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Calculus of a Single Variable

ISBN: 9780618503049 | 0618503048
Edition: 8th
Format: Hardcover
Publisher: ITP DELMAR
Pub. Date: 1/19/2005

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Table of Contents
A Word from the Authorsx
Integrated Learning System for Calculusxii
Featuresxviii
Preparation for Calculus
1(40)
... MORE
Graphs and Models
2(8)
Linear Models and Rates of Change
10(9)
Functions and Their Graphs
19(12)
Fitting Models to Data
31(6)
Review Exercises
37(2)
P.S. Problem Solving
39(2)
Limits and Their Properties
41(54)
A Preview of Calculus
42(6)
Finding Limits Graphically and Numerically
48(11)
Evaluating Limits Analytically
59(11)
Continuity and One-Sided Limits
70(13)
Infinite Limits
83(7)
Section Project: Graphs and Limits of Trigonometric Functions
90(5)
Review Exercises
91(2)
P.S. Problem Solving
93(2)
Differentiation
95(68)
The Derivative and the Tangent Line Problem
96(11)
Basic Differentiation Rules and Rates of Change
107(12)
Product and Quotient Rules and Higher-Order Derivatives
119(11)
The Chain Rule
130(11)
Implicit Differentiation
141(7)
Section Project: Optical Illusions
148(15)
Related Rates
149(9)
Review Exercises
158(3)
P.S. Problem Solving
161(2)
Applications of Differentiation
163(84)
Extrema on an Interval
164(8)
Rolle's Theorem and the Mean Value Theorem
172(7)
Increasing and Decreasing Functions and the First Derivative Test
179(10)
Section Project: Rainbows
189(39)
Concavity and the Second Derivative Test
190(8)
Limits at Infinity
198(11)
A Summary of Curve Sketching
209(9)
Optimization Problems
218(10)
Section Project: Connecticut River
228(19)
Newton's Method
229(6)
Differentials
235(7)
Review Exercises
242(3)
P.S. Problem Solving
245(2)
Integration
247(74)
Antiderivatives and Indefinite Integration
248(11)
Area
259(12)
Riemann Sums and Definite Integrals
271(11)
The Fundamental Theorem of Calculus
282(12)
Section Project: Demonstrating the Fundamental Theorem
294(27)
Integration by Substitution
295(14)
Numerical Integration
309(7)
Review Exercises
316(3)
P.S. Problem Solving
319(2)
Logarithmic, Exponential, and Other Transcendental Functions
321(82)
The Natural Logarithmic Function: Differentiation
322(10)
The Natural Logarithmic Function: Integration
332(9)
Inverse Functions
341(9)
Exponential Functions: Differentiation and Integration
350(10)
Bases Other Than e and Applications
360(10)
Section Project: Using Graphing Utilities to Estimate Slope
370(28)
Inverse Trigonometric Functions: Differentiation
371(9)
Inverse Trigonometric Functions: Integration
380(8)
Hyperbolic Functions
388(10)
Section Project: St. Louis Arch
398(5)
Review Exercises
399(2)
P.S. Problem Solving
401(2)
Differential Equations
403(42)
Slope Fields and Euler's Method
404(9)
Differential Equations: Growth and Decay
413(8)
Separation of Variables and the Logistic Equation
421(11)
First-Order Linear Differential Equations
432(8)
Section Project: Weight Loss
440(5)
Review Exercises
441(2)
P.S. Problem Solving
443(2)
Applications of Integration
445(72)
Area of a Region Between Two Curves
446(10)
Volume: The Disk Method
456(11)
Volume: The Shell Method
467(8)
Section Project: Saturn
475(20)
Arc Length and Surfaces of Revolution
476(11)
Work
487(8)
Section Project: Tidal Energy
495(22)
Moments, Centers of Mass, and Centroids
496(11)
Fluid Pressure and Fluid Force
507(6)
Review Exercises
513(2)
P.S. Problem Solving
515(2)
Integration Techniques, L'Hopital's Rule, and Improper Integrals
517(76)
Basic Integration Rules
518(7)
Integration by Parts
525(9)
Trigonometric Integrals
534(8)
Section Project: Power Lines
542(51)
Trigonometric Substitution
543(9)
Partial Fractions
552(9)
Integration by Tables and Other Integration Techniques
561(6)
Indeterminate Forms and L'Hospital's Rule
567(11)
Improper Integrals
578(11)
Review Exercises
589(2)
P.S. Problem Solving
591(2)
Infinite Series
593(100)
Sequences
594(12)
Series and Convergence
606(10)
Section Project: Cantor's Disappearing Table
616(7)
The Integral Test and p-Series
617(6)
Section Project: The Harmonic Series
623(7)
Comparisons of Series
624(6)
Section Project: Solera Method
630(63)
Alternating Series
631(8)
The Ratio and Root Tests
639(9)
Taylor Polynomials and Approximations
648(11)
Power Series
659(10)
Representation of Functions by Power Series
669(7)
Taylor and Maclaurin Series
676(12)
Review Exercises
688(3)
P.S. Problem Solving
691(2)
Conies, Parametric Equations, and Polar Coordinates
693
Conies and Calculus
694(15)
Plane Curves and Parametric Equations
709(9)
Section Project: Cycloids
718(20)
Parametric Equations and Calculus
719(10)
Polar Coordinates and Polar Graphs
729(9)
Section Project: Anamorphic Art
738
Area and Arc Length in Polar Coordinates
739(9)
Polar Equations of Conies and Kepler's Laws
748(8)
Review Exercises
756(3)
P.S. Problem Solving
759
Appendix A Proofs of Selected Theorems
1(19)
Appendix B Integration Tables
20(7)
Additional Appendices
Appendix C Additional Topics in Differential Equations
Exact First-Order Equations
Second-Order Homogeneous Linear Equations
Second-Order Nonhomogeneous Linear Equations
Series Solutions of Differential Equations
Appendix D Precalculus Review
Real Numbers and the Real Number Line
The Cartesian Plane
Review of Trigonometric Functions
Appendix E Rotation and General Second-Degree Equation
Appendix F Complex Numbers
Appendix G Business and Economic Applications
Answers to Odd-Numbered Exercises27(82)
Index of Applications109(4)
Index113

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