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Books in Mathematics general

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831-840 of 853 results in All results

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.

A Course of Higher Mathematics

  • 1st Edition
  • January 1, 1964
  • V. I. Smirnov
  • I. N. Sneddon + 2 more
  • English
  • eBook
    9 7 8 - 1 - 4 8 3 1 - 4 0 1 3 - 1
International Series of Monographs in Pure and Applied Mathematics, Volume 59: A Course of Higher Mathematics, III/I: Linear Algebra focuses on algebraic methods. The book first ponders on the properties of determinants and solution of systems of equations. The text then gives emphasis to linear transformations and quadratic forms. Topics include coordinate transformations in three-dimensional space; covariant and contravariant affine vectors; unitary and orthogonal transformations; and basic matrix calculus. The selection also focuses on basic theory of groups and linear representations of groups. Representation of a group by linear transformations; linear representations of the unitary group in two variables; linear representations of the rotation group; and Abelian groups and representations of the first degree are discussed. Other considerations include integration over groups, Lorentz transformations, permutations, and classes and normal subgroups. The text is a vital source of information for students, mathematicians, and physicists.

A Course of Higher Mathematics

  • 1st Edition
  • January 1, 1964
  • V. I. Smirnov
  • I. N. Sneddon + 2 more
  • English
  • eBook
    9 7 8 - 1 - 4 8 3 1 - 3 9 3 7 - 1
International Series of Monographs in Pure and Applied Mathematics, Volume 62: A Course of Higher Mathematics, V: Integration and Functional Analysis focuses on the theory of functions. The book first discusses the Stieltjes integral. Concerns include sets and their powers, Darboux sums, improper Stieltjes integral, jump functions, Helly’s theorem, and selection principles. The text then takes a look at set functions and the Lebesgue integral. Operations on sets, measurable sets, properties of closed and open sets, criteria for measurability, and exterior measure and its properties are discussed. The text also examines set functions, absolute continuity, and generalization of the integral. Absolutely continuous set functions; absolutely continuous functions of several variables; supplementary propositions; and the properties of the Hellinger integral are presented. The text also focuses on metric and normed spaces. Separability, compactness, linear functionals, conjugate spaces, and operators in normed spaces are underscored. The book also discusses Hilbert space. Linear functionals, projections, axioms of the space, sequences of operators, and weak convergence are described. The text is a valuable source of information for students and mathematicians interested in studying the theory of functions.

Partial Differential Equations of Mathematical Physics

  • 1st Edition
  • January 1, 1964
  • S. L. Sobolev
  • I. N. Sneddon + 2 more
  • English
  • eBook
    9 7 8 - 1 - 4 8 3 1 - 8 1 3 6 - 3
Pure and Applied Mathematics, Volume 56: Partial Differential Equations of Mathematical Physics provides a collection of lectures related to the partial differentiation of mathematical physics. This book covers a variety of topics, including waves, heat conduction, hydrodynamics, and other physical problems. Comprised of 30 lectures, this book begins with an overview of the theory of the equations of mathematical physics that has its object the study of the integral, differential, and functional equations describing various natural phenomena. This text then examines the linear equations of the second order with real coefficients. Other lectures consider the Lebesgue–Fubini theorem on the possibility of changing the order of integration in a multiple integral. This book discusses as well the Dirichlet problem and the Neumann problem for domains other than a sphere or half-space. The final lecture deals with the properties of spherical functions. This book is a valuable resource for mathematicians.

