**University Calculus: Early Transcendentals 4th Edition by Joel Hass, ISBN-13: 978-0134995540**

[PDF eBook eTextbook]

- Publisher: Pearson; 4th edition (January 1, 2019)
- Language: English
**1104 pages**- ISBN-10: 0134995546
- ISBN-13: 978-0134995540

For 3-semester or 4-quarter¿ courses covering single¿ variable and multivariable calculus, taken by students of * mathematics,* engineering, natural sciences, or economics.

Clear, precise, concise.

* University Calculus: Early Transcendentals *helps students generalize and apply the key ideas of calculus through clear and precise explanations, thoughtfully chosen examples, meticulously crafted figures, and superior exercise sets. This text offers the right mix of basic, conceptual, and challenging exercises, along with meaningful applications. In the

*new co-authors Chris Heil (Georgia Institute of Technology) and Przemyslaw Bogacki (Old Dominion University) partner with author Joel Hass to preserve the text’s time-tested features while revisiting every word, figure, and MyLab™ question with today’s students in mind.*

**4th Edition,****Table of Contents:**

Preface

New to This Edition

Accuracy Checkers

Reviewers for the Fourth Edition

1 Functions

1.1 Functions and Their Graphs

Functions; Domain and Range

Graphs of Functions

Representing a Function Numerically

The Vertical Line Test for a Function

Piecewise-Defined Functions

Increasing and Decreasing Functions

Even Functions and Odd Functions: Symmetry

Common Functions

Linear Functions

Power Functions

Polynomials

Rational Functions

Algebraic Functions

Trigonometric Functions

Exponential Functions

Logarithmic Functions

Transcendental Functions

Exercises 1.1

Functions

Finding Formulas for Functions

Functions and Graphs

Piecewise-Defined Functions

The Greatest and Least Integer Functions

Increasing and Decreasing Functions

Even and Odd Functions

Theory and Examples

1.2 Combining Functions; Shifting and Scaling Graphs

Sums, Differences, Products, and Quotients

Composing Functions

Shifting a Graph of a Function

Scaling and Reflecting a Graph of a Function

For c > 1 the graph is scaled:

For c = −1, the graph is reflected:

Exercises 1.2

Algebraic Combinations

Compositions of Functions

Shifting Graphs

Vertical and Horizontal Scaling

Graphing

Combining Functions

1.3 Trigonometric Functions

Angles

Angle Convention: Use Radians

The Six Basic Trigonometric Functions

Periodicity and Graphs of the Trigonometric Functions

Trigonometric Identities

The Law of Cosines

Two Special Inequalities

Transformations of Trigonometric Graphs

Exercises 1.3

Radians and Degrees

Evaluating Trigonometric Functions

Graphing Trigonometric Functions

Using the Addition Formulas

Using the Half-Angle Formulas

Solving Trigonometric Equations

Theory and Examples

General Sine Curves

1.4 Graphing with Software

Graphing Windows

Obtaining a Complete Graph

Exercises 1.4

Choosing a Viewing Window

Finding a Viewing Window

1.5 Exponential Functions

Exponential Behavior

The Natural Exponential Function ex

Exponential Growth and Decay

Exercises 1.5

Sketching Exponential Curves

Applying the Laws of Exponents

Compositions Involving Exponential Functions

Applications

1.6 Inverse Functions and Logarithms

One-to-One Functions

Inverse Functions

Finding Inverses

Logarithmic Functions

Properties of Logarithms

Applications

Inverse Trigonometric Functions

The Arcsine and Arccosine Functions

Identities Involving Arcsine and Arccosine

Exercises 1.6

Identifying One-to-One Functions Graphically

Graphing Inverse Functions

Formulas for Inverse Functions

Inverses of Lines

Logarithms and Exponentials

Arcsine and Arccosine

Theory and Examples

2 Limits and Continuity

2.1 Rates of Change and Tangent Lines to Curves

Average and Instantaneous Speed

Average Rates of Change and Secant Lines

Defining the Slope of a Curve

Rates of Change and Tangent Lines

Exercises 2.1

Average Rates of Change

Slope of a Curve at a Point

Instantaneous Rates of Change

2.2 Limit of a Function and Limit Laws

Limits of Function Values

An Informal Description of the Limit of a Function

The Limit Laws

Evaluating Limits of Polynomials and Rational Functions

Eliminating Common Factors from Zero Denominators

Using Calculators and Computers to Estimate Limits

The Sandwich Theorem

Exercises 2.2

Limits from Graphs

Existence of Limits

Calculating Limits

Using Limit Rules

Limits of Average Rates of Change

Using the Sandwich Theorem

Estimating Limits

Theory and Examples

Graphical Estimates of Limits

2.3 The Precise Definition of a Limit

Definition of Limit

Examples: Testing the Definition

Finding Deltas Algebraically for Given Epsilons

Using the Definition to Prove Theorems

Exercises 2.3

Centering Intervals About a Point

Finding Deltas Graphically

Finding Deltas Algebraically

Using the Formal Definition

Theory and Examples

When Is a Number L Not the Limit of f(x) As x → c?

2.4 One-Sided Limits

Approaching a Limit from One Side

Limits at Endpoints of an Interval

Precise Definitions of One-Sided Limits

Limits Involving (sin θ) / θ

Exercises 2.4

Finding Limits Graphically

Finding One-Sided Limits Algebraically

Using limθ→0sinθθ=1

Theory and Examples

Formal Definitions of One-Sided Limits

2.5 Continuity

Continuity at a Point

Continuous Functions

Inverse Functions and Continuity

Continuity of Compositions of Functions

Intermediate Value Theorem for Continuous Functions

A Consequence for Graphing: Connectedness

A Consequence for Root Finding

Continuous Extension to a Point

Exercises 2.5

Continuity from Graphs

Applying the Continuity Test

Limits Involving Trigonometric Functions

Continuous Extensions

Theory and Examples

Solving Equations Graphically

2.6 Limits Involving Infinity; Asymptotes of Graphs

Finite Limits as x → ± ∞

Limits at Infinity of Rational Functions

Horizontal Asymptotes

Oblique Asymptotes

Infinite Limits

Precise Definitions of Infinite Limits

Vertical Asymptotes

Dominant Terms

Exercises 2.6

Finding Limits

Limits of Rational Functions

Limits as x → ∞ or x → − ∞

Infinite Limits

Graphing Simple Rational Functions

Domains and Asymptotes

Inventing Graphs and Functions

Finding Limits of Differences When x → ± ∞

Using the Formal Definitions

Oblique Asymptotes

Additional Graphing Exercises

Chapter 2 Questions to Guide Your Review

Chapter 2 Practice Exercises

Limits and Continuity

Finding Limits

[Technology Exercise] Roots

Continuous Extension

Limits at Infinity

Horizontal and Vertical Asymptotes

Chapter 2 Additional and Advanced Exercises

Precise Definition of Limit

Generalized Limits Involving sin θθ

Oblique Asymptotes

Showing an Equation Is Solvable

More Limits

Limits on Arbitrary Domains

3 Derivatives

3.1 Tangent Lines and the Derivative at a Point

Finding a Tangent Line to the Graph of a Function

Rates of Change: Derivative at a Point

Summary

Exercises 3.1

Slopes and Tangent Lines

Interpreting Derivative Values

Rates of Change

Testing for Tangent Lines

Vertical Tangent Lines

3.2 The Derivative as a Function

Calculating Derivatives from the Definition

Notation

Graphing the Derivative

Differentiability on an Interval; One-Sided Derivatives

When Does a Function Not Have a Derivative at a Point?

