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## Calculus Early Transcendentals 6th Edition

**FUNCTIONS AND MODELS**

1.1 Four Ways to Represent a Function

1.2 Mathematical Models: A Catalog of Essential Functions

1.3 New Functions from Old Functions

1.4 Graphing Calculators and Computers

1.5 Exponential Functions

1.6 Inverse Functions and Logarithms

Review

Principles of Problem Solving

**LIMITS AND DERIVATIVES**

2.1 The Tangent and Velocity Problems

2.2 The Limit of a Function

2.3 Calculating Limits Using the Limit Laws

2.4 The Precise Definition of a Limit

2.5 Continuity

2.6 Limits at Infinity; Horizontal Asymptotes

2.7 Derivatives and Rates of Change

Writing Project @ Early Methods for Finding Tangents

2.8 The Derivative as a Function

Review

**DIFFERENTIATION RULE**

3.1 Derivatives of Polynomials and Exponential Functions

Applied Project @ Building a Better Roller Coaster

3.2 The Product and Quotient Rules

3.3 Derivatives of Trigonometric Functions

3.4 The Chain Rule

Applied Project @ Where Should a Pilot Start Descent?

3.5 Implicit Differentiation

3.6 Derivatives of Logarithmic Functions

3.7 Rates of Change in the Natural and Social Sciences

3.8 Exponential Growth and Decay

3.9 Related Rates

3.10 Linear Approximations and Differentials

Laboratory Project @ Taylor Polynomials

3.11 Hyperbolic Functions

Review

Problems Plus

**APPLICATIONS OF DIFFERENTIATION**

4.1 Maximum and Minimum Values

Applied Project N The Calculus of Rainbows

4.2 The Mean Value Theorem

4.3 How Derivatives Affect the Shape of a Graph

4.4 Indeterminate Forms and L’Hospital’s Rule

Writing Project N The Origins of L’Hospital’s Rule

4.5 Summary of Curve Sketching

4.6 Graphing with Calculus and Calculators

4.7 Optimization Problems

Applied Project N The Shape of a Can

4.8 Newton’s Method

4.9 Antiderivatives

Review

**INTEGRALS**

5.1 Areas and Distances

5.2 The Definite Integral

Discovery Project @ Area Functions

5.3 The Fundamental Theorem of Calculus

5.4 Indefinite Integrals and the Net Change Theorem

Writing Project @ Newton, Leibniz, and the Invention of Calculus

5.5 The Substitution Rule

Review

Problems Plus

**INTEGRALS**

6.1 Areas between Curves

6.2 Volumes

6.3 Volumes by Cylindrical Shells

6.4 Work

6.5 Average Value of a Function

Applied Project @ Where to Sit at the Movies

Review

Problems Plus

**TECHNIQUES OF INTEGRATION**

7.1 Integration by Parts

7.2 Trigonometric Integrals

7.3 Trigonometric Substitution

7.4 Integration of Rational Functions by Partial Fractions

7.5 Strategy for Integration

7.6 Integration Using Tables and Computer Algebra Systems

Discovery Project @ Patterns in Integrals

7.7 Approximate Integration

7.8 Improper Integrals

Review

Problems Plus

**FURTHER APPLICATIONS OF INTEGRATION**

8.1 Arc Length

Discovery Project @ Arc Length Contest

8.2 Area of a Surface of Revolution

Discovery Project N Rotating on a Slant

8.3 Applications to Physics and Engineering

Discovery Project N Complementary Coffee Cups

8.4 Applications to Economics and Biology

8.5 Probability

Review

Problems Plus

**DIFFERENTIAL EQUATIONS**

9.1 Modeling with Differential Equations

9.2 Direction Fields and Euler’s Method

9.3 Separable Equations

Applied Project N How Fast Does a Tank Drain?

Applied Project @ Which Is Faster, Going Up or Coming Down?

