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Calculus with Analytic Geometry : Early Transecentals Version,9780137930760
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Calculus with Analytic Geometry : Early Transecentals Version

by Edwards, C. H.; Penney, David E.
Edition:
5th
ISBN13:

9780137930760

ISBN10:
0137930763
Format:
Hardcover
Pub. Date:
10/1/1997
Publisher(s):
Pearson College Div
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Summary

Appropriate for standard undergraduate Calculus courses. The mainstream calculus text with the most flexible approach to new ideas and calculator/computer technology.

Table of Contents

ABOUT THE AUTHORS ix(1)
PREFACE x
CHAPTER 1 FUNCTIONS AND GRAPHS
1(52)
1.1 Functions and Mathematical Modeling
2(10)
PROJECT: A Square Wading Pool
11(1)
1.2 Graphs of Equations and Functions
12(12)
PROJECT: A Broken Tree
23(1)
1.3 A Brief Catalog of Functions, Part 1
24(9)
PROJECT: A Leaning Ladder
33(1)
1.4 A Brief Catalog of Functions, Part 2
33(12)
PROJECT: A Spherical Asteroid
44(1)
1.5 PREVIEW: What Is Calculus?
45(3)
REVIEW: Definitions and Concepts
48(5)
CHAPTER 2 PRELUDE TO CALCULUS
53(46)
2.1 Tangent Lines and Slope Predictors
54(9)
PROJECT: Numerical Slope Investigations
63(1)
2.2 The Limit Concept
63(14)
PROJECT: Slopes and Logarithms
76(1)
2.3 More About Limits
77(9)
2.4 The Concept of Continuity
86(10)
PROJECT: The Broken Tree Again
95(1)
REVIEW: Definitions, Concepts, Results
96(3)
CHAPTER 3 THE DERIVATIVE
99(114)
3.1 The Derivative and Rates of Change
100(14)
PROJECT: A City's Population Growth
113(1)
3.2 Basic Differentiation Rules
114(11)
PROJECT: A Cold Liter of Water
125(1)
3.3 The Chain Rule
125(8)
3.4 Derivatives of Algebraic Functions
133(8)
3.5 Maxima and Minima of Functions on Closed Intervals
141(8)
PROJECT: Zooming in on Zeros of the Derivative
148(1)
3.6 Applied Maximum-Minimum Problems
149(14)
PROJECT A: Making a Candy Box with a Lid
162(1)
PROJECT B: Power Line Design
163(1)
3.7 Derivatives of Trigonometric Functions
163(11)
3.8 Exponentials, Logarithms, and Inverse Functions
174(12)
PROJECT: Discovering the Number e For Yourself
186(1)
3.9 Implicit Differentiation and Related Rates
186(9)
3.10 Successive Approximations and Newton's Method
195(13)
PROJECT: How Deep Does a Floating Ball Sink?
207(1)
REVIEW: Formulas, Concepts, Definitions
208(5)
CHAPTER 4 ADDITIONAL APPLICATIONS OF THE DERIVATIVE
213(68)
4.1 Introduction
214(1)
4.2 Increments, Differentials, and Linear Approximation
214(8)
4.3 Increasing and Decreasing Functions and the Mean Value Theorem
222(11)
4.4 The First Derivative Test and Applications
233(10)
PROJECT: Constructing a Box at Minimal Cost
243(1)
4.5 Simple Curve Sketching
243(10)
PROJECT: Some Exotic Graphs
252(1)
4.6 Higher Derivatives and Concavity
253(13)
PROJECT: Invisible Critical Points and Inflection Points
266(1)
4.7 Curve Sketching and Asymptotes
266(12)
PROJECT: Locating Special Points on Exotic Graphs
278(1)
REVIEW: Definitions, Concepts, Results
278(3)
CHAPTER 5 THE INTEGRAL
281(94)
5.1 Introduction
282(1)
5.2 Antiderivatives and Initial Value Problems
282(1)
5.3 Elementary Area Computations
283(25)
5.4 Riemann Sums and the Integral
308(12)
PROJECT: Calculator/Computer Riemann Sums
316(4)
5.5 Evaluation of Integrals
320(8)
5.6 Average Values and the Fundamental Theorem of Calculus
328(10)
5.7 Integration by Substitution
338(8)
5.8 Areas of Plane Regions
346(11)