Differentiable Functions Are Continuous

Exercises 3.2

Finding Derivative Functions and Values

Slopes and Tangent Lines

Using the Alternative Formula for Derivatives

Graphs

One-Sided Derivatives

Differentiability and Continuity on an Interval

Theory and Examples

3.3 Differentiation Rules

Powers, Multiples, Sums, and Differences

Derivatives of Exponential Functions

Products and Quotients

Second- and Higher-Order Derivatives

Exercises 3.3

Derivative Calculations

Slopes and Tangent Lines

Theory and Examples

3.4 The Derivative as a Rate of Change

Instantaneous Rates of Change

Motion Along a Line: Displacement, Velocity, Speed, Acceleration, and Jerk

Derivatives in Economics and Biology

Exercises 3.4

Motion Along a Coordinate Line

Free-Fall Applications

Understanding Motion from Graphs

Economics

Additional Applications

Analyzing Motion Using Graphs

3.5 Derivatives of Trigonometric Functions

Derivative of the Sine Function

Derivative of the Cosine Function

Simple Harmonic Motion

Derivatives of the Other Basic Trigonometric Functions

Exercises 3.5

Derivatives

Tangent Lines

Trigonometric Limits

Theory and Examples

3.6 The Chain Rule

Derivative of a Composite Function

“Outside-Inside” Rule

Repeated Use of the Chain Rule

The Chain Rule with Powers of a Function

Exercises 3.6

Derivative Calculations

Second Derivatives

Finding Derivative Values

Theory and Examples

Trigonometric Polynomials

3.7 Implicit Differentiation

Implicitly Defined Functions

Derivatives of Higher Order

Lenses, Tangent Lines, and Normal Lines

Exercises 3.7

Differentiating Implicitly

Second Derivatives

Slopes, Tangent Lines, and Normal Lines

Theory and Examples

3.8 Derivatives of Inverse Functions and Logarithms

Derivatives of Inverses of Differentiable Functions

Derivative of the Natural Logarithm Function

Alternative Derivation

The Derivatives of au and loga u

Logarithmic Differentiation

Irrational Exponents and the Power Rule (General Version)

The Number e Expressed as a Limit

Exercises 3.8

Derivatives of Inverse Functions

Derivatives of Logarithms

Logarithmic Differentiation

Finding Derivatives

Powers with Variable Bases and Exponents

Theory and Applications

3.9 Inverse Trigonometric Functions

Inverses of tan x, cot x, sec x, and csc x

The Derivative of y = sin−1 u

The Derivative of y = tan−1 u

The Derivative of y = sec−1 u

Derivatives of the Other Three Inverse Trigonometric Functions

Exercises 3.9

Common Values

Evaluations

Limits

Finding Derivatives

Theory and Examples

3.10 Related Rates

Related Rates Equations

Exercises 3.10

3.11 Linearization and Differentials

Linearization

Differentials

Estimating with Differentials

Error in Differential Approximation

Proof of the Chain Rule

Sensitivity to Change

Exercises 3.11

Finding Linearizations

Linearization for Approximation

Derivatives in Differential Form

Approximation Error

Differential Estimates of Change

Applications

Chapter 3 Questions to Guide Your Review

Chapter 3 Practice Exercises

Derivatives of Functions

Implicit Differentiation

Numerical Values of Derivatives

Applying the Derivative Definition

Slopes, Tangent Lines, and Normal Lines

Analyzing Graphs

Trigonometric Limits

Logarithmic Differentiation

Related Rates

Linearization

Differential Estimates of Change

Chapter 3 Additional and Advanced Exercises

4 Applications of Derivatives

4.1 Extreme Values of Functions on Closed Intervals

Local (Relative) Extreme Values

Finding Extrema

Exercises 4.1

Finding Extrema from Graphs

Absolute Extrema on Finite Closed Intervals

Finding Critical Points

Theory and Examples

4.2 The Mean Value Theorem

Rolle’s Theorem

The Mean Value Theorem

A Physical Interpretation

Mathematical Consequences

Finding Velocity and Position from Acceleration

Proofs of the Laws of Logarithms

Laws of Exponents

Exercises 4.2

Checking the Mean Value Theorem

Roots (Zeros)

Finding Functions from Derivatives

Finding Position from Velocity or Acceleration

Applications

Theory and Examples

4.3 Monotonic Functions and the First Derivative Test

Increasing Functions and Decreasing Functions

First Derivative Test for Local Extrema

Exercises 4.3

Analyzing Functions from Derivatives

Identifying Extrema

Theory and Examples

4.4 Concavity and Curve Sketching

Concavity

Points of Inflection

Second Derivative Test for Local Extrema

Graphical Behavior of Functions from Derivatives

Exercises 4.4

Analyzing Functions from Graphs

Graphing Functions

Sketching the General Shape, Knowing y′

Sketching y from Graphs of y′ and y″

Theory and Examples

4.5 Indeterminate Forms and L’Hôpital’s Rule

Indeterminate Form 0/0

Indeterminate Forms ∞/∞ , ∞ ⋅ 0 , ∞ − ∞

Indeterminate Powers

Exercises 4.5

Finding Limits in Two Ways

Applying l’Hôpital’s Rule

Indeterminate Powers and Products

Theory and Applications

4.6 Applied Optimization

Examples from Mathematics and **Physics**

Examples from Economics

Exercises 4.6

Mathematical Applications

Physical Applications

Business and Economics

Biology

Theory and Examples

4.7 Newton’s Method

Procedure for Newton’s Method

Applying Newton’s Method

Convergence of the Approximations

Exercises 4.7

Root Finding

Dependence on Initial Point

Theory and Examples

4.8 Antiderivatives

Finding Antiderivatives

Initial Value Problems and Differential Equations

Antiderivatives and Motion

Indefinite Integrals

Exercises 4.8

Finding Antiderivatives

Finding Indefinite Integrals

Checking Antiderivative Formulas

Initial Value Problems

Solution (Integral) Curves

Applications

Chapter 4 Questions to Guide Your Review

Chapter 4 Practice Exercises

Finding Extreme Values

Extreme Values

The Mean Value Theorem

Analyzing Graphs

Graphs and Graphing

Using L’Hôpital’s Rule

Optimization

Newton’s Method

Finding Indefinite Integrals

Initial Value Problems

Applications and Examples

Chapter 4 Additional and Advanced Exercises

Functions and Derivatives

Optimization

Limits

Theory and Examples

5 Integrals

5.1 Area and Estimating with Finite Sums

Area

Distance Traveled

Displacement Versus Distance Traveled

Average Value of a Nonnegative Continuous Function

Summary

Exercises 5.1

Area

Distance

Average Value of a Function

Examples of Estimations

5.2 Sigma Notation and Limits of Finite Sums

Finite Sums and Sigma Notation

Limits of Finite Sums

Riemann Sums

Exercises 5.2

Sigma Notation

Values of Finite Sums

Riemann Sums

Limits of Riemann Sums

5.3 The Definite Integral

Definition of the Definite Integral

Integrable and Nonintegrable Functions

Properties of Definite Integrals

Area Under the Graph of a Nonnegative Function

Average Value of a Continuous Function Revisited

Exercises 5.3

Interpreting Limits of Sums as Integrals

Using the Definite Integral Rules

Using Known Areas to Find Integrals

Evaluating Definite Integrals

Finding Area by Definite Integrals

Finding Average Value

Definite Integrals as Limits of Sums

Theory and Examples

5.4 The Fundamental Theorem of Calculus

Mean Value Theorem for Definite Integrals

Fundamental Theorem, Part 1

Fundamental Theorem, Part 2 (The Evaluation Theorem)

