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" What is calculus? : "
R. Michael Range, State University of New York at Albany, USA.
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BL
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| Record Number
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890724
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| Main Entry
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Range, R. Michael.
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| Title & Author
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What is calculus? : : from simple algebra to deep analysis /\ R. Michael Range, State University of New York at Albany, USA.
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| Publication Statement
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New Jersey :: World Scientific,, 2016.
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| Page. NO
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xxxi, 340 pages :: illustrations ;; 24 cm
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| ISBN
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9789814644471
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: 9789814644488
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: 9814644471
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: 981464448X
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| Notes
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Includes index.
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| Contents
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Tangents to circles -- Tangents to parabolas -- Motion with variable speed -- Tangents to graphs of polynomials -- Rules for differentiation -- More general algebraic functions -- Beyond algebraic functions -- The cast : functions of a real variable -- Real numbers -- Functions -- Simple periodic functions -- Exponential functions -- Natural operations on functions -- Algebraic operations and functions -- Derivatives : how to measure change -- Algebraic derivatives by approximation -- Derivatives of exponential functions -- Differentiability and local linear approximation -- Properties of continuous functions -- Derivatives of trigonometric functions -- Simple differentiation rules -- Product and quotient rules -- Some applications of derivatives -- Exponential models -- The inverse problem and antiderivatives -- "Explosive growth" models -- Acceleration and motion with constant acceleration -- Periodic motions -- Geometric properties of graphs -- An algorithm for solving equations -- Applications to optimization -- Higher order approximations and Taylor polynomials -- The definite integral -- The area problem -- More applications of definite integrals -- Properties of definite integrals -- The fundamental theorem of calculus -- Existence of definite integrals -- Reversing the chain rule : substitution -- Reversing the product rule : integration by parts -- Higher order approximations, part 2: Taylor's theorem -- Excursion into complex numbers and the Euler identity.
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| Subject
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Calculus, Textbooks.
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Algebra
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Calculus, Textbooks.
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Calculus.
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Infinitesimalrechnung
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| Dewey Classification
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515
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| LC Classification
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QA303.2.R36 2016
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| NLM classification
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O172clc
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