Calculus: Early Transcendentals, Global Edition

Höfundar: William L. Briggs; Lyle Cochran; Bernard Gillett; Eric Schulz (Útgáfa: 3)
Calculus: Early Transcendentals, Global Edition

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For 3- to 4-semester courses covering single-variable and multivariable calculus, taken by students of mathematics, engineering, natural sciences, or economics. The most successful new calculus text in the last two decades The much-anticipated 3rd Edition of Briggs' Calculus retains its hallmark features while introducing important advances and refinements. Briggs, Cochran, Gillett, and Schulz build from a foundation of meticulously crafted exercise sets, then draw students into the narrative through writing that reflects the voice of the instructor.

Examples are stepped out and thoughtfully annotated, and figures are designed to teach rather than simply supplement the narrative. The groundbreaking eText contains approximately 700 Interactive Figures that can be manipulated to shed light on key concepts. For the 3rd Edition, the authors synthesized feedback on the text and MyLabâ„¢ Math content from over 140 instructors. This thorough and extensive review process, paired with the authors' own teaching experiences, helped create a text that is designed for today's calculus instructors and students.

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Útgefandi
Pearson International Content
ISBN
9781292755038
Print ISBN
9781292755052
Format
ePub
Útgáfa
3
Höfundar
William L. Briggs; Lyle Cochran; Bernard Gillett; Eric Schulz
Tungumál
English
Útgefið
2025-09-03
Prent takmörkun á líftíma
100
Prent takmörkun
2
Afritunar takmörkun
2

Kaflar

  • Front Matter
  • Cover
  • Cover
  • Title Page
  • Title Page
  • Copyright Page
  • Copyright Page
  • Dedication
  • Dedication
  • Contents
  • Contents
  • Preface
  • Preface
  • Credits
  • Credits
  • List of Videos in This eTextbook
  • List of Videos in This eTextbook
  • Get the Most Out of MyLab Math
  • Get the Most Out of MyLab Math
  • Chapter 1: Functions
  • Chapter 1: Functions
  • 1.1: Review of Functions
  • 1.1: Review of Functions
  • Composite Functions
  • Secant Lines and the Difference Quotient
  • Symmetry
  • Section 1.1: Exercises
  • Practice Exercises
  • Explorations and Challenges
  • 1.2: Representing Functions
  • 1.2: Representing Functions
  • Using Formulas
  • Using Graphs
  • Using Tables
  • Using Words
  • Transformations of Functions and Graphs
  • Section 1.2: Exercises
  • Practice Exercises
  • Explorations and Challenges
  • 1.3: Inverse, Exponential, and Logarithmic Functions
  • 1.3: Inverse, Exponential, and Logarithmic Functions
  • Properties of Exponential Functions f(x) = bx
  • Inverse Functions
  • Graphing Inverse Functions
  • Change of Base
  • Section 1.3: Exercises
  • Practice Exercises
  • Explorations and Challenges
  • 1.4: Trigonometric Functions and Their Inverses
  • 1.4: Trigonometric Functions and Their Inverses
  • Radian Measure
  • Trigonometric Functions
  • Trigonometric Identities
  • Graphs of the Trigonometric Functions
  • Transforming Graphs
  • Inverse Trigonometric Functions
  • Other Inverse Trigonometric Functions
  • Section 1.4: Exercises
  • Practice Exercises
  • Explorations and Challenges
  • Chapter 1: Review Exercises
  • Chapter 1: Review Exercises
  • Chapter 1: Guided Projects
  • Chapter 1: Guided Projects
  • Chapter 1: Test Your Understanding
  • Chapter 1: Test Your Understanding
  • Chapter 2: Limits
  • Chapter 2: Limits
  • 2.1: The Idea of Limits
  • 2.1: The Idea of Limits
  • Average Velocity
  • Instantaneous Velocity
  • Slope of the Tangent Line
  • Section 2.1: Exercises
  • Practice Exercises
  • Explorations and Challenges
  • 2.2: Definitions of Limits
  • 2.2: Definitions of Limits
  • One-Sided Limits
  • Section 2.2: Exercises
  • Practice Exercises
  • Explorations and Challenges
  • 2.3: Techniques for Computing Limits
  • 2.3: Techniques for Computing Limits
  • Limits of Linear Functions​​
  • Limit Laws
  • Limits of Polynomial and Rational Functions
  • One-Sided Limits
  • Other Techniques
  • An Important Limit
  • The Squeeze Theorem
  • Trigonometric Limits
  • Section 2.3: Exercises
  • Practice Exercises
  • Explorations and Challenges
  • 2.4: Infinite Limits
  • 2.4: Infinite Limits
  • An Overview
  • Infinite Limits
  • Finding Infinite Limits Analytically
  • Section 2.4: Exercises
  • Practice Exercises
  • Explorations and Challenges
  • 2.5: Limits at Infinity
  • 2.5: Limits at Infinity
  • Limits at Infinity and Horizontal Asymptotes
  • Infinite Limits at Infinity
  • End Behavior
  • End Behavior
  • Section 2.5: Exercises
  • Practice Exercises
  • Explorations and Challenges
  • 2.6: Continuity
  • 2.6: Continuity
  • Continuity at a Point
  • Continuity on an Interval
  • Functions Involving Roots
  • Continuity of Transcendental Functions
  • Intermediate Value Theorem
  • Section 2.6: Exercises
  • Practice Exercises
  • Explorations and Challenges
  • 2.7: Precise Definitions of Limits
  • 2.7: Precise Definitions of Limits
  • Moving Toward a Precise Definition
  • A Precise Definition
  • Limit Proofs
  • Justifying Limit Laws
  • Infinite Limits
  • Limits at Infinity
  • Section 2.7: Exercises
  • Practice Exercises