PROJECT: Approximate Area Calculations
356(1)
5.9 Numerical Integration
357(15)
PROJECT: Approximating In2 and Pie by Numerical Integration
368(4)
REVIEW: Definitions, Concepts, Results
372(3)
CHAPTER 6 APPLICATIONS OF THE INTEGRAL
375(58)
6.1 Setting Up Integral Formulas
376(7)
6.2 Volumes by the Method of Cross Sections
383(12)
PROJECT: Approximating Volumes of Solids of Revolution
394(1)
6.3 Volumes by the Method of Cylinderical Shells
395(8)
PROJECT: Design Your Own Ring!
402(1)
6.4 Are Length and Surface Area of Revolution
403(9)
PROJECT: Approximating Are Length and Surface Area
412(1)
6.5 Separable Differential Equations
412(8)
6.6 Force and Work
420(10)
REVIEW: Definitions, Concepts, Results
430(3)
CHAPTER 7 EXPONENTIAL AND LOGARITHMIC FUNCTIONS
433(44)
7.1 Exponentials, Logarithms, and Inverse Functions
434(1)
7.2 The Natural Logarithm
434(10)
PROJECT: Discovering the Number e by Numerical Integration
444(1)
7.3 The Exponential Function
444(8)
PROJECT: Discovering the Number e as a Limit
451(1)
7.4 General Exponential and Logarithmic Functions
452(7)
PROJECT: Going Where No One Has Gone Before
459(1)
7.5 Natural Growth and Decay
459(9)
PROJECT: The Rule of 72-True or False?
468(1)
*7.6 Linear First-Order Equations and Applications
468(6)
REVIEW: Definitions, Concepts, Results
474(3)
CHAPTER 8 FURTHER CALCULUS OF TRANSCENDENTAL FUNCTIONS
477(36)
8.1 Introduction
478(1)
8.2 Inverse Trigonometric Functions
478(10)
8.3 Indeterminate Forms and l'Hopital's Rule
488(7)
PROJECT: Graphical Investigation of Indeterminate Forms
494(1)
8.4 Additional Indeterminate Forms
495(5)
8.5 Hyperbolic Functions and Inverse Hyperbolic Functions
500(10)
PROJECT: Your First Sky-Dive
509(1)
REVIEW: Definitions and Formulas
510(3)
CHAPTER 9 TECHNIQUES OF INTEGRATION
513(56)
9.1 Introduction
514(1)
9.2 Integral Tables and Simple Substitutions
514(5)
PROJECT: Comparing Different Answers
518(1)
9.3 Integration by Parts
519(7)
9.4 Trigonometric Integrals
526(7)
9.5 Rational Functions and Partial Fractions
533(10)
PROJECT: Bounded Population Growth
542(1)
9.6 Trigonometric Substitution
543(5)
9.7 Integrals Containing Quadratic Polynomials
548(6)
9.8 Improper Integrals
554(9)
PROJECT: Numerical Approximation of Improper Integrals
562(1)
SUMMARY:
563(6)
CHAPTER 10 POLAR COORDINATES AND PLANE CURVES
569(56)
10.1 Analytic Geometry and the Conic Sections
570(5)
10.2 Polar Coordinates
575(8)
PROJECT: Calculator/Computer-Generated Polar Coordinates Graphs
582(1)
10.3 Area Computations in Polar Coordinates
583(5)
10.4 Parametric Curves
588(9)
PROJECT: Calculator/Computer Graphing of Parametric Curves
596(1)
10.5 Integral Computations with Parametric Curves
597(9)
PROJECT: Moon Orbits and Race Tracks
604(2)
10.6 The Parabola
606(4)
10.7 The Ellipse
610(5)
10.8 The Hyperbola
615(6)
REVIEW: Concepts and Definitions
621(4)
CHAPTER 11 INFINITE SERIES
625(84)
11.1 Introduction
626(1)
11.2 Infinite Sequences
626(10)
PROJECT: Nested Radicals and Continued Fractions
635(1)
11.3 Infinite Series and Convergence
636(11)
PROJECT: Numerical Summation and Geometric Series
646(1)
11.4 Taylor Series and Taylor Polynomials
647(14)
PROJECT: Calculating Logarithms on a Deserted Island
660(1)
11.5 The Integral Test
661(8)
PROJECT: The Number Pie. Once and For All
668(1)
11.6 Comparison Tests for Positive-Term Series
669(6)
11.7 Alternating Series and Absolute Convergence
675(9)
11.8 Power Series
684(12)
