9780005245828

CALCULUS,EARLY TRANSCENDENTALS

James Stewart

5th Edition

This edition of James Stewart's best-selling calculus book has been revised with the consistent dedication to excellence that has characterized all his books. Stewart's Calculus is successful throughout the world because he explains the material in a way that makes sense to a wide variety of readers. His explanations make ideas come alive, and his problems challenge, to re

1.1

Four Ways to Represent a Function

Exercises

p.22

1.2

Mathematical Models: A Catalog of Essential Functions

Exercises

p.35

1.3

New Functions from Old Functions

Exercises

p.45

1.4

Graphing Calculators and Computers

Exercises

p.53

1.5

Exponential Functions

Exercises

p.62

1.6

Inverse Functions and Logarithms

Exercises

p.74

Concept Check

p.77

True-False Quiz

p.78

Review Exercises

p.78

2.1

The Tangent and Velocity Problems

Exercises

p.91

2.2

The Limit of a Function

Exercises

p.102

2.3

Calculating Limits Using the Limit Laws

Exercises

p.111

2.4

The Precise Definition of a Limit

Exercises

p.122

2.5

Continuity

Exercises

p.133

2.6

Limits at Infinity; Horizontal Asymptotes

Exercises

p.146

2.7

Tangents, Velocities, and Other Rates of Change

Exercises

p.155

2.8

Derivatives

Exercises

p.163

2.9

The Derivative as a Function

Exercises

p.173

Concept Check

p.176

True-False Quiz

p.176

Review Exercises

p.177

3.1

Derivatives of Polynomials and Exponential Functions

Exercises

p.191

3.2

The Product and Quotient Rules

Exercises

p.197

3.3

Rates of Change in the Natural and Social Sciences

Exercises

p.208

3.4

Derivatives of Trigonometric Functions

Exercises

p.216

3.5

The Chain Rule

Exercises

p.224

3.6

Implicit Differentiation

Exercises

p.233

3.7

Higher Derivatives

Exercises

p.240

3.8

Derivatives of Logarithmic Functions

Exercises

p.249

3.9

Hyperbolic Functions

Exercises

p.254

3.10

Related Rates

Exercises

p.260

3.11

Linear Approximations and Differentials

Exercises

p.267

Concept Check

p.270

True-False Quiz

p.270

Review Exercises

p.271

4.1

Maximum and Minimum Values

Exercises

p.285

4.2

The Mean Value Theorem

Exercises

p.295

4.3

How Derivatives Affect the Shape of a Graph

Exercises

p.304

4.4

Indeterminate Forms and L'Hospital's Rule

Exercises

p.313

4.5

Summary of Curve Sketching

Exercises

p.323

4.6

Graphing with Calculus and Calculators

Exercises

p.330

4.7

Optimization Problems

Exercises

p.336

4.8

Applications to Business and Economics

Exercises

p.346

4.9

Newton's Method

Exercises

p.351

4.10

Antiderivatives

Exercises

p.358

Concept Check

p.361

True-False Quiz

p.361

Review Exercises

p.362

5.1

Areas and Distances

Exercises

p.378

5.2

The Definite Integral

Exercises

p.390

5.3

The Fundamental Theorem of Calculus

Exercises

p.402

5.4

Indefinite Integrals and the Net Change Theorem

Exercises

p.411

5.5

The Substitution Rule

Exercises

p.420

5.6

The Logarithm Defined as an Integral

Exercises

p.429

True-False Quiz

p.430

Concept Check

p.430

Review Exercises

p.431

7.1

Integration by Parts

Exercises

p.480

7.2

Trigonometric Integrals

Exercises

p.488

7.3

Trigonometric Substitution

Exercises

p.494

7.4

Integration of Rational Functions by Partial Fractions

Exercises

p.504

7.5

Strategy for Integration

Exercises

p.510

7.6

Integration Using Tables and Computer Algebra Systems

Exercises

p.515

7.7

Approximate Integration

Exercises

p.527

7.8

Improper Integrals

Exercises

p.537

Concept Check

p.540