  • ​​​Explorations and Challenges​
  • Chapter 2: Review Exercises
  • Chapter 2: Review Exercises
  • Chapter 2: Guided Projects
  • Chapter 2: Guided Projects
  • Chapter 2: Test Your Understanding
  • Chapter 2: Test Your Understanding
  • Chapter 3: Derivatives
  • Introduction: Derivatives
  • 3.1: Introducing the Derivative
  • 3.1: Introducing the Derivative
  • Tangent Lines and Rates of Change
  • The Derivative
  • Interpreting the Derivative
  • Section 3.1: Exercises
  • Practice Exercises
  • Explorations and Challenges
  • 3.2: The Derivative as a Function
  • 3.2: The Derivative as a Function
  • The Derivative Function
  • Derivative Notation
  • Graphs of Derivatives
  • Continuity
  • Section 3.2: Exercises
  • Practice Exercises
  • Explorations and Challenges
  • 3.3: Rules of Differentiation
  • 3.3: Rules of Differentiation
  • The Constant and Power Rules for Derivatives
  • Constant Multiple Rule
  • Sum Rule
  • The Derivative of the Natural Exponential Function
  • Slopes of Tangent Lines
  • Higher-Order Derivatives
  • Section 3.3: Exercises
  • Practice Exercises
  • Explorations and Challenges
  • 3.4: The Product and Quotient Rules
  • 3.4: The Product and Quotient Rules
  • Product Rule
  • Quotient Rule
  • Extending the Power Rule to Negative Integers
  • Rates of Change
  • Combining Derivative Rules
  • Section 3.4: Exercises
  • Practice Exercises
  • Explorations and Challenges
  • 3.5: Derivatives of Trigonometric Functions
  • 3.5: Derivatives of Trigonometric Functions
  • Two Special Limits
  • Derivatives of Sine and Cosine Functions
  • Section 3.5: Exercises
  • Practice Exercises
  • Explorations and Challenges
  • 3.6: Derivatives as Rates of Change
  • 3.6: Derivatives as Rates of Change
  • One-Dimensional Motion
  • Growth Models
  • Economics and Business
  • Section 3.6: Exercises
  • Practice Exercises
  • Explorations and Challenges
  • 3.7: The Chain Rule
  • 3.7: The Chain Rule
  • Chain Rule Formulas
  • Chain Rule for Powers
  • The Composition of Three or More Functions
  • Proof of the Chain Rule
  • Section 3.7: Exercises
  • Practice Exercises
  • Explorations and Challenges
  • 3.8: Implicit Differentiation
  • 3.8: Implicit Differentiation
  • Slopes of Tangent Lines
  • Higher-Order Derivatives of Implicit Functions
  • Section 3.8: Exercises
  • Practice Exercises
  • Explorations and Challenges
  • 3.9: Derivatives of Logarithmic and Exponential Functions
  • 3.9: Derivatives of Logarithmic and Exponential Functions
  • The Derivative of y = In x
  • The Derivative of bx
  • The General Power Rule
  • Derivatives of General Logarithmic Functions
  • Logarithmic Differentiation
  • Section 3.9: Exercises
  • Practice Exercises
  • Explorations and Challenges
  • 3.10: Derivatives of Inverse Trigonometric Functions
  • 3.10: Derivatives of Inverse Trigonometric Functions
  • Inverse Sine and Its Derivative
  • Derivatives of Inverse Tangent and Secant
  • Derivatives of Inverse Functions in General
  • Section 3.10: Exercises
  • Practice Exercises
  • Explorations and Challenges
  • 3.11: Related Rates
  • 3.11: Related Rates
  • Section 3.11: Exercises
  • Practice Exercises
  • Explorations and Challenges
  • Chapter 3: Review Exercises
  • Chapter 3: Review Exercises
  • Chapter 3: Guided Projects
  • Chapter 3: Guided Projects
  • Chapter 3: Test Your Understanding
  • Chapter 3: Test Your Understanding
  • Chapter 4: Applications of the Derivative
  • Introduction: Applications of the Derivative
  • 4.1: Maxima and Minima
  • 4.1: Maxima and Minima
  • Absolute Maxima and Minima
  • Local Maxima and Minima
  • Locating Absolute Maxima and Minima
  • Section 4.1: Exercises
  • Practice Exercises
  • Explorations and Challenges
  • 4.2: Mean Value Theorem
  • 4.2: Mean Value Theorem
  • Rolle’s Theorem
  • Mean Value Theorem
  • Consequences of the Mean Value Theorem
  • Section 4.2: Exercises
  • Practice Exercises
  • Explorations and Challenges
  • 4.3: What Derivatives Tell Us
  • 4.3: What Derivatives Tell Us
  • Increasing and Decreasing Functions
  • Identifying Local Maxima and Minima
  • Concavity and Inflection Points
  • Recap of Derivative Properties
  • Section 4.3: Exercises
  • Practice Exercises
  • Explorations and Challenges
  • 4.4: Graphing Functions
  • 4.4: Graphing Functions
  • Calculators and Analysis
  • Graphing Guidelines
  • Section 4.4: Exercises
  • Practice Exercises
  • Explorations and Challenges
  • 4.5: Optimization Problems
  • 4.5: Optimization Problems
  • Section 4.5: Exercises
  • Practice Exercises
  • Explorations and Challenges
  • 4.6: Linear Approximation and Differentials
  • 4.6: Linear Approximation and Differentials
  • Linear Approximation
  • Linear Approximation and Concavity
  • Differentials
  • Section 4.6: Exercises
  • Practice Exercises
  • Explorations and Challenges
  • 4.7: L’Hôpital’s Rule
  • 4.7: L’Hôpital’s Rule
  • L’ Hôpital’s Rule for the Form 0/0
  • Indeterminate Form (∞ | ∞)
  • Related Indeterminate Forms: and 0·∞ and ∞ – ∞
  • Indeterminate Forms and 1∞, 00, and ∞0
  • Growth Rates of Functions
  • Pitfalls in Using l’Hôpital’s Rule
  • Section 4.7: Exercises
  • Practice Exercises
  • Explorations and Challenges
  • 4.8: Newton’s Method
  • 4.8: Newton’s Method
  • Why Approximate?