The Integral of a Rate

The Relationship Between Integration and Differentiation

Total Area

Exercises 5.4

Evaluating Integrals

Derivatives of Integrals

Area

Initial Value Problems

Theory and Examples

5.5 Indefinite Integrals and the Substitution Method

Substitution: Running the Chain Rule Backwards

Trying Different Substitutions

Exercises 5.5

Evaluating Indefinite Integrals

Initial Value Problems

5.6 Definite Integral Substitutions and the Area Between Curves

The Substitution Formula

Definite Integrals of Symmetric Functions

Areas Between Curves

Integration with Respect to y

Exercises 5.6

Evaluating Definite Integrals

Area

Area Between Curves

Theory and Examples

Chapter 5 Questions to Guide Your Review

Chapter 5 Practice Exercises

Finite Sums and Estimates

Definite Integrals

Area

Initial Value Problems

Evaluating Indefinite Integrals

Evaluating Definite Integrals

Average Values

Differentiating Integrals

Chapter 5 Additional and Advanced Exercises

Theory and Examples

Piecewise Continuous Functions

Limits

Defining Functions Using the Fundamental Theorem

Theory and Examples

6 Applications of Definite Integrals

6.1 Volumes Using Cross-Sections

Slicing by Parallel Planes

Solids of Revolution: The Disk Method

Solids of Revolution: The Washer Method

Exercises 6.1

Volumes by Slicing

Volumes by the Disk Method

Volumes by the Washer Method

Volumes of Solids of Revolution

Theory and Applications

6.2 Volumes Using Cylindrical Shells

Slicing with Cylinders

The Shell Method

Exercises 6.2

Revolution About the Axes

Revolution About the y-Axis

Revolution About the x-Axis

Revolution About Horizontal and Vertical Lines

Choosing the Washer Method or the Shell Method

Theory and Examples

6.3 Arc Length

Length of a Curve y = f(x)