True-False Quiz

p.540

Review Exercises

p.541

9.1

Modeling with Differential Equations

Exercises

p.591

9.2

Direction FIelds and Euler's Method

Exercises

p.599

9.3

Separable Equations

Exercises

p.607

9.4

Exponential Growth and Decay

Exercises

p.620

9.5

The Logistic Equation

Exercises

p.629

9.6

Linear Equations

Exercises

p.636

9.7

Predator-Prey Systems

Exercises

p.642

Concept Check

p.644

True-False Quiz

p.645

Review Exercises

p.645

10.1

Curves Defined by Parametric Equations

Exercises

p.656

10.2

Calculus with Parametric Curves

Exercises

p.666

10.3

Polar Coordinates

Exercises

p.677

10.4

Areas and Lengths in Polar Coordinates

Exercises

p.683

10.5

Conic Sections

Exercises

p.690

10.6

Conic Sections in Polar Coordinates

Exercises

p.695

Concept Check

p.696

True-False Quiz

p.697

Review Exercises

p.697

11.1

Sequences

Exercises

p.710

11.2

Series

Exercises

p.720

11.3

The Integral Test and Estimates of Sums

Exercises

p.729

11.4

The Comparison Tests

Exercises

p.734

11.5

Alternating Series

Exercises

p.739

11.6

Absolute Convergence and the Ratio and Root Tests

Exercises

p.745

11.7

Strategy for Testing Series

Exercises

p.748

11.8

Power Series

Exercises

p.753

11.9

Representations of Functions as Power Series

Exercises

p.759

11.10

Taylor and Maclaurin Series

Exercises

p.770

11.11

The Binomial Series

Exercises

p.775

11.12

Applications of Taylor Polynomials

Exercises

p.783

True-False Quiz

p.786

Concept Check

p.786

Review Exercises

p.787

12.1

Three-Dimensional Coordinate Systems

Exercises

p.797

12.2

Vectors

Exercises

p.805

12.3

The Dot Product

Exercises

p.812

12.4

The Cross Product

Exercises

p.820

12.5

Equations of Lines and Planes

Exercises

p.829

12.6

Cylinders and Quadric Surfaces

Exercises

p.837

12.7

Cylindrical and Spherical Coordinates

Exercises

p.842

Concept Check

p.844

True-False Quiz

p.845

Review Exercises

p.845

14.1

Functions of Several Variables

Exercises

p.897

14.2

Limits and Continuity

Exercises

p.908

14.3

Partial Derivatives

Exercises

p.919

14.4

Tangent Planes and Linear Approximations

Exercises

p.930

14.5

The Chain Rule

Exercises

p.938

14.6

Directional Derivatives and the Gradient Vector

Exercises

p.950

14.7

Maximum and Minimum Values

Exercises

p.961

14.8

Lagrange Multipliers

Exercises

p.970

Concept Check

p.974

True-False Quiz

p.975

Review Exercises

p.975

15.1

Double Integrals over Rectangles

Exercises

p.988

15.2

Iterated Integrals

Exercises

p.994

15.3

Double Integrals over General Regions

Exercises

p.1002

15.4

Double Integrals in Polar Coordinates

Exercises

p.1008

15.5

Applications of Double Integrals

Exercises

p.1018

15.6

Surface Area

Exercises

p.1022

15.7

Triple Integrals

Exercises

p.1030

15.8

Triple Integrals in Cylindrical and Spherical Coordinates

Exercises

p.1037

15.9

Change of Variables in Multiple Integrals

Exercises

p.1048

Concept Check

p.1049

True-False Quiz

p.1049

Review Exercises

p.1050

16.1

Vector Fields

Exercises

p.1060

16.2

Line Integrals

Exercises

p.1071

16.3

The Fundamental Theorem for Line Integrals

Exercises

p.1081

16.4

Green's Theorem

Exercises

p.1089

16.5

Curl and Divergence

Exercises

p.1096

16.6

Parametric Surfaces and Their Areas

Exercises

p.1106

16.7

Surface Integrals

Exercises

p.1119

16.8

Stokes' Theorem

Exercises

p.1125

16.9

The Divergence Theorem

Exercises

p.1132

True-False Quiz

p.1135

Concept Check

p.1135

Review Exercises

p.1136