Calculus: Graphical, Numerical, Algebraic, AP Edition,9780132014083

Calculus: Graphical, Numerical, Algebraic, AP Edition

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Edition: 3rd
ISBN13: 9780132014083
ISBN10: 0132014084
Format: Hardcover
Pub. Date: 2006-02-01
Publisher(s): Savvas Learning Company
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Table of Contents

Prerequisites for Calculus
2(56)
Lines
3(9)
Increments
Slope of a Line
Parallel and Perpendicular Lines
Equations of Lines
Applications
Functions and Graphs
12(10)
Functions
Domains and Ranges
Viewing and Interpreting Graphs
Even Functions and Odd Functions---Symmetry
Functions Defined in Pieces
Absolute Value Function
Composite Functions
Exponential Functions
22(8)
Exponential Growth
Exponential Decay
Applications
The Number e
Parametric Equations
30(7)
Relations
Circles
Ellipses
Lines and Other Curves
Functions and Logarithms
37(9)
One-to-One Functions
Inverses
Finding Inverses
Logarithmic Functions
Properties of Logarithms
Applications
Trigonometric Functions
46(12)
Radian Measure
Graphs of Trigonometric Functions
Periodicity
Even and Odd Trigonometric Functions
Transformations of Trigonometric Graphs
Inverse Trigonometric Functions
Key Terms
55(1)
Review Exercises
56(2)
Limits and Continuity
58(40)
Rates of Change and Limits
59(11)
Average and Instantaneous Speed
Definition of Limit
Properties of Limits
One-sided and Two-sided Limits
Sandwich Theorem
Limits Involving Infinity
70(8)
Finite Limits as x → ± ∞
Sandwich Theorem Revisited
Infinite Limits as x → α
End Behavior Models
``Seeing'' Limits as x → ± ∞
Continuity
78(9)
Continuity at a Point
Continuous Functions
Algebraic Combinations
Composites
Intermediate Value Theorem for Continuous Functions
Rates of Change and Tangent Lines
87(11)
Average Rates of Change
Tangent to a Curve
Slope of a Curve
Normal to a Curve
Speed Revisited
Key Terms
95(1)
Review Exercises
95(3)
Derivatives
98(88)
Derivative of a Function
99(10)
Definition of a Derivative
Notation
Relationship Between the Graphs of f and f'
Graphing the Derivative from Data
One-sided Derivatives
Differentiability
109(7)
How f'(a) Might Fail to Exist
Differentiability Implies Local Linearity
Derivatives on a Calculator
Differentiability Implies Continuity
Intermediate Value Theorem for Derivatives
Rules for Differentiation
116(11)
Positive Integer Powers, Multiples, Sums, and Differences
Products and Quotients
Negative Integer Powers of x
Second and Higher Order Derivatives
Velocity and Other Rates of Change
127(14)
Instantaneous Rates of Change
Motion along a Line
Sensitivity to Change
Derivatives in Economics
Derivatives of Trigonometric Functions
141(7)
Derivative of the Sine Function
Derivative of the Cosine Function
Simple Harmonic Motion
Jerk
Derivatives of Other Basic Trigonometric Functions
Chain Rule
148(9)
Derivative of a Composite Function
``Outside-Inside'' Rule
Repeated Use of the Chain Rule
Slopes of Parametrized Curves
Power Chain Rule
Implicit Differentiation
157(8)
Implicitly Defined Functions
Lenses, Tangents, and Normal Lines
Derivatives of Higher Order
Rational Powers of Differentiable Functions
Derivatives of Inverse Trigonometric Functions
165(7)
Derivatives of Inverse Functions
Derivative of the Arcsine
Derivative of the Arctangent
Derivative of the Arcsecant
Derivatives of the Other Three
Derivatives of Exponential and Logarithmic Functions
172(14)
Derivative of ex
Derivative of αx
Derivative of In x
Derivative of logαx
Power Rule for Arbitrary Real Powers
Calculus at Work
181(1)
Key Terms
181(1)
Review Exercises
181(5)
Applications of Derivatives
186(76)
Extreme Values of Functions
187(9)
Absolute (Global) Extreme Values
Local (Relative) Extreme Values
Finding Extreme Values
Mean Value Theorem
196(9)
Mean Value Theorem
Physical Interpretation
Increasing and Decreasing Functions
Other Consequences
Connecting f' and f'' with the Graph of f
205(14)
First Derivative Test for Local Extrema
Concavity
Points of Inflection
Second Derivative Test for Local Extrema
Learning about Functions from Derivatives
Modeling and Optimization
219(14)
Examples from Mathematics
Examples from Business and Industry
Examples from Economics
Modeling Discrete Phenomena with Differentiable Functions
Linearization and Newton's Method
233(13)
Linear Approximation
Newton's Method
Differentials
Estimating Change with Differentials
Absolute, Relative, and Percentage Change
Sensitivity to Change
Related Rates
246(16)
Related Rate Equations
Solution Strategy
Simulating Related Motion
Key Terms
255(1)
Review Exercises
256(6)
The Definite Integral
262(58)
Estimating with Finite Sums
263(11)
Distance Traveled