9.4 Models for Population Growth

Applied Project @ Calculus and Baseball

9.5 Linear Equations

9.6 Predator-Prey Systems

Review

Problems Plus

**PARAMETRIC EQUATIONS AND POLAR COORDINATES**

10.1 Curves Defined by Parametric Equations

Laboratory Project @ Running Circles around Circles

10.2 Calculus with Parametric Curves

Laboratory Project @ Bézier Curves

10.3 Polar Coordinates

10.4 Areas and Lengths in Polar Coordinates

10.5 Conic Sections

10.6 Conic Sections in Polar Coordinates

Review

Problems Plus

**INFINITE SEQUENCES AND SERIES**

11.1 Sequences

Laboratory Project N Logistic Sequences

11.2 Series

11.3 The Integral Test and Estimates of Sums

11.4 The Comparison Tests

11.5 Alternating Series

11.6 Absolute Convergence and the Ratio and Root Tests

11.7 Strategy for Testing Series

11.8 Power Series

11.9 Representations of Functions as Power Series

11.10 Taylor and Maclaurin Series

Laboratory Project N An Elusive Limit

Writing Project N How Newton Discovered the Binomial Series

11.11 Applications of Taylor Polynomials

Applied Project N Radiation from the Stars

Review

Problems Plus

**VECTORS AND THE GEOMETRY OF SPACE**

12.1 Three-Dimensional Coordinate Systems

12.2 Vectors

12.3 The Dot Product

12.4 The Cross Product

Discovery Project N The Geometry of a Tetrahedron

12.5 Equations of Lines and Planes

Laboratory Project N Putting 3D in Perspective

12.6 Cylinders and Quadric Surfaces

Review

Problems Plus

**VECTOR FUNCTIONS**

13.1 Vector Functions and Space Curves

13.2 Derivatives and Integrals of Vector Functions

13.3 Arc Length and Curvature

13.4 Motion in Space: Velocity and Acceleration

Applied Project N Kepler’s Laws

Review

Problems Plus

**PARTIAL DERIVATIVES**

14.1 Functions of Several Variables

14.2 Limits and Continuity

14.3 Partial Derivatives

14.4 Tangent Planes and Linear Approximations

14.5 The Chain Rule

14.6 Directional Derivatives and the Gradient Vector

14.7 Maximum and Minimum Values

Applied Project @ Designing a Dumpster

Discovery Project @ Quadratic Approximations and Critical Points

14.8 Lagrange Multipliers

Applied Project @ Rocket Science

Applied Project @ Hydro-Turbine Optimization

Review

Problems Plus

**MULTIPLE INTEGRALS**

15.1 Double Integrals over Rectangles

15.2 Iterated Integrals

15.3 Double Integrals over General Regions

15.4 Double Integrals in Polar Coordinates

15.5 Applications of Double Integrals

15.6 Triple Integrals

Discovery Project @ Volumes of Hyperspheres

15.7 Triple Integrals in Cylindrical Coordinates

Discovery Project @ The Intersection of Three Cylinders

15.8 Triple Integrals in Spherical Coordinates

Applied Project @ Roller Derby

15.9 Change of Variables in Multiple Integrals

Review

Problems Plus

**VECTOR CALCULUS**

16.1 Vector Fields

16.2 Line Integrals

16.3 The Fundamental Theorem for Line Integrals

16.4 Green’s Theorem

16.5 Curl and Divergence

16.6 Parametric Surfaces and Their Areas

16.7 Surface Integrals

16.8 Stokes’ Theorem

Writing Project @ Three Men and Two Theorems

16.9 The Divergence Theorem

16.10 Summary

Review

Problems Plus

**SECOND-ORDER DIFFERENTIAL EQUATIONS**

17.1 Second-Order Linear Equations

17.2 Nonhomogeneous Linear Equations

17.3 Applications of Second-Order Differential Equations

17.4 Series Solutions

Review

**APPENDIXES A1**

A Numbers, Inequalities, and Absolute Values

B Coordinate Geometry and Lines

C Graphs of Second-Degree Equations

D Trigonometry

E Sigma Notation

F Proofs of Theorems

G The Logarithm Defined as an Integral

H Complex Numbers

I Answers to Odd-Numbered Exercises

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