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Infinitesimal Calculus

Author: James M. Henle
Publisher: Courier Corporation
ISBN: 9780486428864
Size: 49.63 MB
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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, topology of the real line, and standard calculus and sequences of functions. Only high school mathematics needed. 1979 edition.

The Origins Of Infinitesimal Calculus

Author: Margaret E. Baron
Publisher: Elsevier
ISBN: 1483280926
Size: 28.87 MB
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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.

Elementary Calculus

Author: H. Jerome Keisler
Publisher: Courier Corporation
ISBN: 0486310469
Size: 73.37 MB
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This first-year calculus book is centered around the use of infinitesimals. It contains all the ordinary calculus topics, including approximation problems, vectors, partial derivatives, and multiple integrals. 2007 edition.

Great Currents Of Mathematical Thought

Author: François Le Lionnais
Publisher: Courier Corporation
ISBN: 9780486495781
Size: 59.61 MB
Format: PDF
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50 essays by eminent scholars include meditations on "Structures," Disciplines," "Space," "Function," "Group," "Probability," and "The Mathematical Epic" (Volume I) and on "Mathematics and the Human Intellect," "Mathematics and Technology," and "Mathematics and Civilization" (Volume II). 1962 edition.

The Early Mathematical Manuscripts Of Leibniz

Author: G. W. Leibniz
Publisher: Courier Corporation
ISBN: 0486154718
Size: 70.25 MB
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Leibniz's own accounts of his work, plus critical and historical notes and essays, include his "Historia et Origio Calculi Differentialis," manuscripts of the period 1673-77, and essays by C. I. Gerhardt.

An Essay On The Psychology Of Invention In The Mathematical Field

Author: Jacques Hadamard
Publisher: Courier Corporation
ISBN: 9780486201078
Size: 71.52 MB
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Thoughtful and articulate study of the origin of ideas. Role of the unconscious in invention; the medium of ideas — do they come to mind in words? in pictures? in mathematical terms? Much more. "It is essential for the mathematician, and the layman will find it good reading." — Library Journal.

Elementary Mathematics From An Advanced Standpoint

Author: Felix Klein
Publisher: Courier Corporation
ISBN: 048643480X
Size: 39.14 MB
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Discusses calculating with natural numbers, the first extension of the notion of number, special properties of integers, and complex numbers; algebra-related subjects such as real equations with real unknowns and equations in the field of complex quantities. Also explores elements of analysis, with discussions of logarithmic and exponential functions, the goniometric functions, and infinitesimal calculus. 1932 edition. 125 figures.