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The creation of algebraic topology is a major accomplishment of the 20th century. The goal of this book is to show how geometric and algebraic ideas met and grew together into an important branch of mathematics in the recent past. The book also conveys the fun and adventure that can be part of a mathematical investigation.
This brief monograph bridges a gap between sketchy and over-complicated treatments. Topics include functions, Euler integrals and Gauss formula, connection with sin x, applications to definite integrals, and other subjects. 1964 edition.
Well-known, respected introduction, updated to integrate concepts and procedures associated with computers. Computation, approximation, interpolation, numerical differentiation and integration, smoothing of data, more. Includes 150 additional problems in this edition.
Physics, chemistry, and engineering undergraduates will benefit from this straightforward guide to special functions. Its topics possess wide applications in quantum mechanics, electrical engineering, and many other fields. 1968 edition. Includes 25 figures.
This text contains an elementary introduction to continuous groups and differential invariants; an extensive treatment of groups of motions in euclidean, affine, and riemannian geometry; more. Includes exercises and 62 figures.
Traditionally, linear algebra, vector analysis, and the calculus of functions of several variables are taught as separate subjects. This text explores their close relationship and establishes the underlying links. A rigorous and comprehensive introductory treatment, it features clear, readable proofs that illustrate the classical theorems of vector calculus, including the inverse and implicit function theorems. Prerequisites include a knowledge of elementary linear algebra and one-variable calculus.Starting with basic linear algebra and concluding with the integration theorems of Green, Stokes, and Gauss, the text pays particular attention to the relationships between different parametrizations of curves and surfaces, and it surveys their application in line and surface integrals. Concepts are amply illustrated with figures, worked examples, and physical applications. Numerous exercises, with hints and answers, range from routine calculations to theoretical problems.Dover (2008) republication of the edition published by Oxford University Press, New York, 1986. 560pp. 53/8 x 81/2. Paperbound.See every Dover book in print at www.doverpublications.com
Written for junior and senior undergraduates, this remarkably clear and accessible treatment covers set theory, the real number system, metric spaces, continuous functions, Riemann integration, multiple integrals, and more. 1968 edition.
A thorough, systematic first course in elementary differential equations for undergraduates in mathematics and science, requiring only basic calculus for a background. Includes many exercises and problems, with answers. Index.
This influential treatise presents a mathematical analysis of choice behavior. It begins with the statement of a general axiom, then explores applications of the theory to substantive problems: psychophysics, utility, and learning. Includes considerations of the Fechnerian assumption and signal detectability theory; utility theory; stochastic theories; more. 1959 edition.
Written by physicists for physics students, this text assumes no detailed background in topology or geometry. Topics include differential forms, homotopy, homology, cohomology, fiber bundles, connection and covariant derivatives, and Morse theory. 1983 edition.
This text features examinations of classic models and a variety of applications. Each section is preceded by an abstract and statement of prerequisites. Includes exercises. 1984 edition.
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