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Calculus

by ; ;
Edition:
8th
ISBN13:

9780618502981

ISBN10:
061850298X
Format:
Hardcover
Pub. Date:
1/11/2005
Publisher(s):
Brooks Cole
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Summary

Designed for the three-semester calculus course for math and science majors, Calculus continues to offer instructors and students new and innovative teaching and learning resources. This was the first calculus text to use computer-generated graphics, to include exercises involving the use of computers and graphing calculators, to be available in an interactive CD-ROM format, to be offered as a complete, online calculus course, and to offer a two-semester Calculus I with Precalculus text. Every edition of the series has made the mastery of traditional calculus skills a priority, while embracing the best features of new technology and, when appropriate, calculus reform ideas. Now, the Eighth Edition is the first calculus program to offer algorithmic homework and testing created in Maple so that answers can be evaluated with complete mathematical accuracy. Two primary objectives guided the authors in writing this book: to develop precise, readable materials for students that clearly define and demonstrate concepts and rules of calculus and to design comprehensive teaching resources for instructors that employ proven pedagogical techniques and saves the instructor time. The Eighth Edition continues to provide an evolving range of conceptual, technological, and creative tools that enable instructors to teach the way they want to teach and students to learn they way they learn best.

Table of Contents

A Word from the Authors x
Integrated Learning System for Calculus xii
Features xviii
Preparation for Calculus
1(40)
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'Hopital'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)
Conics, Parametric Equations, and Polar Coordinates
693(68)
Conics 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(23)
Area and Arc Length in Polar Coordinates
739(9)
Polar Equations of Conics and Kepler's Laws
748(8)
Review Exercises
756(3)
P.S. Problem Solving
759(2)
Vectors and the Geometry of Space
761(70)
Vectors in the Plane
762(11)
Space Coordinates and Vectors in Space
773(8)
The Dot Product of Two Vectors
781(9)
The Cross Product of Two Vectors in Space
790(8)
Lines and Planes in Space
798(11)
Section Project: Distances in Space
809(22)
Surfaces in Space
810(10)
Cylindrical and Spherical Coordinates
820(7)
Review Exercises
827(2)
P.S. Problem Solving
829(2)
Vector-Valued Functions
831(52)
Vector-Valued Functions
832(7)
Section Project: Witch of Agnesi
839(44)
Differentiation and Integration of Vector-Valued Functions
840(8)
Velocity and Acceleration
848(9)
Tangent Vectors and Normal Vectors
857(10)
Arc Length and Curvature
867(12)
Review Exercises
879(2)
P.S. Problem Solving
881(2)
Functions of Several Variables
883(98)
Introduction to Functions of Several Variables
884(12)
Limits and Continuity
896(10)
Partial Derivatives
906(9)
Section Project: Moire Fringes
915(36)
Differentials
916(7)
Chain Rules for Functions of Several Variables
923(8)
Directional Derivatives and Gradients
931(12)
Tangent Planes and Normal Lines
943(8)
Section Project: Wildflowers
951(16)
Extrema of Functions of Two Variables
952(8)
Applications of Extrema of Functions of Two Variables
960(7)
Section Project: Building a Pipeline
967(14)
Lagrange Multipliers
968(8)
Review Exercises
976(3)
P.S. Problem Solving
979(2)
Multiple Integration
981(72)
Iterated Integrals and Area in the Plane
982(8)
Double Integrals and Volume
990(11)
Change of Variables: Polar Coordinates
1001(8)
Center of Mass and Moments of Inertia
1009(7)
Section Project: Center of Pressure on a Sail
1016(7)
Surface Area
1017(6)
Section Project: Capillary Action
1023(18)
Triple Integrals and Applications
1024(11)
Triple Integrals in Cylindrical and Spherical Coordinates
1035(6)
Section Project: Wrinkled and Bumpy Spheres
1041(12)
Change of Variables: Jacobians
1042(6)
Review Exercises
1048(3)
P.S. Problem Solving
1051(2)
Vector Analysis
1053
Vector Fields
1054(11)
Line Integrals
1065(14)
Conservative Vector Fields and Independence of Path
1079(10)
Green's Theorem
1089(8)
Section Project: Hyperbolic and Trigonometric Functions
1097(22)
Parametric Surfaces
1098(10)
Surface Integrals
1108(11)
Section Project: Hyperboloid of One Sheet
1119(17)
Divergence Theorem
1120(8)
Stokes's Theorem
1128(6)
Review Exercises
1134(2)
Section Project: The Planimeter
1136
P.S. Problem Solving
1137
Appendix A Proofs of Selected Theorems
1(19)
Appendix B Integration Tables
20(7)
Answers to Odd-Numbered Exercises 27(116)
Index of Applications 143(4)
Index 147


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