Elementary Vectors

  • 1st Edition
  • January 1, 1964
  • E. Å’. Wolstenholme
  • W. J. Langford + 1 more
  • English
  • eBook
    9 7 8 - 1 - 4 8 3 1 - 8 1 9 2 - 9
Elementary Vectors is an introductory course in vector analysis which is both rigorous and elementary, and demonstrates the elegance of vector methods in geometry and mechanics. Topics covered range from scalar and vector products of two vectors to differentiation and integration of vectors, as well as central forces and orbits. Comprised of seven chapters, this book begins with an introduction to relevant definitions; addition and subtraction of vectors; multiplication of a vector by a real number; position vectors and distance between two points; and direction cosines and direction ratios. The discussion then turns to scalar and vector products of two vectors; application of vector methods to simple kinematical and dynamical problems concerning the motion of a particle; and differentiation and integration of vectors. Central forces and orbits are also considered, along with the equation of a straight line and that of a plane. A parametric treatment of certain three-dimensional curves and curved surfaces, including the helix, is presented. This monograph will be of value to students, teachers, and practitioners of mathematics.

Methods of Matrix Algebra

  • 1st Edition
  • Volume 16
  • January 1, 1964
  • Pease
  • English
  • eBook
    9 7 8 - 0 - 0 8 - 0 9 5 5 2 2 - 3

NonEuclidean Geometry

  • 1st Edition
  • January 1, 1964
  • Herbert Meschkowski
  • D. Allan Bromley + 2 more
  • English
  • eBook
    9 7 8 - 1 - 4 8 3 2 - 5 9 2 1 - 5
Noneuclidean Geometry focuses on the principles, methodologies, approaches, and importance of noneuclidean geometry in the study of mathematics. The book first offers information on proofs and definitions and Hilbert's system of axioms, including axioms of connection, order, congruence, and continuity and the axiom of parallels. The publication also ponders on lemmas, as well as pencil of circles, inversion, and cross ratio. The text examines the elementary theorems of hyperbolic geometry, particularly noting the value of hyperbolic geometry in noneuclidian geometry, use of the Poincaré model, and numerical principles in proving hyperparallels. The publication also tackles the issue of construction in the Poincaré model, verifying the relations of sides and angles of a plane through trigonometry, and the principles involved in elliptic geometry. The publication is a valuable source of data for mathematicians interested in the principles and applications of noneuclidean geometry.

Sixth Form Pure Mathematics

  • 1st Edition
  • January 1, 1963
  • C. Plumpton + 1 more
  • English
  • eBook
    9 7 8 - 1 - 4 8 3 1 - 4 0 8 8 - 9
Sixth Form Pure Mathematics, Volume 2, provides an introduction to inverse trigonometric functions, hyperbolic and inverse hyperbolic functions, and a range of mathematical methods including the use of determinants, the manipulation of inequalities, the solution of easy differential equations, and the use of approximate numerical methods. Complex numbers are defined and the various ways of representing and manipulating them are considered. Polar coordinates, curvature, an elementary study of lengths of curves and areas of surfaces of revolution, a more mature discussion of two-dimensional coordinate geometry than was possible in Volume 1, and an elementary introduction to the methods of three dimensional coordinate geometry comprise the geometrical content of the book. Throughout, the authors have tried to preserve the concentric style which they used in Volume 1 and the many worked examples and exercises in each chapter are designed or chosen to provide a continuous reminder of the work of the preceding chapters. Except for Pure Geometry, the two volumes cover almost all of the syllabuses for Advanced Pure Mathematics of the nine Examining Boards. This book provides an adequate course for mathematical pupils at Grammar Schools and a useful introductory course for Science and Engineering students in their first year at University or Technical College or engaged in private study.

Concise Vector Analysis

  • 1st Edition
  • January 1, 1963
  • C. J. Eliezer
  • W. J. Langford + 2 more
  • English
  • eBook
    9 7 8 - 1 - 4 8 3 1 - 4 1 9 3 - 0
Concise Vector Analysis is a five-chapter introductory account of the methods and techniques of vector analysis. These methods are indispensable tools in mathematics, physics, and engineering. The book is based on lectures given by the author in the University of Ceylon. The first two chapters deal with vector algebra. These chapters particularly present the addition, representation, and resolution of vectors. The next two chapters examine the various aspects and specificities of vector calculus. The last chapter looks into some standard applications of vector algebra and calculus. This book will prove useful to applied mathematicians, students, and researchers.