  • Deriving Newton’s Method
  • When Do You Stop?
  • Pitfalls of Newton’s Method
  • Section 4.8: Exercises
  • Practice Exercises
  • Explorations and Challenges
  • 4.9: Antiderivatives
  • 4.9: Antiderivatives
  • Thinking Backward
  • Indefinite Integrals
  • Indefinite Integrals of Trigonometric Functions
  • Other Indefinite Integrals
  • Introduction to Differential Equations
  • Motion Problems Revisited
  • Section 4.9: Exercises
  • Practice Exercises
  • Explorations and Challenges
  • Chapter 4: Review Exercises
  • Chapter 4: Review Exercises
  • Chapter 4: Guided Projects
  • Chapter 4: Guided Projects
  • Chapter 4: Test Your Understanding
  • Chapter 4: Test Your Understanding
  • Chapter 5: Integration
  • Chapter 5: Integration
  • 5.1: Approximating Areas Under Curves
  • 5.1: Approximating Areas Under Curves
  • Area Under a Velocity Curve
  • Approximating Areas by Riemann Sums
  • Sigma (Summation) Notation
  • Riemann Sums Using Sigma Notation
  • Section 5.1: Exercises
  • Practice Exercises
  • Explorations and Challenges
  • 5.2: Definite Integrals
  • 5.2: Definite Integrals
  • Net Area
  • The Definite Integral
  • Evaluating Definite Integrals
  • Properties of Definite Integrals
  • Bounds on Definite Integrals
  • Evaluating Definite Integrals Using Limits
  • Section 5.2: Exercises
  • Practice Exercises
  • Explorations and Challenges
  • 5.3: Fundamental Theorem of Calculus
  • 5.3: Fundamental Theorem of Calculus
  • Fundamental Theorem of Calculus
  • The Inverse Relationship Between Differentiation and Integration
  • Section 5.3: Exercises
  • Practice Exercises
  • Explorations and Challenges
  • 5.4: Working with Integrals
  • 5.4: Working with Integrals
  • Integrating Even and Odd Functions
  • Average Value of a Function
  • Mean Value Theorem for Integrals
  • Section 5.4: Exercises
  • Section 5.4: Exercises (39-60)
  • Explorations and Challenges
  • 5.5: Substitution Rule
  • 5.5: Substitution Rule
  • Indefinite Integrals
  • General Formulas for Indefinite Integrals
  • Definite Integrals
  • Geometry of Substitution
  • Section 5.5: Exercises
  • Practice Exercises
  • Explorations and Challenges
  • Chapter 5: Review Exercises
  • Chapter 5: Review Exercises
  • Chapter 5: Guided Projects
  • Chapter 5: Guided Projects
  • Chapter 5: Test Your Understanding
  • Chapter 5: Test Your Understanding
  • Chapter 6: Applications of Integration
  • Introduction: Applications of Integration
  • 6.1: Velocity and Net Change
  • 6.1: Velocity and Net Change
  • Velocity, Position, and Displacement
  • Future Value of the Position Function
  • Acceleration
  • Net Change and Future Value
  • Section 6.1: Exercises
  • Practice Exercises
  • Explorations and Challenges
  • 6.2: Regions Between Curves
  • 6.2: Regions Between Curves
  • Integrating with Respect to y
  • Section 6.2: Exercises
  • Practice Exercises
  • Explorations and Challenges
  • 6.3: Volume by Slicing
  • 6.3: Volume by Slicing
  • The Disk Method
  • Washer Method
  • Revolving about the y-Axis
  • Section 6.3: Exercises
  • Practice Exercises
  • Explorations and Challenges
  • 6.4: Volume by Shells
  • 6.4: Volume by Shells
  • Cylindrical Shells
  • Restoring Order
  • Section 6.4: Exercises
  • Practice Exercises
  • Explorations and Challenges
  • 6.5: Length of Curves
  • 6.5: Length of Curves
  • Arc Length for y = f(x)
  • Arc Length for x = g(y)
  • Section 6.5: Exercises
  • Practice Exercises
  • Explorations and Challenges
  • 6.6: Surface Area
  • 6.6: Surface Area
  • Some Preliminary Calculations
  • Surface Area Formula
  • Section 6.6: Exercises
  • Practice Exercises
  • Explorations and Challenges
  • 6.7: Physical Applications
  • 6.7: Physical Applications
  • Density and Mass
  • Work
  • Lifting Problems
  • Force and Pressure
  • Section 6.7: Exercises
  • Practice Exercises
  • Explorations and Challenges
  • Chapter 6: Review Exercises
  • Chapter 6: Review Exercises
  • Chapter 6: Review Exercises (68-86)
  • Chapter 6: Guided Projects
  • Chapter 6: Guided Projects
  • Chapter 6: Test Your Understanding
  • Chapter 6: Test Your Understanding
  • Chapter 7: Logarithmic, Exponential, and Hyperbolic Functions
  • Introduction: Logarithmic, Exponential, and Hyperbolic Functions
  • 7.1: Logarithmic and Exponential Functions Revisited
  • 7.1: Logarithmic and Exponential Functions Revisited
  • Step 1: The Natural Logarithm
  • Step 2: The Exponential Function
  • Step 3: General Logarithmic and Exponential Functions
  • Step 4: General Power Rule
  • Computing e
  • Section 7.1: Exercises
  • Practice Exercises
  • Explorations and Challenges
  • 7.2: Exponential Models
  • 7.2: Exponential Models
  • Exponential Growth
  • A Financial Model
  • Resource Consumption
  • Exponential Decay
  • Radiometric Dating
  • Pharmacokinetics
  • Section 7.2: Exercises