Rectangular Approximation Method (RAM)
Volume of a Sphere
Cardiac Output
Definite Integrals
274(11)
Riemann Sums
Terminology and Notation of Integration
Definite Integral and Area
Constant Functions
Integrals on a Calculator
Discontinuous Integrable Functions
Definite Integrals and Antiderivatives
285(9)
Properties of Definite Integrals
Average Value of a Function
Mean Value Theorem for Definite Integrals
Connecting Differential and Integral Calculus
Fundamental Theorem of Calculus
294(12)
Fundamental Theorem, Part 1
Graphing the Function ∫ x/α f(t)dt
Fundamental Theorem, Part 2
Area Connection
Analyzing Antiderivatives Graphically
Trapezoidal Rule
306(14)
Trapezoidal Approximations
Other Algorithms
Error Analysis
Key Terms
315(1)
Review Exercises
315(4)
Calculus at Work
319(1)
Differential Equations and Mathematical Modeling
320(58)
Slope Fields and Euler's Method
321(10)
Differential Equations
Slope Fields
Euler's Method
Antidifferentiation by Substitution
331(10)
Indefinite Integrals
Leibniz Notation and Antiderivatives
Substitution in Indefinite Integrals
Substitution in Definite Integrals
Antidifferentiation by Parts
341(9)
Product Rule in Integral Form
Solving for the Unknown Integral
Tabular Integration
Inverse Trigonometric and Logarithmic Functions
Exponential Growth and Decay
350(12)
Separable Differential Equations
Law of Exponential Change
Continuously Compounded Interest
Radioactivity
Modeling Growth with Other Bases
Newton's Law of Cooling
Logistic Growth
362(16)
How Populations Grow
Partial Fractions
The Logistic Differential Equation
Logistic Growth Models
Key Terms
372(1)
Review Exercises
372(4)
Calculus at Work
376(2)
Applications of Definite Integrals
378(41)
Integral As Net Change
379(11)
Linear Motion Revisited
General Strategy
Consumption Over Time
Net Change from Data
Work
Areas in the Plane
390(9)
Area Between Curves
Area Enclosed by Intersecting Curves
Boundaries with Changing Functions
Integrating with Respect to y
Saving Time with Geometry Formulas
Volumes
399(13)
Volume As an Integral
Square Cross Sections
Circular Cross Sections
Cylindrical Shells
Other Cross Sections
Lengths of Curves
412(7)
A Sine Wave
Length of Smooth Curve
Vertical Tangents, Corners, and Cusps
Applications from Science and Statistics
419(15)
Work Revisited
Fluid Force and Fluid Pressure
Normal Probabilities
Calculus at Work
430(1)
Key Terms
430(1)
Review Exercises
430(4)
Sequences, L'Hopital's Rule, and Improper Integrals
434(38)
Sequences
435(9)
Defining a Sequence
Arithmetic and Geometric Sequences
Graphing a Sequence
Limit of a Sequence
L'Hopital's Rule
444(9)
Indeterminate Form 0/0
Indeterminate Forms ∞/∞, ∞ 0, and ∞ - ∞
Indeterminate Forms 1∞, 00, ∞0
Relative Rates of Growth
453(6)
Comparing Rates of Growth
Using L'Hopital's Rule to Compare Growth Rates
Sequential versus Binary Search
Improper Integrals
459(13)
Infinite Limits of Integration
Integrands with Infinite Discontinuities
Test for Convergence and Divergence
Applications
Key Terms
470(1)
Review Exercises
470(2)
Infinite Series
472(58)
Power Series
473(11)
Geometric Series
Representing Functions by Series
Differentiation and Integration
Identifying a Series
Taylor Series
484(11)
Constructing a Series
Series for sin x and cos x
Beauty Bare
Maclaurin and Taylor Series
Combining Taylor Series
Table of Maclaurin Series
Taylor's Theorem
495(8)
Taylor Polynomials
The Remainder
Remainder Estimation Theorem
Euler's Formula
Radius of Convergence
503(10)
Convergence
nth-Term Test
Comparing Nonnegative Series
Ratio Test
Endpoint Convergence
Testing Convergence at Endpoints
513(17)
Integral Test
Harmonic Series and p-series
Comparison Tests
Alternating Series
Absolute and Conditional Convergence
Intervals of Convergence
A Word of Caution
Key Terms
526(1)
Review Exercises
526(3)
Calculus at Work
529(1)
Parametric, Vector, and Polar Functions
530(88)
Parametric Functions
531(7)
Parametric Curves in the Plane
Slope and Concavity
Arc Length
Cycloids
Vectors in the Plane
538(10)
Two-Dimensional Vectors
Vector Operations
Modeling Planar Motion
Velocity, Acceleration, and Speed
Displacement and Distance Traveled
Polar Functions
548(14)
Polar Coordinates
Polar Curves
Slopes of Polar Curves
Areas Enclosed by Polar Curves
A Small Polar Gallery
Key Terms
559(1)
Review Exercises
560(2)
APPENDIX
Formulas from Precalculus Mathematics
562(4)
Mathematical Induction
566(3)
Using the Limit Definition
569(8)
Proof of the Chain Rule
577(1)
Conic Sections
578(25)
Hyperbolic Functions
603(9)
A Brief Table of Integrals
612(6)
Glossary 618(11)
Selected Answers 629(51)
Applications Index 680(4)
Index 684

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