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Calculus from Graphical,Numerical,and Symbolic Points of View,Volume 1 / Edition 2

Calculus from Graphical,Numerical,and Symbolic Points of View,Volume 1 / Edition 2

by Arnold Ostebee, Paul Zorn


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Product Details

ISBN-13: 9780030256714
Publisher: Brooks/Cole
Publication date: 07/26/2001
Pages: 592

Table of Contents

1. FUNCTIONS AND DERIVATIVES: THE GRAPHICAL VIEW. Functions, Calculus Style. Graphs. A Field Guide to Elementary Functions. Amount Functions and Rate Functions: The Idea of the Derivative. Estimating Derivatives: A Closer Look. The Geometry of Derivatives. The Geometry of Higher-Order Derivatives. Chapter Summary. Interlude: Zooming in on Differences. 2. FUNCTIONS AND DERIVATIVES: THE SYMBOLIC VIEW. Defining the Derivative. Derivatives of Power Functions ad Polynomials. Limits. Derivatives, Antiderivatives, and Their Uses. Differential Equations; Modeling Motion. Derivatives of Exponential and Logarithm Functions; Modeling Growth. Derivatives of Trigonometric Functions; Modeling Oscillation. Chapter Summary. Interlude: Tangent Lines in History. Interlude: Limit—the Formal Definition. 3. NEW DERIVATIVES FROM OLD. Algebraic Combinations: The Product and Quotient Rules. Composition and the Chain Rule. Implicit Functions and Implicit Differentiation. Inverse Functions and their Derivatives; Inverse Trigonometric Functions. Miscellaneous Derivatives and Antiderivatives. Chapter Summary. Interlude: Vibrations—Simple and Damped. Interlude: Hyperbolic Functions. 4. USING THE DERIVATIVE. Direction Fields; More on Growth and Motion. Limits Involving Infinity; l'Hôspital's Rule: Comparing Rates. More on Optimization. Parametric Equations. Related Rates. Newton's Method. Linear Approximation and Taylor Polynomials. Continuity. The Mean Value Theorem. Chapter Summary. Interlude: Growth with Interest. Interlude: Logistic Growth. Interlude: Digging Deeper for Roots (More on Newton's Method). 5. THE INTEGRAL. Areas and Integrals. TheArea Function. The Fundamental Theorem of Calculus. Finding Antiderivatives by Substitution. Finding Antiderivatives Using Tables and Computers. Approximating Sums: The Integral as a Limit. Working with Approximating Sums. Chapter Summary. Interlude: Mean Value Theorems and Integrals.

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