Infinitesimal Calculus

Author: James M. Henle
Publisher: Courier Corporation
ISBN: 0486151018
Format: PDF
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Introducing calculus at the basic level, this text covers hyperreal numbers and hyperreal line, continuous functions, integral and differential calculus, fundamental theorem, infinite sequences and series, infinite polynomials, more. 1979 edition.

Elementary Calculus

Author: H. Jerome Keisler
Publisher: Courier Corporation
ISBN: 0486484521
Format: PDF, Mobi
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This first-year calculus book is centered around the use of infinitesimals. It contains all the ordinary calculus topics, including the basic concepts of the derivative, continuity, and the integral, plus traditional limit concepts and approximation problems. Additional subjects include transcendental functions, series, vectors, partial derivatives, and multiple integrals. 2007 edition.

Infinitesimal Calculus

Author: James M. Henle
Publisher: Courier Corporation
ISBN: 0486151018
Format: PDF, ePub
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Introducing calculus at the basic level, this text covers hyperreal numbers and hyperreal line, continuous functions, integral and differential calculus, fundamental theorem, infinite sequences and series, infinite polynomials, more. 1979 edition.

The Origins of Infinitesimal Calculus

Author: Margaret E. Baron
Publisher: Elsevier
ISBN: 1483280926
Format: PDF, Kindle
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The Origins of Infinitesimal Calculus focuses on the evolution, development, and applications of infinitesimal calculus. The publication first ponders on Greek mathematics, transition to Western Europe, and some center of gravity determinations in the later 16th century. Discussions focus on the growth of kinematics in the West, latitude of forms, influence of Aristotle, axiomatization of Greek mathematics, theory of proportion and means, method of exhaustion, discovery method of Archimedes, and curves, normals, tangents, and curvature. The manuscript then examines infinitesimals and indivisibles in the early 17th century and further advances in France and Italy. Topics include the link between differential and integral processes, concept of tangent, first investigations of the cycloid, and arithmetization of integration methods. The book reviews the infinitesimal methods in England and Low Countries and rectification of arcs. The publication is a vital source of information for historians, mathematicians, and researchers interested in infinitesimal calculus.

A Primer of Infinitesimal Analysis

Author: John L. Bell
Publisher: Cambridge University Press
ISBN: 0521887186
Format: PDF, Mobi
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A rigorous, axiomatically formulated presentation of the 'zero-square', or 'nilpotent' infinitesimal.

Applied Nonstandard Analysis

Author: Martin Davis
Publisher: Courier Corporation
ISBN: 0486152340
Format: PDF, ePub
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This applications-oriented text assumes no knowledge of mathematical logic in its development of nonstandard analysis techniques and their applications to elementary real analysis and topological and Hilbert space. 1977 edition.

A Concept of Limits

Author: Donald W. Hight
Publisher: Courier Corporation
ISBN: 0486153126
Format: PDF, ePub, Mobi
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An exploration of conceptual foundations and the practical applications of limits in mathematics, this text offers a concise introduction to the theoretical study of calculus. Many exercises with solutions. 1966 edition.

An Outline of Set Theory

Author: James M. Henle
Publisher: Courier Corporation
ISBN: 0486453375
Format: PDF, Docs
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An innovative problem-oriented introduction to set theory, this volume is intended for undergraduate courses in which students work in groups on projects and present their solutions to the class. The three-part treatment consists of problems, hints for their solutions, and complete answers. 1986 edition.

Non standard Analysis

Author: Abraham Robinson
Publisher: Princeton University Press
ISBN: 1400884225
Format: PDF, Kindle
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Considered by many to be Abraham Robinson's magnum opus, this book offers an explanation of the development and applications of non-standard analysis by the mathematician who founded the subject. Non-standard analysis grew out of Robinson's attempt to resolve the contradictions posed by infinitesimals within calculus. He introduced this new subject in a seminar at Princeton in 1960, and it remains as controversial today as it was then. This paperback reprint of the 1974 revised edition is indispensable reading for anyone interested in non-standard analysis. It treats in rich detail many areas of application, including topology, functions of a real variable, functions of a complex variable, and normed linear spaces, together with problems of boundary layer flow of viscous fluids and rederivations of Saint-Venant's hypothesis concerning the distribution of stresses in an elastic body.

The Calculus Primer

Author: William L. Schaaf
Publisher: Courier Corporation
ISBN: 0486172643
Format: PDF, ePub, Mobi
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Comprehensive but concise, this introduction to differential and integral calculus covers all the topics usually included in a first course. The straightforward development places less emphasis on mathematical rigor, and the informal manner of presentation sets students at ease. Many carefully worked-out examples illuminate the text, in addition to numerous diagrams, problems, and answers. Bearing the needs of beginners constantly in mind, the treatment covers all the basic concepts of calculus: functions, derivatives, differentiation of algebraic and transcendental functions, partial differentiation, indeterminate forms, general and special methods of integration, the definite integral, partial integration, and other fundamentals. Ample exercises permit students to test their grasp of subjects before moving forward, making this volume appropriate not only for classroom use but also for review and home study.