Dealing with Discontinuities in dy/dx

The Differential Formula for Arc Length

Exercises 6.3

Finding Lengths of Curves

[Technology Exercise] Finding Integrals for Lengths of Curves

Theory and Examples

6.4 Areas of Surfaces of Revolution

Defining Surface Area

Revolution About the y-Axis

Exercises 6.4

Finding Integrals for Surface Area

Finding Surface Area

6.5 Work

Work Done by a Constant Force

Work Done by a Variable Force Along a Line

Hooke’s Law for Springs: F = kx

Lifting Objects and Pumping Liquids from Containers

Exercises 6.5

Springs

Work Done by a Variable Force

Pumping Liquids from Containers

Work and Kinetic Energy

6.6 Moments and Centers of Mass

Masses Along a Line

Thin Wires

Masses Distributed over a Plane Region

Thin, Flat Plates

Plates Bounded by Two Curves

Centroids

Exercises 6.6

Mass of a wire

Thin Plates with Constant Density

Thin Plates with Varying Density

Centroids of Triangles

Thin Wires

Plates Bounded by Two Curves

Chapter 6 Questions to Guide Your Review

Chapter 6 Practice Exercises

Volumes

Lengths of Curves

Areas of Surfaces of Revolution

Work

Centers of Mass and Centroids

Chapter 6 Additional and Advanced Exercises

Volume and Length

Surface Area

Work

Centers of Mass

7 Integrals and Transcendental Functions

7.1 The Logarithm Defined as an Integral

Definition of the Natural Logarithm Function

The Derivative of y = ln x

The Graph and Range of ln x

The Integral ∫ 1/u du

The Inverse of ln x and the Number e

The Derivative and Integral of ex

Laws of Exponents

The General Exponential Function ax

Logarithms with Base a

Derivatives and Integrals Involving loga x

Summary

Exercises 7.1

Integration

Initial Value Problems

Theory and Applications

Calculations with Other Bases

7.2 Exponential Change and Separable Differential Equations

Exponential Change

Separable Differential Equations

Unlimited Population Growth

Radioactivity

Heat Transfer: Newton’s Law of Cooling

Exercises 7.2

Verifying Solutions

Initial Value Problems

Separable Differential Equations

Applications and Examples

7.3 Hyperbolic Functions

Definitions and Identities

Derivatives and Integrals of Hyperbolic Functions

Inverse Hyperbolic Functions

Useful Identities

Derivatives of Inverse Hyperbolic Functions

Exercises 7.3

Values and Identities

Finding Derivatives

Integration Formulas

Evaluating Integrals

Inverse Hyperbolic Functions and Integrals

Applications and Examples

Chapter 7 Questions to Guide Your Review

Chapter 7 Practice Exercises

Integration

Solving Equations with Logarithmic or Exponential Terms

Theory and Applications

Chapter 7 Additional and Advanced Exercises

8 Techniques of Integration

8.1 Integration by Parts

Product Rule in Integral Form

Evaluating Definite Integrals by Parts

Exercises 8.1

Integration by Parts

Using Substitution

Evaluating Integrals

Theory and Examples

Reduction Formulas

Integrating Inverses of Functions

8.2 Trigonometric Integrals

Products of Powers of Sines and Cosines

Eliminating Square Roots

Integrals of Powers of tan x and sec x

Products of Sines and Cosines

Exercises 8.2

Powers of Sines and Cosines

Integrating Square Roots

Powers of Tangents and Secants

Products of Sines and Cosines

Assorted Integrations

Applications

8.3 Trigonometric Substitutions

Exercises 8.3

Using Trigonometric Substitutions

Assorted Integrations

Complete the Square Before Using Trigonometric Substitutions

Initial Value Problems

Applications and Examples

8.4 Integration of Rational Functions by Partial Fractions

General Description of the Method

Determining Coefficients by Differentiating

Exercises 8.4

Expanding Quotients into Partial Fractions

Nonrepeated Linear Factors

Repeated Linear Factors

Irreducible Quadratic Factors

Improper Fractions

Evaluating Integrals

Initial Value Problems

Applications and Examples

8.5 Integral Tables and Computer Algebra Systems

Integral Tables

Reduction Formulas

Integration with a CAS

Nonelementary Integrals

Exercises 8.5

Using Integral Tables

Substitution and Integral Tables

Using Reduction Formulas

Applications

8.6 Numerical Integration

Trapezoidal Approximations

Simpson’s Rule: Approximations Using Parabolas

Error Analysis

Exercises 8.6

Estimating Definite Integrals

Estimating the Number of Subintervals

Estimates with Numerical Data

Theory and Examples

Applications

8.7 Improper Integrals

Infinite Limits of Integration

The Integral ∫1∞dxxp

Integrands with Vertical Asymptotes

Improper Integrals with a CAS

Tests for Convergence and Divergence

Exercises 8.7

Evaluating Improper Integrals

Testing for Convergence

Theory and Examples

Chapter 8 Questions to Guide Your Review

Chapter 8 Practice Exercises

Integration by Parts

Partial Fractions

Trigonometric Substitutions

Trigonometric Integrals

Numerical Integration

Improper Integrals

Assorted Integrations

Chapter 8 Additional and Advanced Exercises

Evaluating Integrals

Applications

The Gamma Function and Stirling’s Formula

9 Infinite Sequences and Series

9.1 Sequences

Representing Sequences

Convergence and Divergence

Calculating Limits of Sequences

Using L’Hôpital’s Rule

Commonly Occurring Limits

Recursive Definitions

Bounded Monotonic Sequences

Exercises 9.1

Finding Terms of a Sequence

Finding a Sequence’s Formula

Convergence and Divergence

Recursively Defined Sequences

Theory and Examples

9.2 Infinite Series

Geometric Series

The nth-Term Test for a Divergent Series

Combining Series

Adding or Deleting Terms

Reindexing

Exercises 9.2

Finding nth Partial Sums

Series with Geometric Terms

Repeating Decimals

Using the nth-Term Test

Telescoping Series

Convergence or Divergence

Geometric Series with a Variable x

Theory and Examples

9.3 The Integral Test

Nondecreasing Partial Sums

The Integral Test

Error Estimation

Exercises 9.3

Applying the Integral Test

Determining Convergence or Divergence

Theory and Examples

9.4 Comparison Tests

The Limit Comparison Test

Exercises 9.4

Direct Comparison Test

Limit Comparison Test

Determining Convergence or Divergence

Theory and Examples

9.5 Absolute Convergence; The Ratio and Root Tests

The Ratio Test

The Root Test

Exercises 9.5

Using the Ratio Test

Using the Root Test

Determining Convergence or Divergence

Convergence or Divergence

Theory and Examples

9.6 Alternating Series and Conditional Convergence

Conditional Convergence

Rearranging Series

Summary of Tests to Determine Convergence or Divergence

Exercises 9.6

Convergence of Alternating Series

Absolute and Conditional Convergence

Error Estimation

Determining Convergence or Divergence

Theory and Examples

9.7 Power Series

Power Series and Convergence

The Radius of Convergence of a Power Series

Operations on Power Series

Exercises 9.7

Intervals of Convergence

Using the Geometric Series

Theory and Examples

9.8 Taylor and Maclaurin Series

Series Representations

Taylor and Maclaurin Series

Taylor Polynomials

Exercises 9.8

Finding Taylor Polynomials

Finding Taylor Series at x = 0 (Maclaurin Series)

Finding Taylor and Maclaurin Series

Theory and Examples

9.9 Convergence of Taylor Series

Estimating the Remainder

Using Taylor Series

Exercises 9.9

Finding Taylor Series

Error Estimates

Theory and Examples

9.10 Applications of Taylor Series

The Binomial Series for Powers and Roots

Evaluating Nonelementary Integrals

Arctangents

Evaluating Indeterminate Forms

Euler’s Identity

Exercises 9.10

Taylor Series

Approximations and Nonelementary Integrals

Indeterminate Forms

Using Table 9.1

Theory and Examples

Euler’s Identity

Chapter 9 Questions to Guide Your Review

Chapter 9 Practice Exercises

Determining Convergence of Sequences

Convergent Series

Determining Convergence of Series

Power Series

Maclaurin Series

Taylor Series

Nonelementary Integrals

Using Series to Find Limits

Theory and Examples

Chapter 9 Additional and Advanced Exercises

Determining Convergence of Series

Choosing Centers for Taylor Series

Theory and Examples

10 Parametric Equations and Polar Coordinates

10.1 Parametrizations of Plane Curves

Parametric Equations

Cycloids

Brachistochrones and Tautochrones

Exercises 10.1

Finding Cartesian from Parametric Equations

Finding Parametric Equations

Distance Using Parametric Equations

10.2 Calculus with Parametric Curves

Tangent Lines and Areas

Length of a Parametrically Defined Curve

Length of a Curve y = f(x)