  • Practice Exercises
  • Explorations and Challenges
  • 7.3: Hyperbolic Functions
  • 7.3: Hyperbolic Functions
  • Relationship Between Trigonometric and Hyperbolic Functions
  • Definitions, Identities, and Graphs of the Hyperbolic Functions
  • Derivatives and Integrals of Hyperbolic Functions
  • Inverse Hyperbolic Functions
  • Derivatives of the Inverse Hyperbolic Functions and Related Integral Formulas
  • Applications of Hyperbolic Functions
  • Velocity of a Wave
  • Section 7.3: Exercises
  • Practice Exercises
  • Explorations and Challenges
  • Chapter 7: Review Exercises
  • Chapter 7: Review Exercises
  • Chapter 7: Guided Projects
  • Chapter 7: Guided Projects
  • Test Your Understanding
  • Test Your Understanding
  • Chapter 8: Integration Techniques
  • Introduction: Integration Techniques
  • 8.1: Basic Approaches
  • 8.1: Basic Approaches
  • Section 8.1: Exercises
  • Practice Exercises
  • Explorations and Challenges
  • 8.2: Integration by Parts
  • 8.2: Integration by Parts
  • Integration by Parts for Indefinite Integrals
  • Integration by Parts for Definite Integrals
  • Section 8.2: Exercises
  • Practice Exercises
  • Explorations and Challenges
  • 8.3: Trigonometric Integrals
  • 8.3: Trigonometric Integrals
  • Integrating Powers of sinx or cosx
  • Integrating Products of Powers of sin x and cos x
  • Reduction Formulas
  • Integrating Products of Powers of tanx and secx
  • Section 8.3: Exercises
  • Practice Exercises
  • Explorations and Challenges
  • 8.4: Trigonometric Substitutions
  • 8.4: Trigonometric Substitutions
  • Integrals Involving ​​a2 − x2
  • Integrals Involving or a2 + x2 or x2 − a2
  • Section 8.4: Exercises
  • Practice Exercises
  • Explorations and Challenges
  • 8.5: Partial Fractions
  • 8.5: Partial Fractions
  • Method of Partial Fractions
  • Simple Linear Factors
  • Repeated Linear Factors
  • Irreducible Quadratic Factors
  • Section 8.5: Exercises
  • Practice Exercises
  • Explorations and Challenges
  • 8.6: Integration Strategies
  • 8.6: Integration Strategies
  • Integration Strategies
  • Be persistent
  • Multiple techniques
  • Section 8.6: Exercises
  • Practice Exercises
  • Explorations and Challenges
  • 8.7: Other Methods of Integration
  • 8.7: Other Methods of Integration
  • Using Tables of Integrals
  • Symbolic Methods
  • Section 8.7: Exercises
  • Practice Exercises
  • Explorations and Challenges
  • 8.8: Numerical Integration
  • 8.8: Numerical Integration
  • Absolute and Relative Error
  • The Midpoint Rule
  • The Trapezoid Rule
  • Simpson’s Rule
  • Section 8.8: Exercises
  • Practice Exercises
  • Explorations and Challenges
  • 8.9: Improper Integrals
  • 8.9: Improper Integrals
  • Infinite Intervals
  • Unbounded Integrands
  • The Comparison Test
  • Section 8.9: Exercises
  • Practice Exercises
  • Explorations and Challenges
  • Chapter 8: Review Exercises
  • Chapter 8: Review Exercises
  • Chapter 8: Guided Projects
  • Chapter 8: Guided Projects
  • Chapter 8: Test Your Understanding
  • Chapter 8: Test Your Understanding
  • Chapter 9: Differential Equations
  • Introduction: Differential Equations
  • 9.1: Basic Ideas
  • 9.1: Basic Ideas
  • Differential Equations in Action
  • Section 9.1: Exercises
  • Practice Exercises
  • Explorations and Challenges
  • 9.2: Direction Fields and Euler’s Method
  • 9.2: Direction Fields and Euler’s Method
  • Direction Fields
  • Euler’s Method
  • Section 9.2: Exercises
  • Practice Exercises
  • Explorations and Challenges
  • 9.3: Separable Differential Equations
  • 9.3: Separable Differential Equations
  • Method of Solution
  • Logistic Equation Revisited
  • Section 9.3: Exercises
  • Practice Exercises
  • Explorations and Challenges
  • 9.4: Special First-Order Linear Differential Equations
  • 9.4: Special First-Order Linear Differential Equations
  • Method of Solution
  • Newton’s Law of Cooling
  • Section 9.4: Exercises
  • Practice Exercises
  • Explorations and Challenges
  • 9.5: Modeling with Differential Equations
  • 9.5: Modeling with Differential Equations
  • Population Models
  • Stirred Tank Reactions
  • Predator-Prey Models
  • Section 9.5: Exercises
  • Practice Exercises
  • Explorations and Challenges
  • Chapter 9: Review Exercises
  • Chapter 9: Review Exercises
  • Chapter 9: Guided Projects
  • Chapter 9: Guided Projects
  • Chapter 9: Test Your Understanding
  • Chapter 9: Test Your Understanding
  • Chapter 10: Sequences and Infinite Series
  • Introduction: Sequences and Infinite Series
  • 10.1: An Overview
  • 10.1: An Overview
  • Examples of Sequences
  • Limit of a Sequence
  • Infinite Series and the Sequence of Partial Sums
  • Summary
  • Section 10.1: Exercises
  • Practice Exercises
  • Explorations and Challenges
  • 10.2: Sequences
  • 10.2: Sequences
  • Limit of a Sequence and Limit Laws
