar textbooks through its dedication to the principle that, whenever possible, definitions and theorems should be stated in a form which is independent of the notion of the dimension of a vector space. A second feature of this book which is worthy of mention is the early introduction of inner product spaces and the associated metric concepts. Students soon feel at ease with this class of spaces because they share so many properties with physical space when equipped with a rectangular coordinate system. Finally, the book includes a chapter concerned with several applications to other fields of the theory that have been developed.

  • A Syntax-Oriented Translator

    • 1st Edition
    • Peter Zilahy Ingerman
    • English
    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.

  • Graph Theory and Computing

    • 1st Edition
    • Ronald C. Read
    • English
    Graph Theory and Computing focuses on the processes, methodologies, problems, and approaches involved in graph theory and computer science. The book first elaborates on alternating chain methods, average height of planted plane trees, and numbering of a graph. Discussions focus on numbered graphs and difference sets, Euclidean models and complete graphs, classes and conditions for graceful graphs, and maximum matching problem. The manuscript then elaborates on the evolution of the path number of a graph, production of graphs by computer, and graph-theoretic programming language. Topics include FORTRAN characteristics of GTPL, design considerations, representation and identification of graphs in a computer, production of simple graphs and star topologies, and production of stars having a given topology. The manuscript examines the entropy of transformed finite-state automata and associated languages; counting hexagonal and triangular polyominoes; and symmetry of cubical and general polyominoes. Graph coloring algorithms, algebraic isomorphism invariants for graphs of automata, and coding of various kinds of unlabeled trees are also discussed. The publication is a valuable source of information for researchers interested in graph theory and computing.

  • A Course in Ordinary and Partial Differential Equations

    • 1st Edition
    • Zalman Rubinstein
    • English
    A Course in Ordinary and Partial Differential Equations discusses ordinary differential equations and partial differential equations. The book reviews the solution of elementary first-order differential equations, existence theorems, singular solutions, and linear equations of arbitrary order. It explains the solutions of linear equations with constant coefficients, operational calculus, and the solutions of linear differential equations. It also explores the techniques of computing for the solution of systems of linear differential equations, which is similar to the solutions of linear equations of arbitrary order. The text proves that if the coefficients of some differential equations possess certain restricted types of singularities, the solution will have Taylor series expansions about the singular points. The investigator can calculate a divergent series whose partial sums numerically approximate the solution for large x if the point in question is infinity, of which the series will be a Taylor series of negative powers of x. The book also explains the Fourier transform, its applications to partial differential equations, as well as the Hilbert space approach to partial differential equations. The book is a stimulating material for mathematicians, for professors, or for students of pure and applied mathematics, physics, or engineering.

  • Computing Methods in Optimization Problems

    Proceedings of a Conference Held at University of California, Los Angeles January 30-31, 1964
    • 1st Edition
    • A. V. Balakrishnan + 1 more
    • English
    Computing Methods in Optimization Problems deals with hybrid computing methods and optimization techniques using computers. One paper discusses different numerical approaches to optimizing trajectories, including the gradient method, the second variation method, and a generalized Newton-Raphson method. The paper cites the advantages and disadvantages of each method, and compares the second variation method (a direct method) with the generalized Newton-Raphson method (an indirect method). An example problem illustrates the application of the three methods in minimizing the transfer time of a low-thrust ion rocket between the orbits of Earth and Mars. Another paper discusses an iterative process for steepest-ascent optimization of orbit transfer trajectories to minimize storage requirements such as in reduced memory space utilized in guidance computers. By eliminating state variable storage and control schedule storage, the investigator can achieve reduced memory requirements. Other papers discuss dynamic programming, invariant imbedding, quasilinearization, Hilbert space, and the computational aspects of a time-optimal control problem. The collection is suitable for computer programmers, engineers, designers of industrial processes, and researchers involved in aviation or control systems technology.

  • Computer Programming

    A Mixed Language Approach
    • 3rd Edition
    • Marvin L. Stein + 1 more
    • English
    Computer Programming: A Mixed Language Approach describes computer programming from a mixed language perspective. More specifically, it examines how to make effective use of the hardware and software aspects of the total system using the mixed languages that are a composite of the absolute machine languages and the more facile problem-oriented languages. In addition to the absolute machine language required by the computer "hardware" and the problem-oriented language provided by the "software" of symbolic assembly programs and compilers, a third kind of programming language is considered, namely, the symbolic machine language. Comprised of nine chapters, this book illustrates mixed language programming using Fortran and the Fortran Symbolic Assembly Program. The discussion begins by describing a modern digital computer and introducing the general theory of number systems. Subsequent chapters focus on the way in which computing machines are organized to perform their functions; how a computer executes the sequence of instructions and performs a given calculation, a process known as coding; and non-arithmetic instructions used on computers. Subroutines, input-output, and assembly of complete programs are also explored. The final chapter is devoted to Fortran and programs written completely in Fortran, as well as executive programs and programs in mixed languages. This monograph is intended for both professional programmers-to-be and non-professionals in computer programming.

  • College Algebra and Trigonometry

    • 2nd Edition
    • Bernard Kolman + 1 more
    • English
    College Algebra and Trigonometry, Second Edition provides a comprehensive approach to the fundamental concepts and techniques of college algebra and trigonometry. The book incorporates improvements from the previous edition to provide a better learning experience. It contains chapters that are devoted to various mathematical concepts, such as the real number system, the theory of polynomial equations, trigonometric functions, and the geometric definition of each conic section. Progress checks, warnings, and features are inserted. Every chapter contains a summary, including terms and symbols with appropriate page references; key ideas for review to stress the concepts; review exercises to provide additional practice; and progress tests to provide self-evaluation and reinforcement. The answers to all Review Exercises and Progress Tests appear in the back of the book. College students will find the book very useful and invaluable.

  • Multi-Objective Programming in the USSR

    • 1st Edition
    • Elliot R. Lieberman
    • Gerald J. Lieberman + 1 more
    • English
    Statistical Modeling and Decision Science: Multi-Objective Programming in the USSR provides information pertinent to multi-objective programming that has emerged as an increasingly active area of research in the fields of applied mathematics, operations research, and decision and management science. This book traces and analyzes the development of Soviet multi-objective programming. Organized into 24 chapters, this book begins with an overview of the research institutes most actively involved in multi-objective programming research. This text then presents an analytical framework for grouping and classifying the diverse Soviet methods. Other chapters consider the methods and then evaluated according to the significance and soundness of its basic approach and its kinship to other methods. This book discusses as well some significant Soviet theoretical research and several distinctive approaches proposed by Soviet researchers for comparing the effectiveness of alternative interactive multi-objective programming method. The final chapter deals with distinctive Soviet tendencies in multi-objective research. This book is a valuable resource for economists.

  • The Remarkable Sine Functions

    • 1st Edition
    • A. I. Markushevich
    • English
    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.

Related subjects