Rent 9780534393397 | Calculus | STEWART @knetbooks.com

Summary Table of Contents

Stewart's CALCULUS, Fifth Edition has the mathematical precision, accuracy, clarity of exposition and outstanding examples and problem sets that have characterized the first four editions. Stewart retains the focus on problem solving and the pedagogical system that has made the book a favorite of students and instructors in a wide variety of colleges and universities throughout the world. In this Fifth Edition, he has made hundreds of small improvements: new examples, additional steps in existing examples, updating of data in existing examples and exercises, new phrases and margin notes to clarify the exposition, references to other sources and web sites, redrawn art, and references to the TEC CD (Tools for Enriching Calculus). These refinements ensure that students and instructors have the best materials available. The number of pages in the book, however, remains unchanged from the 4th edition. Further support for students and instructors is now available through a vast array of supplementary material.

Preface

xiv

To the Student

xxvi

A Preview of Calculus

(8)

Functions and Models

(54)

... MORE

Four Ways to Represent a Function

(14)

Mathematical Models: A Catalog of Essential Functions

(13)

New Functions from Old Functions

(10)

Graphing Calculators and Computers

(16)

Review

(3)

Principles of Problem Solving

(6)

Limits and Rates of Change

(62)

The Tangent and Velocity Problems

(5)

The Limit of a Function

(12)

Calculating Limits Using the Limit Laws

(10)

The Precise Definition of a Limit

(10)

Continuity

102

(10)

Tangents, Velocities, and Other Rates of Change

112

(14)

Review

121

(3)

Problems Plus

124

(2)

Derivatives

126

(96)

Derivatives

127

(7)

Writing Project Early Methods for Finding Tangents

133

(1)

The Derivative as a Function

134

(11)

Differentiation Formulas

145

(12)

Rates of Change in the Natural and Social Sciences

157

(12)

Derivatives of Trigonometric Functions

169

(6)

The Chain Rule

175

(9)

Implicit Differentiation

184

(6)

Higher Derivatives

190

(8)

Applied Project Where Should a Pilot Start Descent?

197

(1)

Applied Project Building a Better Roller Coaster

198

(1)

Related Rates

198

(7)

Linear Approximations and Differentials

205

(17)

Laboratory Project Taylor Polynomials

212

(1)

Review

213

(5)

Problems Plus

218

(4)

Applications of Differentiation

222

(92)

Maximum and Minimum Values

223

(11)

Applied Project The Calculus of Rainbows

232

(2)

The Mean Value Theorem

234

(6)

How Derivatives Affect the Shape of a Graph

240

(9)

Limits at Infinity; Horizontal Asymptotes

249

(14)

Summary of Curve Sketching

263

(8)

Graphing with Calculus and Calculators

271

(7)

Optimization Problems

278

(11)

Applied Project The Shape of a Can

288

(1)

Applications to Business and Economics

289

(5)

Newton's Method

294

(6)

Antiderivatives

300

(14)

Review

308

(3)

Problems Plus

311

(3)

Integrals

314

(60)

Areas and Distances

315

(11)

The Definite Integral

326

(14)

Discovery Project Area Functions

339

(1)

The Fundamental Theorem of Calculus

340

(10)

Indefinite Integrals and the Net Change Theorem

350

(10)

Writing Project Newton, Leibniz, and the Invention of Calculus

359

(1)

The Substitution Rule

360

(14)

Review

368

(4)

Problems Plus

372

(2)

Applications of Integration

374

(38)

Areas between Curves

375

(7)

Volumes

382

(11)

Volumes by Cylindrical Shells

393

(5)

Work

398

(4)

Average Value of a Function

402

(10)

Review

406

(2)

Problems Plus

408

(4)

Inverse Functions: Exponential, Logarithmic, and Inverse Trigonometric Functions

412

(98)

Inverse Functions

413

(8)

Instructors may cover either Sections 7.2--7.4 or Sections 7.2*--7.4*. See the Preface

Exponential Functions and Their Derivatives

421

(13)

Logarithmic Functions

434

(7)

Derivatives of Logarithmic Functions

441

(10)

The Natural Logarithmic Function

451

(9)

The Natural Exponential Function

460

(7)

General Logarithmic and Exponential Functions

467

(10)

Inverse Trigonometric Functions

477

(9)

Applied Project Where to Sit at the Movies

485

(1)

Hyperbolic Functions

486

(7)

Indeterminate Forms and L'Hospital's Rule

493

(17)

Writing Project The Origins of L'Hospital's Rule

504

(1)

Review

504

(4)

Problems Plus

508

(2)

Techniques of Integration

510

(72)

Integration by Parts

511

(7)

Trigonometric Integrals

518

(7)

Trigonometric Substitution

525

(7)

Integration of Rational Functions by Partial Fractions

532

(9)

Strategy for Integration

541

(6)

Integration Using Tables and Computer Algebra Systems

547

(7)

Discovery Project Patterns in Integrals

553

(1)

Approximate Integration

554

(12)

Improper Integrals

566

(16)

Review

576

(3)

Problems Plus

579

(3)

Further Applications of Integration

582

(40)

Arc Length

583

(7)

Discovery Project Arc Length Contest

590

(1)

Area of a Surface of Revolution

590

(7)

Discovery Project Rotating on a Slant

596

(1)

Applications to Physics and Engineering

597

(10)

Applications to Economics and Biology

607

(4)

Probability

611

(11)

Review

618

(2)

Problems Plus

620

(2)

Differential Equations

622

(64)

Modeling with Differential Equations

623

(5)

Direction Fields and Euler's Method

628

(9)

Separable Equations

637

(10)

Applied Project How Fast Does a Tank Drain?

