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Calculus of a Single Variable: Early...,9780395933213

Calculus of a Single Variable: Early...

by
ISBN13:

9780395933213

ISBN10:
0395933218
Format:
Hardcover
Pub. Date:
8/1/1998
Publisher(s):
Cengage Learning
List Price: $121.96

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Table of Contents

A Word from the Authors (Preface) ix
Index of Applications xxxi
Preparation for Calculus
1(54)
Graphs and Models
3(8)
Linear Models and Rates of Change
11(9)
Functions and Their Graphs
20(11)
Fitting Models to Data
31(6)
Inverse Functions
37(11)
Exponential and Logarithmic Functions
48(7)
Limits and Their Properties
55(52)
A Preview of Calculus
57(6)
Finding Limits Graphically and Numerically
63(9)
Evaluating Limits Analytically
72(12)
Continuity and One-Sided Limits
84(12)
Infinite Limits
96(11)
Review Exercises
104(3)
Differentiation
107(86)
The Derivative and the Tangent Line Problem
109(11)
Basic Differentiation Rules and Rates of Change
120(13)
The Product and Quotient Rules and Higher-Order Derivatives
133(10)
The Chain Rule
143(15)
Implicit Differentiation
158(8)
Derivatives of Inverse Functions
166(7)
Related Rates
173(9)
Newton's Method
182(11)
Review Exercises
188(5)
Applications of Differentiation
193(82)
Extrema on an Interval
195(8)
Rolle's Theorem and the Mean Value Theorem
203(6)
Increasing and Decreasing Functions and the First Derivative Test
209(10)
Concavity and the Second Derivative Test
219(8)
Limits at Infinity
227(9)
A Summary of Curve Sketching
236(10)
Optimization Problems
246(11)
Differentials
257(7)
Business and Economics Applications
264(11)
Review Exercises
271(4)
Integration
275(96)
Antiderivatives and Indefinite Integration
277(11)
Area
288(12)
Riemann Sums and Definite Integrals
300(10)
The Fundamental Theorem of Calculus
310(13)
Integration by Substitution
323(12)
Numerical Integration
335(7)
The Natural Logarithmic Function and Integration
342(8)
Inverse Trigonometric Functions and Integration
350(7)
Hyperbolic Functions
357(14)
Review Exercises
367(4)
Differential Equations
371(34)
Differential Equations: Growth and Decay
373(8)
Differential Equations: Separation of Variables
381(13)
First-Order Linear Differential Equations
394(11)
Review Exercises
403(2)
Applications of Integration
405(68)
Area of a Region Between Two Curves
407(9)
Volume: The Disc Method
416(11)
Volume: The Shell Method
427(8)
Arc Length and Surfaces of Revolution
435(10)
Work
445(9)
Moments, Centers of Mass, and Centroids
454(11)
Fluid Pressure and Fluid Force
465(8)
Review Exercises
471(2)
Integration Techniques, L'Hopital's Rule, and Improper Integrals
473(72)
Basic Integration Rules
475(6)
Integration by Parts
481(9)
Trigonometric Integrals
490(9)
Trigonometric Substitution
499(9)
Partial Fractions
508(9)
Integration by Tables and Other Integration Techniques
517(6)
Indeterminate Forms and L'Hopital's Rule
523(10)
Improper Integrals
533(12)
Review Exercises
542(3)
Infinite Series
545(90)
Sequences
547(11)
Series and Convergence
558(10)
The Integral Test and p-Series
568(6)
Comparisons of Series
574(7)
Alternating Series
581(7)
The Ratio and Root Tests
588(8)
Taylor Polynomials and Approximations
596(10)
Power Series
606(9)
Representation of Functions by Power Series
615(7)
Taylor and Maclaurin Series
622(13)
Review Exercises
632(3)
Conics, Parametric Equations, and Polar Coordinates
635(2)
Conics and Calculus
637(15)
Plane Curves and Parametric Equations
652(10)
Parametric Equations and Calculus
662(9)
Polar Coordinates and Polar Graphs
671(10)
Area and Arc Length in Polar Coordinates
681(8)
Polar Equations of Conics and Kepler's Laws
689(7)
Review Exercises
696
Appendix A Precalculus Review A1
A.1 Real Numbers and the Real Line
A1
A.2 The Cartesian Plane
A10
A.3 Review of Trigonometric Functions
A17
Appendix B Proofs of Selected Theorems A28
Appendix C Basic Differentiation Rules for Elementary Functions A44
Appendix D Integration Tables A45
Appendix E Rotation and the General Second-Degree Equation A51
Answers to Odd-Numbered Exercises A57
Index A145


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