  • Terminology for Sequences
  • Geometric Sequences
  • The Squeeze Theorem
  • Bounded Monotonic Sequence Theorem
  • An Application: Recurrence Relations
  • Growth Rates of Sequences
  • Formal Definition of a Limit of a Sequence
  • Section 10.2: Exercises
  • Practice Exercises
  • Explorations and Challenges
  • 10.3: Infinite Series
  • 10.3: Infinite Series
  • Geometric Sums and Series
  • Telescoping Series
  • Properties of Convergent Series
  • Section 10.3: Exercises
  • Practice Exercises
  • Explorations and Challenges
  • 10.4: The Divergence and Integral Tests
  • 10.4: The Divergence and Integral Tests
  • The Divergence Test
  • The Harmonic Series
  • The Integral Test
  • The p-series
  • Estimating the Value of Infinite Series
  • Section 10.4: Exercises
  • Practice Exercises
  • Explorations and Challenges
  • 10.5: Comparison Tests
  • 10.5: Comparison Tests
  • The Comparison Test
  • The Limit Comparison Test
  • Section 10.5: Exercises
  • Practice Exercises
  • Explorations and Challenges
  • 10.6: Alternating Series
  • 10.6: Alternating Series
  • Alternating Harmonic Series
  • Alternating Series Test
  • Remainders in Alternating Series
  • Absolute and Conditional Convergence
  • Section 10.6: Exercises
  • Practice Exercises
  • Explorations and Challenges
  • 10.7: The Ratio and Root Tests
  • 10.7: The Ratio and Root Tests
  • The Ratio Test
  • The Root Test
  • Section 10.7: Exercises
  • Practice Exercises
  • Explorations and Challenges
  • 10.8: Choosing a Convergence Test
  • 10.8: Choosing a Convergence Test
  • Series Strategies
  • Section 10.8: Exercises
  • Practice Exercises
  • Explorations and Challenges
  • Chapter 10: Review Exercises
  • Chapter 10: Review Exercises
  • Chapter 10: Guided Projects
  • Chapter 10: Guided Projects
  • Chapter 10: Test Your Understanding
  • Chapter 10: Test Your Understanding
  • Chapter 11: Power Series
  • Introduction: Power Series
  • 11.1: Approximating Functions with Polynomials
  • 11.1: Approximating Functions with Polynomials
  • What Is a Power Series?
  • Polynomial Approximation
  • Linear and Quadratic Approximation
  • Taylor Polynomials
  • Approximations with Taylor Polynomials
  • Remainder in a Taylor Polynomial
  • Estimating the Remainder
  • Section 11.1: Exercises
  • Practice Exercises
  • Explorations and Challenges
  • 11.2: Properties of Power Series
  • 11.2: Properties of Power Series
  • Geometric Series as Power Series
  • Convergence of Power Series
  • Combining Power Series
  • Differentiating and Integrating Power Series
  • Section 11.2: Exercises
  • Practice Exercises
  • Explorations and Challenges
  • 11.3: Taylor Series
  • 11.3: Taylor Series
  • Taylor Series for a Function
  • The Binomial Series
  • Convergence of Taylor Series
  • Section 11.3: Exercises
  • Practice Exercises
  • Explorations and Challenges
  • 11.4: Working with Taylor Series
  • 11.4: Working with Taylor Series
  • Limits by Taylor Series
  • Differentiating Power Series
  • Integrating Power Series
  • Representing Real Numbers
  • Representing Functions as Power Series
  • Section 11.4: Exercises
  • Practice Exercises
  • Explorations and Challenges
  • Chapter 11: Review Exercises
  • Chapter 11: Review Exercises
  • Chapter 11: Guided Projects
  • Chapter 11: Guided Projects
  • Chapter 11: Test Your Understanding
  • Chapter 11: Test Your Understanding
  • Chapter 12: Parametric and Polar Curves
  • Introduction: Parametric and Polar Curves
  • 12.1: Parametric Equations
  • 12.1: Parametric Equations
  • Basic Ideas
  • Derivatives and Parametric Equations
  • Arc Length
  • Section 12.1: Exercises
  • Practice Exercises
  • Explorations and Challenges
  • 12.2: Polar Coordinates
  • 12.2: Polar Coordinates
  • Defining Polar Coordinates
  • Converting Between Cartesian and Polar Coordinates
  • Basic Curves in Polar Coordinates
  • Graphing in Polar Coordinates
  • Using Graphing Utilities
  • Section 12.2: Exercises
  • Practice Exercises
  • Explorations and Challenges
  • 12.3: Calculus in Polar Coordinates
  • 12.3: Calculus in Polar Coordinates
  • Slopes of Tangent Lines
  • Area of Regions Bounded by Polar Curves
  • Arc Length of a Polar Curve
  • Section 12.3: Exercises
  • Practice Exercises
  • Explorations and Challenges
  • 12.4: Conic Sections
  • 12.4: Conic Sections
  • Parabolas
  • Ellipses
  • Hyperbolas
  • Eccentricity and Directrix
  • Polar Equations of Conic Sections
  • Section 12.4: Exercises
  • Practice Exercises
  • Explorations and Challenges
  • Chapter 12: Review Exercises
  • Chapter 12: Review Exercises
  • Chapter 12: Guided Projects
  • Chapter 12: Guided Projects
  • Chapter 12: Test Your Understanding
  • Chapter 12: Test Your Understanding
  • Chapter 13: Vectors and the Geometry of Space
  • Introduction: Vectors and the Geometry of Space