The Arc Length Differential

Areas of Surfaces of Revolution

Exercises 10.2

Tangent Lines to Parametrized Curves

Implicitly Defined Parametrizations

Area

Lengths of Curves

Surface Area

Centroids

Theory and Examples

10.3 Polar Coordinates

Definition of Polar Coordinates

Polar Equations and Graphs

Relating Polar and Cartesian Coordinates

Exercises 10.3

Polar Coordinates

Polar to Cartesian Coordinates

Cartesian to Polar Coordinates

Graphing Sets of Polar Coordinate Points

Polar to Cartesian Equations

Cartesian to Polar Equations

10.4 Graphing Polar Coordinate Equations

Symmetry

Slope

Converting a Graph from the rθ-Plane to the xy-Plane

Exercises 10.4

Symmetries and Polar Graphs

Slopes of Polar Curves in the xy-Plane

Concavity of Polar Curves in the xy-Plane

Graphing Limaçons

Graphing Polar Regions and Curves in the xy-Plane

10.5 Areas and Lengths in Polar Coordinates

Area in the Plane

Length of a Polar Curve

Exercises 10.5

Finding Polar Areas

Finding Lengths of Polar Curves

Theory and Examples

Chapter 10 Questions to Guide Your Review

Chapter 10 Practice Exercises

Identifying Parametric Equations in the Plane

Finding Parametric Equations and Tangent Lines

Lengths of Curves

Surface Areas

Polar to Cartesian Equations

Cartesian to Polar Equations

Graphs in Polar Coordinates

Area in Polar Coordinates

Length in Polar Coordinates

Chapter 10 Additional and Advanced Exercises

Polar Coordinates

Theory and Examples

11 Vectors and the Geometry of Space

11.1 Three-Dimensional Coordinate Systems

Distance and Spheres in Space

Exercises 11.1

Geometric Interpretations of Equations

Geometric Interpretations of Inequalities and Equations

Distance

Inequalities to Describe Sets of Points

Spheres

Theory and Examples

11.2 Vectors

Component Form

Vector Algebra Operations

Unit Vectors

Midpoint of a Line Segment

Applications

Exercises 11.2

Vectors in the Plane

Vectors in Space

Geometric Representations

Length and Direction

Direction and Midpoints

Theory and Applications

11.3 The Dot Product

Angle Between Vectors

Orthogonal Vectors

Dot Product Properties and Vector Projections

Work

Exercises 11.3

Dot Product and Projections

Angle Between Vectors

Theory and Examples

Equations for Lines in the Plane

Work

Angles Between Lines in the Plane

11.4 The Cross Product

The Cross Product of Two Vectors in Space

|u × v| Is the Area of a Parallelogram

Determinant Formula for u × v

Torque

Triple Scalar or Box Product

Exercises 11.4

Cross Product Calculations

Triangles in Space

Triple Scalar Products

Theory and Examples

Area of a Parallelogram

Area of a Triangle

Volume of a Tetrahedron

11.5 Lines and Planes in Space

Lines and Line Segments in Space

The Distance from a Point to a Line in Space

An Equation for a Plane in Space

Lines of Intersection

The Distance from a Point to a Plane

Angles Between Planes

Exercises 11.5

Lines and Line Segments

Planes

Distances

Angles

Intersecting Lines and Planes

Theory and Examples

11.6 Cylinders and Quadric Surfaces

Cylinders

Quadric Surfaces

General Quadric Surfaces

Exercises 11.6

Matching Equations with Surfaces

Drawing

Cylinders

Ellipsoids

Paraboloids and Cones

Hyperboloids

Hyperbolic Paraboloids

Assorted

Theory and Examples

Viewing Surfaces

Chapter 11 Questions to Guide Your Review

Chapter 11 Practice Exercises

Vector Calculations in Two Dimensions

Vector Calculations in Three Dimensions

Lines, Planes, and Distances

Quadric Surfaces

Chapter 11 Additional and Advanced Exercises

12 Vector-Valued Functions and Motion in Space

12.1 Curves in Space and Their Tangents

Limits and Continuity

Derivatives and Motion

Differentiation Rules

Vector Functions of Constant Length

Exercises 12.1

Motion in the Plane

Motion in Space

Tangents to Curves

Theory and Examples

12.2 Integrals of Vector Functions; Projectile Motion

Integrals of Vector Functions

The Vector and Parametric Equations for Ideal Projectile Motion

Exercises 12.2

Integrating Vector-Valued Functions

Initial Value Problems

Motion Along a Straight Line

Projectile Motion

Theory and Examples

12.3 Arc Length in Space

Arc Length Along a Space Curve

Speed on a Smooth Curve

Unit Tangent Vector

Exercises 12.3

Finding Tangent Vectors and Lengths

Arc Length Parameter

Theory and Examples

12.4 Curvature and Normal Vectors of a Curve

Curvature of a Plane Curve

Circle of Curvature for Plane Curves

Curvature and Normal Vectors for Space Curves

Exercises 12.4

Plane Curves

Space Curves

More on Curvature

12.5 Tangential and Normal Components of Acceleration

The TNB Frame

Tangential and Normal Components of Acceleration

Exercises 12.5

Finding Tangential and Normal Components

Finding the TNB Frame

Physical Applications

Theory and Examples

12.6 Velocity and Acceleration in Polar Coordinates

Motion in Polar and Cylindrical Coordinates

Planets Move in Planes

Kepler’s First Law (Ellipse Law)

Kepler’s Second Law (Equal Area Law)

Kepler’s Third Law (Time Distance Law)

Exercises 12.6

Chapter 12 Questions to Guide Your Review

Chapter 12 Practice Exercises

Motion in the Plane

Projectile Motion

Motion in Space

Theory and Examples

Chapter 12 Additional and Advanced Exercises

Applications

Motion in Polar and Cylindrical Coordinates

13 Partial Derivatives

13.1 Functions of Several Variables

Domains and Ranges

Functions of Two Variables

Graphs, Level Curves, and Contours of Functions of Two Variables

Functions of Three Variables

Computer Graphing

Exercises 13.1

Domain, Range, and Level Curves

Matching Surfaces with Level Curves

Functions of Two Variables

Finding Level Curves

Sketching Level Surfaces

Finding Level Surfaces

13.2 Limits and Continuity in Higher Dimensions

Limits for Functions of Two Variables

Continuity

Functions of More Than Two Variables

Extreme Values of Continuous Functions on Closed, Bounded Sets

Exercises 13.2

Limits with Two Variables

Limits of Quotients

Limits with Three Variables

Continuity for Two Variables

Continuity for Three Variables

No Limit Exists at the Origin

Theory and Examples

Changing Variables to Polar Coordinates

Using the Limit Definition

13.3 Partial Derivatives

Partial Derivatives of a Function of Two Variables

Calculations

Functions of More Than Two Variables

Partial Derivatives and Continuity

Second-Order Partial Derivatives

The Mixed Derivative Theorem

Partial Derivatives of Still Higher Order

Differentiability

Exercises 13.3

Calculating First-Order Partial Derivatives

Calculating Second-Order Partial Derivatives

Mixed Partial Derivatives

Using the Partial Derivative Definition

Differentiating Implicitly

Theory and Examples

13.4 The Chain Rule

Functions of Two Variables

Functions of Three Variables

Functions Defined on Surfaces

Implicit Differentiation Revisited

Functions of Many Variables

Exercises 13.4

Chain Rule: One Independent Variable

Chain Rule: Two and Three Independent Variables

Using a Dependency Diagram

Implicit Differentiation

Finding Partial Derivatives at Specified Points

Theory and Examples

13.5 Directional Derivatives and Gradient Vectors

Directional Derivatives in the Plane

Interpretation of the Directional Derivative

Calculation and Gradients

Gradients and Tangents to Level Curves

Functions of Three Variables

The Chain Rule for Paths

Exercises 13.5

Calculating Gradients

Finding Directional Derivatives

Tangent Lines to Level Curves

Theory and Examples

13.6 Tangent Planes and Differentials

Tangent Planes and Normal Lines

Estimating Change in a Specific Direction

How to Linearize a Function of Two Variables

Differentials

Functions of More Than Two Variables

Exercises 13.6

Tangent Planes and Normal Lines to Surfaces

Tangent Lines to Intersecting Surfaces

Estimating Change

Finding Linearizations

Bounding the Error in Linear Approximations

Linearizations for Three Variables

Estimating Error; Sensitivity to Change

Theory and Examples

13.7 Extreme Values and Saddle Points

Derivative Tests for Local Extreme Values

Absolute Maxima and Minima on Closed Bounded Regions

Exercises 13.7

Finding Local Extrema

Finding Absolute Extrema

Theory and Examples

13.8 Lagrange Multipliers

Constrained Maxima and Minima

The Method of Lagrange Multipliers

Lagrange Multipliers with Two Constraints

Exercises 13.8

Two Independent Variables with One Constraint

Three Independent Variables with One Constraint

Extreme Values Subject to Two Constraints

Theory and Examples

Chapter 13 Questions to Guide Your Review

Chapter 13 Practice Exercises

Domain, Range, and Level Curves

Evaluating Limits

Partial Derivatives

Second-Order Partials

Chain Rule Calculations

Implicit Differentiation

Directional Derivatives

Gradients, Tangent Planes, and Normal Lines

Tangent Lines to Curves

Linearizations

Estimates and Sensitivity to Change

Local Extrema

Absolute Extrema

Lagrange Multipliers

Theory and Examples

Chapter 13 Additional and Advanced Exercises

Partial Derivatives

Gradients and Tangents

Extreme Values

Theory and Examples

14 Multiple Integrals

14.1 Double and Iterated Integrals over Rectangles

Double Integrals

Double Integrals as Volumes

Fubini’s Theorem for Calculating Double Integrals

Exercises 14.1

Evaluating Iterated Integrals

Evaluating Double Integrals over Rectangles

14.2 Double Integrals over General Regions

Double Integrals over Bounded, Nonrectangular Regions

Volumes

Finding Limits of Integration

Using Vertical Cross-Sections

Using Horizontal Cross-Sections

Properties of Double Integrals

Exercises 14.2

Sketching Regions of Integration

Finding Limits of Integration

Finding Regions of Integration and Double Integrals

Reversing the Order of Integration

Volume Beneath a Surface z = f(x, y)