11.9 Power Series Computations
696(9)
PROJECT: Calculating Trigonometric Functions on a Deserted Island
704(1)
REVIEW: Definitions, Concepts, Results
705(4)
CHAPTER 12 VECTORS, CURVES, AND SURFACES IN SPACE
709(88)
12.1 Vectors in the Plane
710(6)
12.2 Rectangular Coordinates and Three-Dimensional Vectors
716(11)
12.3 The Cross Product of Two Vectors
727(8)
12.4 Lines and Planes in Space
735(9)
12.5 Curves and Motion in Space
744(15)
PROJECT: Does a Pitched Baseball Really Curve?
758(1)
12.6 Curvature and Acceleration
759(15)
12.7 Cylinders and Quadric Surfaces
774(11)
12.8 Cylindricals and Spherical Coordinates
785(8)
PROJECT: Personal Cylindrical and Spherical Plots
792(1)
REVIEW: Definitions, Concepts, Results
793(4)
CHAPTER 13 PARTIAL DIFFERENTIATION
797(90)
13.1 Introduction
798(1)
13.2 Functions of Several Variables
798(10)
PROJECT: Your Personal Portfolio of Surfaces
807(1)
13.3 Limits and Continuity
808(6)
13.4 Partial Derivatives
814(11)
13.5 Maxima and Minima of Functions of Several Variables
825(12)
PROJECT: Exotic Critical Points
836(1)
13.6 Increments and Differentials
837(7)
13.7 The Chain Rule
844(11)
13.8 Directional Derivatives and the Gradient Vector
855(10)
13.9 Lagrange Multipliers and Constrained Maximum-Minimum Problems
865(10)
PROJECT: Numerical Investigation of Lagrange Multiplier Problems
874(1)
13.10 The Second Derivative Test for Functions of Two Variables
875(8)
PROJECT: Critical Point Investigations
882(1)
REVIEW: Definitions, Concepts, Results
883(4)
CHAPTER 14 MULTIPLE INTEGRALS
887(74)
14.1 Double Integrals
888(7)
PROJECT: Midpoint Approximation of Double Integrals
894(1)
14.2 Double Integrals over More General Regions
895(6)
14.3 Area and Volume by Double Integration
901(6)
14.4 Double Integrals in Polar Coordinates
907(7)
14.5 Applications of Double Integrals
914(12)
PROJECT: Optimal Design of Downhill Race Car Wheels
924(2)
14.6 Triple Integrals
926(8)
PROJECT: Archimedes' Floating Paraboloid
934(1)
14.7 Integration in Cylindrical and Spherical Coordinates
934(8)
PROJECT: The Earth's Mantle
942(1)
14.8 Surface Area
942(7)
PROJECT: Computer-Generated Parametric Surfaces
948(1)
14.9 Change of Variables in Multiple Integrals
949(7)
REVIEW: Definitions, Concepts, Results
956(5)
CHAPTER 15 VECTOR CALCULUS
961
15.1 Vector Fields
962(5)
15.2 Line Integrals
967(11)
15.3 The Fundamental Theorem and Independence of Path
978(8)
15.4 Green's Theorem
986(9)
PROJECT: Green's Theorem and Loop Areas
994(1)
15.5 Surface Integrals
995(11)
PROJECT: Surface Integrals and Rocket Nose Cones
1005(1)
15.6 The Divergence Theorem
1006(7)
15.7 Stokes' Theorem
1013(7)
REVIEW: Definitions, Concepts, Results
1020
APPENDICES A-1(49)
A: Real Number and Inequalities A-1(5)
B: The Coordinate Plane and Straight Lines A-6(8)
C: Review of Trigonometry A-14(6)
D: Proofs of the Limit Laws A-20(6)
E: The Completeness of the Real Number System A-26(5)
F: Proof of the Chain Rule A-31(1)
G: Existence of the Integral A-32(6)
H: Approximations and Riemann Sums A-38(3)
I: L' Hopital's Rule and Cauchy's Mean Value Theorem A-41(3)
J: Proof of Taylor's Formula A-44(1)
K: Conic Sections as Sections of a Cone A-45(1)
L: Units of Measurement and Conversion Factors A-46(1)
M: Formulas from Algebra, Geometry, and Trigonometry A-47(2)
N: The Greek Alphabet A-49(1)
ANSWERS TO ODD-NUMBERED PROBLEMS A-50(42)
REFERENCES FOR FURTHER STUDY A-92
INDEX 1-1


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