  • 13.1: Vectors in the Plane
  • 13.1: Vectors in the Plane
  • Basic Vector Operations
  • Scalar Multiplication
  • Vector Addition and Subtraction
  • Vector Components
  • Magnitude
  • Vector Operations in Terms of Components
  • Unit Vectors
  • Properties of Vector Operations
  • Applications of Vectors
  • Section 13.1: Exercises
  • Practice Exercises
  • Explorations and Challenges
  • 13.2: Vectors in Three Dimensions
  • 13.2: Vectors in Three Dimensions
  • The ​xy​z​​-Coordinate System
  • Equations of Simple Planes
  • Distances in xyz-Space
  • Equation of a Sphere
  • Vectors in R3
  • Magnitude and Unit Vectors
  • Section 13.2: Exercises
  • Practice Exercises
  • Explorations and Challenges
  • 13.3: Dot Products
  • 13.3: Dot Products
  • Two Forms of the Dot Product
  • Orthogonal Projections
  • Applications of Dot Products
  • Section 13.3: Exercises
  • Practice Exercises
  • Explorations and Challenges
  • 13.4: Cross Products
  • 13.4: Cross Products
  • The Cross Product
  • Properties of the Cross Product
  • Applications of the Cross Product
  • Section 13.4: Exercises
  • Practice Exercises
  • Explorations and Challenges
  • 13.5: Lines and Planes in Space
  • 13.5: Lines and Planes in Space
  • Lines in Space
  • Distance from a Point to a Line
  • Equations of Planes
  • Parallel and Orthogonal Planes
  • Section 13.5: Exercises
  • Practice Exercises
  • Explorations and Challenges
  • 13.6: Cylinders and Quadric Surfaces
  • 13.6: Cylinders and Quadric Surfaces
  • Cylinders and Traces
  • Quadric Surfaces
  • Section 13.6: Exercises
  • Practice Exercises
  • Explorations and Challenges
  • Chapter 13: Review Exercises
  • Chapter 13: Review Exercises
  • Chapter 13: Guided Projects
  • Chapter 13: Guided Projects
  • Chapter 13: Test Your Understanding
  • Chapter 13: Test Your Understanding
  • Chapter 14: Vector-Valued Functions
  • Introduction: Vector-Valued Functions
  • 14.1: Vector-Valued Functions
  • 14.1: Vector-Valued Functions
  • Vector-Valued Functions
  • Curves in Space
  • Limits and Continuity for Vector-Valued Functions
  • Section 14.1: Exercises
  • Practice Exercises
  • Explorations and Challenges
  • 14.2: Calculus of Vector-Valued Functions
  • 14.2: Calculus of Vector-Valued Functions
  • The Derivative and Tangent Vector
  • Integrals of Vector-Valued Functions
  • Section 14.2: Exercises
  • Practice Exercises
  • Explorations and Challenges
  • 14.3: Motion in Space
  • 14.3: Motion in Space
  • Position, Velocity, Speed, Acceleration
  • Straight-Line and Circular Motion
  • Two-Dimensional Motion in a Gravitational Field
  • Three-Dimensional Motion
  • Section 14.3: Exercises
  • Practice Exercises
  • Explorations and Challenges
  • 14.4: Length of Curves
  • 14.4: Length of Curves
  • Arc Length
  • Arc Length as a Parameter
  • Section 14.4: Exercises
  • Practice Exercises
  • Explorations and Challenges
  • 14.5: Curvature and Normal Vectors
  • 14.5: Curvature and Normal Vectors
  • Curvature
  • Principal Unit Normal Vector
  • Components of the Acceleration
  • The Binormal Vector and Torsion
  • Section 14.5: Exercises
  • Practice Exercises
  • Explorations and Challenges
  • Chapter 14: Review Exercises
  • Chapter 14: Review Exercises
  • Chapter 14: Guided Projects
  • Chapter 14: Guided Projects
  • Chapter 14: Test Your Understanding
  • Chapter 14: Test Your Understanding
  • Chapter 15: Functions of Several Variables
  • Introduction: Functions of Several Variables
  • 15.1: Graphs and Level Curves
  • 15.1: Graphs and Level Curves
  • Functions of Two Variables
  • Graphs of Functions of Two Variables
  • Applications of Functions of Two Variables
  • Functions of More Than Two Variables
  • Graphs of Functions of More Than Two Variables
  • Section 15.1: Exercises
  • Practice Exercises
  • Explorations and Challenges
  • 15.2: Limits and Continuity
  • 15.2: Limits and Continuity
  • Limit of a Function of Two Variables
  • Limits at Boundary Points
  • Continuity of Functions of Two Variables
  • Functions of Three Variables
  • Section 15.2: Exercises
  • Practice Exercises
  • Explorations and Challenges
  • 15.3: Partial Derivatives
  • 15.3: Partial Derivatives
  • Derivatives with Two Variables
  • Higher-Order Partial Derivatives
  • Functions of Three Variables
  • Differentiability
  • Section 15.3: Exercises
  • Practice Exercises
  • Explorations and Challenges
  • 15.4: The Chain Rule
  • 15.4: The Chain Rule
  • The Chain Rule with One Independent Variable
  • The Chain Rule with Several Independent Variables
  • Implicit Differentiation
  • Section 15.4: Exercises
  • Practice Exercises
  • Explorations and Challenges
  • 15.5: Directional Derivatives and the Gradient
  • 15.5: Directional Derivatives and the Gradient
  • Directional Derivatives
  • The Gradient Vector