Integrals over Unbounded Regions

Approximating Integrals with Finite Sums

Theory and Examples

14.3 Area by Double Integration

Areas of Bounded Regions in the Plane

Average Value

Exercises 14.3

Area by Double Integrals

Identifying the Region of Integration

Finding Average Values

Theory and Examples

14.4 Double Integrals in Polar Form

Integrals in Polar Coordinates

Finding Limits of Integration

Changing Cartesian Integrals into Polar Integrals

Exercises 14.4

Regions in Polar Coordinates

Evaluating Polar Integrals

Area in Polar Coordinates

Average Values

Theory and Examples

14.5 Triple Integrals in Rectangular Coordinates

Triple Integrals

Volume of a Region in Space

Finding Limits of Integration in the Order dz dy dx

Average Value of a Function in Space

Properties of Triple Integrals

Exercises 14.5

Triple Integrals in Different Iteration Orders

Evaluating Triple Iterated Integrals

Finding Equivalent Iterated Integrals

Finding Volumes Using Triple Integrals

Average Values

Changing the Order of Integration

Theory and Examples

14.6 Applications

Masses and First Moments

Moments of Inertia

Exercises 14.6

Plates of Constant Density

Plates with Varying Density

Solids with Constant Density

Solids with Varying Density

14.7 Triple Integrals in Cylindrical and Spherical Coordinates

Integration in Cylindrical Coordinates

How to Integrate in Cylindrical Coordinates

Spherical Coordinates and Integration

How to Integrate in Spherical Coordinates

Exercises 14.7

Evaluating Integrals in Cylindrical Coordinates

Changing the Order of Integration in Cylindrical Coordinates

Finding Iterated Integrals in Cylindrical Coordinates

Evaluating Integrals in Spherical Coordinates

Changing the Order of Integration in Spherical Coordinates

Finding Iterated Integrals in Spherical Coordinates

Finding Triple Integrals

Volumes

Average Values

Masses, Moments, and Centroids

14.8 Substitutions in Multiple Integrals

Substitutions in Double Integrals

Substitutions in Triple Integrals

Exercises 14.8

Jacobians and Transformed Regions in the Plane

Substitutions in Double Integrals

Substitutions in Triple Integrals

Theory and Examples

Chapter 14 Questions to Guide Your Review

Chapter 14 Practice Exercises

Evaluating Double Iterated Integrals

Areas and Volumes Using Double Integrals

Average Values

Polar Coordinates

Evaluating Triple Iterated Integrals

Volumes and Average Values Using Triple Integrals

Cylindrical and Spherical Coordinates

Masses and Moments

Substitutions

Chapter 14 Additional and Advanced Exercises

Volumes

Changing the Order of Integration

Masses and Moments

Theory and Examples

15 Integrals and Vector Fields

15.1 Line Integrals of Scalar Functions

Additivity

Mass and Moment Calculations

Line Integrals in the Plane

Exercises 15.1

Graphs of Vector Equations

Evaluating Line Integrals over Space Curves

Line Integrals over Plane Curves

Masses and Moments

15.2 Vector Fields and Line Integrals: Work, Circulation, and Flux

Vector Fields

Gradient Fields

Line Integrals of Vector Fields

Line Integrals with Respect to dx, dy, or dz

Work Done by a Force over a Curve in Space

Flow Integrals and Circulation for Velocity Fields

Flux Across a Simple Closed Plane Curve

Exercises 15.2

Vector Fields

Line Integrals of Vector Fields

Line Integrals with Respect to x, y, and z

Work

Line Integrals in the Plane

Work, Circulation, and Flux in the Plane

Vector Fields in the Plane

Flow Integrals in Space

15.3 Path Independence, Conservative Fields, and Potential Functions

Path Independence

Assumptions on Curves, Vector Fields, and Domains

Line Integrals in Conservative Fields

Finding Potentials for Conservative Fields

Exact Differential Forms

Exercises 15.3

Testing for Conservative Fields

Finding Potential Functions

Exact Differential Forms

Finding Potential Functions to Evaluate Line Integrals

Applications and Examples

15.4 Green’s Theorem in the Plane

Spin Around an Axis: The k-Component of Curl

Divergence

Two Forms for Green’s Theorem

Using Green’s Theorem to Evaluate Line Integrals

Proof of Green’s Theorem for Special Regions

Exercises 15.4

Computing the k-Component of Curl(F)