645

(1)

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

646

(1)

Exponential Growth and Decay

647

(12)

Applied Project Calculus and Baseball

658

(1)

The Logistic Equation

659

(9)

Linear Equations

668

(6)

Predator-Prey Systems

674

(12)

Review

680

(4)

Problems Plus

684

(2)

Parametric Equations and Polar Coordinates

686

(50)

Curves Defined by Parametric Equations

687

(9)

Laboratory Project Running Circles around Circles

695

(1)

Calculus with Parametric Curves

696

(9)

Laboratory Project Bezier Curves

705

(1)

Polar Coordinates

705

(10)

Areas and Lengths in Polar Coordinates

715

(5)

Conic Sections

720

(8)

Conic Sections in Polar Coordinates

728

(8)

Review

732

(3)

Problems Plus

735

(1)

Infinite Sequences and Series

736

(92)

Sequences

737

(12)

Laboratory Project Logistic Sequences

749

(1)

Series

749

(10)

The Integral Test and Estimates of Sums

759

(7)

The Comparison Tests

766

(5)

Alternating Series

771

(5)

Absolute Convergence and the Ratio and Root Tests

776

(7)

Strategy for Testing Series

783

(2)

Power Series

785

(5)

Representations of Functions as Power Series

790

(6)

Taylor and Maclaurin Series

796

(12)

Laboratory Project An Elusive Limit

808

(1)

The Binomial Series

808

(4)

Writing Project How Newton Discovered the Binomial Series

812

(1)

Applications of Taylor Polynomials

812

(16)

Applied Project Radiation from the Stars

821

(1)

Review

822

(3)

Problems Plus

825

(3)

Vectors and the Geometry of Space

828

(56)

Three-Dimensional Coordinate Systems

829

(5)

Vectors

834

(9)

The Dot Product

843

(7)

The Cross Product

850

(8)

Discovery Project The Geometry of a Tetrahedron

858

(1)

Equations of Lines and Planes

858

(10)

Laboratory Project Putting 3D in Perspective

868

(1)

Cylinders and Quadric Surfaces

868

(7)

Cylindrical and Spherical Coordinates

875

(9)

Laboratory Project Families of Surfaces

880

(1)

Review

880

(3)

Problems Plus

883

(1)

Vector Functions

884

(38)

Vector Functions and Space Curves

885

(7)

Derivatives and Integrals of Vector Functions

892

(6)

Arc Length and Curvature

898

(8)

Motion in Space: Velocity and Acceleration

906

(16)

Applied Project Kepler's Laws

916

(1)

Review

917

(3)

Problems Plus

920

(2)

Partial Derivatives

922

(94)

Functions of Several Variables

923

(15)

Limits and Continuity

938

(7)

Partial Derivatives

945

(14)

Tangent Planes and Linear Approximations

959

(8)

The Chain Rule

967

(9)

Directional Derivatives and the Gradient Vector

976

(13)

Maximum and Minimum Values

989

(12)

Applied Project Designing a Dumpster

999

(1)

Discovery Project Quadratic Approximations and Critical Points

1000

(1)

Lagrange Multipliers

1001

(15)

Applied Project Rocket Science

1008

(1)

Applied Project Hydro-Turbine Optimization

1009

(1)

Review

1010

(4)

Problems Plus

1014

(2)

Multiple Integrals

1016

(74)

Double Integrals over Rectangles

1017

(8)

Iterated Integrals

1025

(6)

Double Integrals over General Regions

1031

(8)

Double Integrals in Polar Coordinates

1039

(6)

Applications of Double Integrals

1045

(10)

Surface Area

1055

(4)

Triple Integrals

1059

(10)

Discovery Project Volumes of Hyperspheres

1068

(1)

Triple Integrals in Cylindrical and Spherical Coordinates

1069

(8)

Applied Project Roller Derby

1075

(1)

Discovery Project The Intersection of Three Cylinders

1076

(1)

Change of Variables in Multiple Integrals

1077

(13)

Review

1085

(3)

Problems Plus

1088

(2)

Vector Calculus

1090

(86)

Vector Fields

1091

(7)

Line Integrals

1098

(12)

The Fundamental Theorem for Line Integrals

1110

(9)

Green's Theorem

1119

(7)

Curl and Divergence

1126

(8)

Parametric Surfaces and Their Areas

1134

(11)

Surface Integrals

1145

(12)

Stokes' Theorem

1157

(6)

Writing Project Three Men and Two Theorems

1162

(1)

The Divergence Theorem

1163

(7)

Summary

1170

(6)

Review

1171

(3)

Problems Plus

1174

(2)

Second-Order Differential Equations

1176

Second-Order Linear Equations

1177

(6)

Nonhomogeneous Linear Equations

1183

(8)

Applications of Second-Order Differential Equations

1191

(8)

Series Solutions

1199

Review

1203

Appendixes

(124)

A Numbers, Inequalities, and Absolute Values

(8)

B Coordinate Geometry and Lines

(6)

C Graphs of Second-Degree Equations

(8)

D Trigonometry

(10)

E Sigma Notation

(5)

F Proofs of Theorems

(9)

G Complex Numbers

(8)

H Answers to Odd-Numbered Exercises

(69)

Index

125

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