  • Interpretations of the Gradient
  • The Gradient and Level Curves
  • The Gradient in Three Dimensions
  • Section 15.5: Exercises
  • Practice Exercises
  • Explorations and Challenges
  • 15.6: Tangent Planes and Linear Approximation
  • 15.6: Tangent Planes and Linear Approximation
  • Tangent Planes
  • Linear Approximation
  • Differentials and Change
  • Section 15.6: Exercises
  • Practice Exercises
  • Explorations and Challenges
  • 15.7: Maximum/Minimum Problems
  • 15.7: Maximum/Minimum Problems
  • Local Maximum/Minimum Values
  • Second Derivative Test
  • Absolute Maximum and Minimum Values
  • Section 15.7: Exercises
  • Practice Exercises
  • Explorations and Challenges
  • 15.8: Lagrange Multipliers
  • 15.8: Lagrange Multipliers
  • The Basic Idea
  • Lagrange Multipliers with Two Independent Variables
  • Lagrange Multipliers with Three Independent Variables
  • Section 15.8: Exercises
  • Practice Exercises
  • Explorations and Challenges
  • Chapter 15: Review Exercises
  • Chapter 15: Review Exercises
  • Chapter 15: Guided Projects
  • Chapter 15: Guided Projects
  • Chapter 15: Test Your Understanding
  • Chapter 15: Test Your Understanding
  • Chapter 16: Multiple Integration
  • Introduction: Multiple Integration
  • 16.1: Double Integrals over Rectangular Regions
  • 16.1: Double Integrals over Rectangular Regions
  • Volumes of Solids
  • Iterated Integrals
  • Average Value
  • Section 16.1: Exercises
  • Practice Exercises
  • Explorations and Challenges
  • 16.2: Double Integrals over General Regions
  • 16.2: Double Integrals over General Regions
  • Iterated Integrals
  • Choosing and Changing the Order of Integration
  • Regions Between Two Surfaces
  • Decomposition of Regions
  • Finding Area by Double Integrals
  • Section 16.2: Exercises
  • Practice Exercises
  • Explorations and Challenges
  • 16.3: Double Integrals in Polar Coordinates
  • 16.3: Double Integrals in Polar Coordinates
  • Moving from Rectangular to Polar Coordinates
  • More General Polar Regions
  • Areas of Regions
  • Average Value over a Planar Polar Region
  • Section 16.3: Exercises
  • Practice Exercises
  • Explorations and Challenges
  • 16.4: Triple Integrals
  • 16.4: Triple Integrals
  • Changing the Order of Integration
  • Average Value of a Function of Three Variables
  • Section 16.4: Exercises
  • Practice Exercises
  • Explorations and Challenges
  • 16.5: Triple Integrals in Cylindrical and Spherical Coordinates
  • 16.5: Triple Integrals in Cylindrical and Spherical Coordinates
  • Cylindrical Coordinates
  • Integration in Cylindrical Coordinates
  • Spherical Coordinates
  • Integration in Spherical Coordinates
  • Section 16.5: Exercises
  • Practice Exercises
  • Explorations and Challenges
  • 16.6: Integrals for Mass Calculations
  • 16.6: Integrals for Mass Calculations
  • Sets of Individual Objects
  • Continuous Objects in One Dimension
  • Two-Dimensional Objects
  • Three-Dimensional Objects
  • Section 16.6: Exercises
  • Practice Exercises
  • Explorations and Challenges
  • 16.7: Change of Variables in Multiple Integrals
  • 16.7: Change of Variables in Multiple Integrals
  • Recap of Change of Variables
  • Transformations in the Plane
  • Change of Variables in Triple Integrals
  • Strategies for Choosing New Variables
  • Section 16.7: Exercises
  • Practice Exercises
  • Explorations and Challenges
  • Chapter 16: Review Exercises
  • Chapter 16: Review Exercises
  • Chapter 16: Guided Projects
  • Chapter 16: Guided Projects
  • Chapter 16: Test Your Understanding
  • Chapter 16: Test Your Understanding
  • Chapter 17: Vector Calculus
  • Introduction: Vector Calculus
  • 17.1: Vector Fields
  • 17.1: Vector Fields
  • Vector Fields in Two Dimensions
  • Vector Fields in Three Dimensions
  • Section 17.1: Exercises
  • Practice Exercises
  • Explorations and Challenges
  • 17.2: Line Integrals
  • 17.2: Line Integrals
  • Scalar Line Integrals in the Plane
  • Evaluating Line Integrals
  • Line Integrals in R3
  • Line Integrals of Vector Fields
  • Circulation and Flux of a Vector Field
  • Section 17.2: Exercises
  • Practice Exercises
  • Explorations and Challenges
  • 17.3: Conservative Vector Fields
  • 17.3: Conservative Vector Fields
  • Types of Curves and Regions
  • Test for Conservative Vector Fields
  • Finding Potential Functions
  • Fundamental Theorem for Line Integrals and Path Independence
  • Line Integrals on Closed Curves
  • Summary of the Properties of Conservative Vector Fields
  • Section 17.3: Exercises
  • Practice Exercises
  • Explorations and Challenges
  • 17.4: Green’s Theorem
  • 17.4: Green’s Theorem
  • Circulation Form of Green’s Theorem
  • Flux Form of Green’s Theorem
  • Circulation and Flux on More General Regions
  • Stream Functions
  • Proof of Green’s Theorem on Special Regions