Verifying Green’s Theorem

Circulation and Flux

Work

Using Green’s Theorem

15.5 Surfaces and Area

Parametrizations of Surfaces

Surface Area

Implicit Surfaces

Exercises 15.5

Finding Parametrizations

Surface Area of Parametrized Surfaces

Planes Tangent to Parametrized Surfaces

More Parametrizations of Surfaces

Surface Area for Implicit and Explicit Forms

15.6 Surface Integrals

Surface Integrals

Orientation of a Surface

Surface Integrals of Vector Fields

Computing a Surface Integral for a Parametrized Surface

Moments and Masses of Thin Shells

Exercises 15.6

Surface Integrals of Scalar Functions

Finding Flux or Surface Integrals of Vector Fields

Moments and Masses

15.7 Stokes’ Theorem

The Curl Vector Field

Stokes’ Theorem

Paddle Wheel Interpretation of ∇ × F

Proof Outline of Stokes’ Theorem for Polyhedral Surfaces

Stokes’ Theorem for Surfaces with Holes

An Important Identity

Conservative Fields and Stokes’ Theorem

Exercises 15.7

Using Stokes’ Theorem to Find Line Integrals

Integral of the Curl Vector Field

Stokes’ Theorem for Parametrized Surfaces

Theory and Examples

15.8 The Divergence Theorem and a Unified Theory

Divergence in Three Dimensions

Divergence Theorem

Divergence and the Curl

Proof of the Divergence Theorem for Special Regions

Divergence Theorem for Other Regions

Gauss’s Law: One of the Four Great Laws of Electromagnetic Theory

Unifying the Integral Theorems

Exercises 15.8

Calculating Divergence

Calculating Flux Using the Divergence Theorem

Theory and Examples

Chapter 15 Questions to Guide Your Review

Chapter 15 Practice Exercises

Evaluating Line Integrals

Finding and Evaluating Surface Integrals

Parametrized Surfaces

Conservative Fields

Work and Circulation

Masses and Moments

Flux Across a Plane Curve or Surface

Chapter 15 Additional and Advanced Exercises

Finding Areas with Green’s Theorem

Theory and Applications

16 First-Order Differential Equations

16.1 Solutions, Slope Fields, and Euler’s Method

General First-Order Differential Equations and Solutions

Slope Fields: Viewing Solution Curves

Euler’s Method

Exercises 16.1

Slope Fields

Integral Equations

Using Euler’s Method

16.2 First-Order Linear Equations

Solving Linear Equations

RL Circuits

Exercises 16.2

First-Order Linear Equations

Solving Initial Value Problems

Theory and Examples

16.3 Applications

Motion with Resistance Proportional to Velocity

Inaccuracy of the Exponential Population Growth Model

Orthogonal Trajectories

Mixture Problems

Exercises 16.3

Motion Along a Line

Orthogonal Trajectories

Mixture Problems

16.4 Graphical Solutions of Autonomous Equations

Equilibrium Values and Phase Lines

Stable and Unstable Equilibria

Newton’s Law of Cooling

A Falling Body Encountering Resistance

Logistic Population Growth

Exercises 16.4

Phase Lines and Solution Curves

Models of Population Growth

Applications and Examples

16.5 Systems of Equations and Phase Planes

Phase Planes

A Competitive-Hunter Model

Limitations of the Phase-Plane Analysis Method

Another Type of Behavior

Exercises 16.5

Lotka-Volterra Equations for a Predator-Prey Model

Chapter 16 Questions to Guide Your Review

Chapter 16 Practice Exercises

Initial Value Problems

Euler’s Method

Slope Fields

Autonomous Differential Equations and Phase Lines

Applications

Mixture Problems

Chapter 16 Additional and Advanced Exercises

Theory and Applications

Homogeneous Equations

17 Second-Order Differential Equations

17.1 Second-Order Linear Equations

Constant-Coefficient Homogeneous Equations

Case 1: b2 − 4ac > 0

Case 2: b2 − 4ac = 0

Case 3: b2 − 4ac < 0

Initial Value and Boundary Value Problems

Exercises 17.1

17.2 Nonhomogeneous Linear Equations

Form of the General Solution

The Method of Undetermined Coefficients

The Method of Variation of Parameters

Exercises 17.2

17.3 Applications

Vibrations

Simple Harmonic Motion

Damped Motion

Case 1: b = ω

Case 2: b > ω

Case 3: b < ω

Electric Circuits

Summary

Exercises 17.3

17.4 Euler Equations

The General Solution of Euler Equations

Exercises 17.4

17.5 Power-Series Solutions

Method of Solution

Exercises 17.5

Appendix A

A.1 Real Numbers and the Real Line

Real Numbers

Intervals

Solving Inequalities

Absolute Value

Exercises A.1

A.2 Mathematical Induction

Other Starting Integers

Proof of the Derivative Sum Rule for Sums of Finitely Many Functions

Exercises A.2

A.3 Lines and Circles

Cartesian Coordinates in the Plane

Increments and Straight Lines

Parallel and Perpendicular Lines

Distance and Circles in the Plane

Exercises A.3

Distance, Slopes, and Lines

Circles

Inequalities

Theory and Examples

A.4 Conic Sections

Parabolas

Ellipses

Hyperbolas

Exercises A.4

Identifying Graphs

Parabolas

Ellipses

Hyperbolas

Shifting Conic Sections

A.5 Proofs of Limit Theorems

Exercises A.5

A.6 Commonly Occurring Limits

A.7 Theory of the Real Numbers

A.8 Complex Numbers

The Hierarchy of Numbers

The Complex Numbers

Argand Diagrams

Euler’s Formula

Products

Quotients

Powers

Roots

The Fundamental Theorem of Algebra

Exercises A.8

Operations with Complex Numbers

Graphing and Geometry

Powers and Roots

Theory and Examples

A.9 The Distributive Law for Vector Cross Products

A.10 The Mixed Derivative Theorem and the Increment Theorem

Appendix B

B.1 Relative Rates of Growth

Growth Rates of Functions

Order and Oh-Notation

Sequential vs. Binary Search

Exercises B.1

Comparisons with the Exponential ex

Comparisons with the Power x2

Comparisons with the Logarithm ln x

Ordering Functions by Growth Rates

Big-oh and Little-oh; Order

Other Comparisons

Algorithms and Searches

B.2 Probability

Random Variables

Probability Distributions

Exponentially Decreasing Distributions

Expected Values, Means, and Medians

Variance and Standard Deviation

Uniform Distributions

Normal Distributions

Exercises B.2

Probability Density Functions

Exponential Distributions

[Technology Exercise] Normal Distributions

Discrete Random Variables

B.3 Conics in Polar Coordinates

Eccentricity

Polar Equations

Lines

Circles

Exercises B.3

Ellipses and Eccentricity

Hyperbolas and Eccentricity

Eccentricities and Directrices

Parabolas and Ellipses

Lines

Circles

Examples of Polar Equations

B.4 Taylor’s Formula for Two Variables

Derivation of the Second Derivative Test

The Error Formula for Linear Approximations

Taylor’s Formula for Functions of Two Variables

Exercises B.4

Finding Quadratic and Cubic Approximations

B.5 Partial Derivatives with Constrained Variables

Decide Which Variables Are Dependent and Which Are Independent

How to Find ∂w/∂x When the Variables in w = f(x, y, z) Are Constrained by Another Equation

