Calculus
Graphical, Numerical, Algebraic, AP Edition
Finney, Ross L. (EDT)
Demana, Franklin
Waits, Bert K.
- 出版社：Pearson
- 出版年月：2006年 02月
- ISBN：9780132014083
- 装丁：HRD
-
装丁について
- 言語：ENG
- 版次：3RD
- 巻数・ページ数：696 p.
- DDC分類：515
- 目次：
-
- 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 165(7)
- Functions
- 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 172(14)
- Logarithmic Functions
- 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 320(58)
- Modeling
- 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 434(38)
- Integrals
- 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