  • Section 17.4: Exercises
  • Practice Exercises
  • Explorations and Challenges
  • 17.5: Divergence and Curl
  • 17.5: Divergence and Curl
  • The Divergence
  • The Curl
  • Working with Divergence and Curl
  • Summary of Properties of Conservative Vector Fields
  • Section 17.5: Exercises
  • Practice Exercises
  • Explorations and Challenges
  • 17.6: Surface Integrals
  • 17.6: Surface Integrals
  • Parameterized Surfaces
  • Surface Integrals of Scalar-Valued Functions
  • Surface Integrals of Vector Fields
  • Section 17.6: Exercises
  • Practice Exercises
  • Explorations and Challenges
  • 17.7: Stokes’ Theorem
  • 17.7: Stokes’ Theorem
  • Stokes’ Theorem
  • Interpreting the Curl
  • Proof of Stokes’ Theorem
  • Two Final Notes on Stokes’ Theorem
  • Section 17.7: Exercises
  • Practice Exercises
  • Explorations and Challenges
  • 17.8: Divergence Theorem
  • 17.8: Divergence Theorem
  • Divergence Theorem
  • Proof of the Divergence Theorem
  • Divergence Theorem for Hollow Regions
  • Gauss’ Law
  • A Final Perspective
  • Section 17.8: Exercises
  • Practice Exercises
  • Explorations and Challenges
  • Chapter 17: Review Exercises
  • Chapter 17: Review Exercises
  • Chapter 17: Guided Projects
  • Chapter 17: Guided Projects
  • Chapter 17: Test Your Understanding
  • Chapter 17: Test Your Understanding
  • D2 Second-Order Differential Equations
  • D2 Second-Order Differential Equations
  • Appendix A
  • Appendix A: Proofs of Selected Theorems
  • Theorem 2.3: Limit Laws
  • Theorem 10.20: Ratio Test
  • Theorem 10.21: Root Test
  • Theorem 11.3: Convergence of Power Series
  • Theorem 12.3: Eccentricity-Directrix Theorem
  • Theorem 15.3: Continuity of Composite Functions
  • Theorem 15.5: Conditions for Differentiability
  • Theorem 15.7: Chain Rule (One Independent Variable)
  • Theorem 15.15: Second Derivative Test
  • Appendix B
  • Appendix B
  • Appendix B
  • Algebra
  • Sets of Real Numbers
  • Absolute Value
  • Cartesian Coordinate System
  • Equations of Lines
  • Parallel and Perpendicular Lines
  • Appendix B Exercises
  • Practice Exercises
  • Explorations and Challenges
  • Appendix C
  • Appendix C
  • Complex Numbers
  • Complex Arithmetic
  • Polar Form of Complex Numbers
  • Appendix C Exercises
  • Explorations and Challenges
  • Answers
  • Chapter 1
  • Section 1.1: Exercises
  • Section 1.2: Exercises
  • Section 1.3: Exercises
  • Section 1.4: Exercises
  • Chapter 1: Review Exercises
  • Chapter 2
  • Section 2.1: Exercises
  • Section 2.2: Exercises
  • Section 2.3: Exercise
  • Section 2.4: Exercises
  • Section 2.5: Exercises
  • Section 2.6: Exercises
  • Section 2.7: Exercises
  • Chapter 2 Review Exercises
  • Chapter 3
  • Section 3.2: Exercises
  • Chapter 5
  • Chapter 5 Review Exercises
  • Chapter 6
  • Section 6.2: Exercises
  • Section 6.5: Exercises
  • Section 6.7: Exercises
  • Chapter 7
  • Section 7.2: Exercises
  • Section 7.3: Exercises
  • Chapter 8
  • Section 8.1: Exercises
  • Section 8.3: Exercises
  • Section 8.5: Exercises
  • Section 8.6: Exercises
  • Section 8.8: Exercises
  • Chapter 8: Review Exercises
  • Chapter 9
  • Section 9.1: Exercises
  • Section 9.2: Exercises
  • Section 9.3: Exercises
  • Section 9.4: Exercises
  • Section 9.5: Exercises
  • Chapter 9: Review Exercises
  • Chapter 10
  • Section 10.1: Exercises
  • Section 10.2: Exercises
  • Section 10.3: Exercises
  • Section 10.4: Exercises
  • Section 10.5: Exercises
  • Section 10.6: Exercises
  • Section 10.7: Exercises
  • Section 10.8: Exercises
  • Chapter 10: Review Exercises
  • Chapter 11
  • Section 11.1: Exercises
  • Section 11.2: Exercises
  • Section 11.3: Exercises
  • Section 11.4: Exercises
  • Chapter 11: Review Exercises
  • Chapter 12
  • Section 12.1: Exercises
  • Section 12.2: Exercises
  • Section 12.3: Exercises
  • Section 12.4: Exercises
  • Chapter 12: Review Exercises
  • Chapter 13
  • Section 13.1: Exercises
  • Section 13.2: Exercises
  • Section 13.3: Exercises
  • Section 13.4: Exercises
  • Section 13.5: Exercises
  • Section 13.6: Exercises
  • Chapter 13: Review Exercises
  • Chapter 14
  • Section 14.1: Exercises
  • Section 14.2: Exercises
  • Section 14.3: Exercises
  • Section 14.5: Exercises
  • Chapter 15
  • Section 15.2: Exercises
  • Section 15.3: Exercises
  • Section 15.4: Exercises
  • Section 15.5: Exercises
  • Section 15.6: Exercises
  • Section 15.8: Exercises
  • Chapter 16
  • Section 16.1: Exercises
  • Section 16.3: Exercises
  • Section 16.5: Exercises
  • Section 16.7: Exercises
  • Chapter 17
  • Section 17.1: Exercises
  • Section 17.3: Exercises
  • Section 17.5: Exercises
  • Section 17.7: Exercises
  • Chapter 17: Review Exercises
  • Index
  • Index
  • U
  • V
  • X
  • Z
  • Index of Applications
  • Index of Applications
  • Economics and Business
  • Footnotes
  • Glossary