Notation

Arrow Diagrams

Exercises B.5

Finding Partial Derivatives with Constrained Variables

Theory and Examples

Answers to Odd-Numbered Exercises

Chapter 1

Section 1.1, pp. 11–13

Section 1.2, pp. 18–21

Section 1.3, pp. 27–29

Section 1.4, p. 33

Section 1.5, pp. 37–38

Section 1.6, pp. 48–50

Chapter 2

Section 2.1, pp. 56–58

Section 2.2, pp. 66–69

Section 2.3, pp. 74–77

Section 2.4, pp. 83–85

Section 2.5, pp. 95–97

Section 2.6, pp. 107–110

Practice Exercises, pp. 111–112

Additional and Advanced Exercises, pp. 118–120

Chapter 3

Section 3.1, pp. 118–120

Section 3.2, pp. 125–129

Section 3.3, pp. 137–139

Section 3.4, pp. 145–148

Section 3.5, pp. 152–154

Section 3.6, pp. 159–162

Section 3.7, pp. 165–167

Section 3.8, pp. 176–177

Section 3.9, pp. 182–184

Section 3.10, pp. 189–192

Section 3.11, pp. 201–203

Practice Exercises, pp. 204–208

Additional and Advanced Exercises, pp. 208–211

Chapter 4

Section 4.1, pp. 218–220

Section 4.2, pp. 226–228

Section 4.3, pp. 232–233

Section 4.4, pp. 242–246

Section 4.5, pp. 253–254

Section 4.6, pp. 260–266

Section 4.7, pp. 269–271

Section 4.8, pp. 277–281

Practice Exercises, pp. 282–286

Additional and Advanced Exercises, pp. 286–289

Chapter 5

Section 5.1, pp. 298–300

Section 5.2, pp. 306–307

Section 5.3, pp. 316–319

Section 5.4, pp. 329–331

Section 5.5, pp. 338–339

Section 5.6, pp. 345–349

Practice Exercises, pp. 350–353

Additional and Advanced Exercises, pp. 353–355

Chapter 6

Section 6.1, pp. 363–367

Section 6.2, pp. 372–375

Section 6.3, pp. 379–381

Section 6.4, pp. 384–386

Section 6.5, pp. 389–392

Section 6.6, pp. 400–401

Practice Exercises, pp. 402–403

Additional and Advanced Exercises, pp. 403–404

Chapter 7

Section 7.1, pp. 413–415

Section 7.2, pp. 422–424

Section 7.3, pp. 430–433

Practice Exercises, pp. 433–434

Additional and Advanced Exercises, p. 434–435

Chapter 8

Section 8.1, pp. 442–444

Section 8.2, pp. 449–450

Section 8.3, pp. 454–455

Section 8.4, pp. 461–463

Section 8.5, pp. 467–469

Section 8.6, pp. 476–478

Section 8.7, pp. 487–489

Practice Exercises, pp. 490–492

Additional and Advanced Exercises, pp. 492–494

Chapter 9

Section 9.1, pp. 504–508

Section 9.2, pp. 515–517

Section 9.3, pp. 522–524

Section 9.4, pp. 528–529

Section 9.5, pp. 534–535

Section 9.6, pp. 540–542

Section 9.7, pp. 551–554

Section 9.8, pp. 558–559

Section 9.9, pp. 564–565

Section 9.10, pp. 572–574

Practice Exercises, pp. 575–577

Additional and Advanced Exercises, pp. 577–579

Chapter 10

Section 10.1, pp. 586–588

Section 10.2, pp. 596–598

Section 10.3, pp. 601–602

Section 10.4, pp. 605–606

Section 10.5, pp. 610–611

Practice Exercises, pp. 611–613

Additional and Advanced Exercises, p. 613

Chapter 11

Section 11.1, pp. 617–619

Section 11.2, pp. 626–628

Section 11.3, pp. 634–636

Section 11.4, pp. 641–642

Section 11.5, pp. 649–651

Section 11.6, pp. 655–656

Practice Exercises, pp. 657–659

Additional and Advanced Exercises, pp. 659–661

Chapter 12

Section 12.1, pp. 669–671

Section 12.2, pp. 675–677

Section 12.3, p. 681

Section 12.4, pp. 686–687

Section 12.5, p. 689–690

Section 12.6, p. 693–694

Practice Exercises, pp. 694–695

Additional and Advanced Exercises, pp. 696

Chapter 13

Section 13.1, pp. 812–814

Section 13.2, pp. 820–823

Section 13.3, pp. 833–835

Section 13.4, pp. 842–844

Section 13.5, pp. 852–853

Section 13.6, pp. 860–863

Section 13.7, pp. 870–872

Section 13.8, pp. 879–882

Practice Exercises, pp. 891–894

Additional and Advanced Exercises, pp. 894–896

Chapter 14

Section 14.1, pp. 779–784

Section 14.2, pp. 784–793

Section 14.3, p. 793–796

Section 14.4, pp. 796–803

Section 14.5, pp. 803–813

Section 14.6, pp. 813–820

Section 14.7, pp. 820–831

Section 14.8, pp. 832–841

Practice Exercises, pp. 842–844

Additional and Advanced Exercises, pp. 844–846

Chapter 15

Section 15.1, pp. 847–854

Section 15.2, pp. 854–867

Section 15.3, pp. 867–878

Section 15.4, pp. 878–890

Section 15.5, pp. 890–900

Section 15.6, pp. 900–910

Section 15.7, pp. 910–923

Section 15.8, pp. 923–933

Practice Exercises, pp. 934–936

Additional and Advanced Exercises, pp. 937–938

Appendices

Appendix A.1, p. AP-6

Appendix A.3, pp. AP-15–AP-16

Appendix A.4, pp. AP-22–AP-23

Appendix A.8, pp. AP-37–AP-38

Chapter 16

Section 16.1, pp. 945–947

Section 16.2, pp. 951–953

Section 16.3, pp. 958–959

Section 16.4, pp. 965–966

Section 16.5, pp. 969–972

Practice Exercises, pp. 972–974

Additional and Advanced Exercises, p. 974

Chapter 17

Section 17.1, pp. 17-6–17-7

Section 17.2, pp. 17-14–17-15

Section 17.3, pp. 17-20–17-21

Section 17.4, p. 17-24

Section 17.5, p. 17-29

Appendices

Appendix B.1, pp. B-5–B-6

Appendix B.2, pp. B-17–B-19

Appendix B.3, pp. B-24–B-25

Appendix B.4, pp. B-29

Appendix B.5, pp. B-33–B-34

Applications Index

B * Business* and Economics

E Engineering and Physical Sciences

G General

L Life Sciences

S

*and Behavioral Sciences*

**Social**Subject Index

* Joel Hass *received his PhD from the

**University of California – Berkeley**. He is currently a professor of mathematics at the University of California – Davis. He has coauthored 6 widely used calculus texts as well as 2 calculus study guides. He is currently on the editorial board of Geometriae Dedicata and Media-Enhanced Mathematics. He has been a member of the Institute for Advanced Study at Princeton University and of the Mathematical Sciences Research Institute, and he was a Sloan Research Fellow. Hass’s current areas of research include the geometry of proteins, 3-dimensional manifolds, applied math and computational complexity. In his free time, Hass enjoys kayaking.

* Christopher Heil *received his PhD from the University of Maryland. He is currently a professor of mathematics at the Georgia Institute of Technology. He is the author of a graduate text on analysis and a number of highly cited research survey articles. He serves on the editorial boards of Applied and Computational Harmonic Analysis and The Journal of Fourier Analysis and Its Applications. Heil’s current areas of research include redundant representations, operator theory and applied harmonic analysis. In his spare time, Heil pursues his hobby of astronomy.

* Maurice D. Weir *holds a DA and MS from Carnegie-Mellon University and received his BS at Whitman College. He is a Professor Emeritus of the Department of Applied Mathematics at the Naval Postgraduate School in Monterey, California. Weir enjoys teaching Mathematical Modeling and Differential Equations. His current areas of research include modeling and simulation as well as mathematics education. Weir has been awarded the Outstanding Civilian Service Medal, the Superior Civilian Service Award, and the Schieffelin Award for Excellence in Teaching. He has coauthored 8 books, including the University Calculus series and Thomas’ Calculus.

* Przemyslaw Bogacki *is an Associate Professor of Mathematics and Statistics and a University Professor at Old Dominion University. He received his PhD in 1990 from Southern Methodist University. He is the author of a text on linear algebra. He is actively involved in applications of technology in collegiate mathematics. His areas of research include computer aided geometric design and numerical solution of initial value problems for ordinary differential equations.

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