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Calculus : Early Transcendentals

by: James Stewart

Calculus : Early Transcendentals

by: James Stewart

ISBN 13:
9780534251581
ISBN 10:
0534251587
Edition: 3rd
Format: Paperback
Copyright: 03/02/1995
Publisher: Brooks Cole
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Summary

I have tried to write a book that assists students in discovering calculus--both for its practical power and its surprising beauty. In this edition, as in the first two editions, I aim to convey to the student a sense of the utility of calculus and to develop technical competence, but I also strive to give some appreciation for the intrinsic beauty of the subject. Newton undoubtedly experienced a sense of triumph when he made his great discoveries. I want students to share some of that excitement. - from the Preface by the author.

REVIEW AND PREVIEW

(44)

1 Functions and Their Graphs

(15)

2 Types of Functions; Shifting and Scaling

(9)

3 Graphing Calculators and Computers

(6)

4 Principles of Problem Solving

(7)

5 A Preview of Calculus

(7)

1 LIMITS AND RATES OF CHANGE

(66)

1.1 The Tangent and Velocity Problems

(4)

1.2 The Limit of a Function

(11)

1.3 Calculating Limits using the Limit Laws

(9)

1.4 The Precise Definition of a Limit

(10)

1.5 Continuity

(10)

1.6 Limits at Infinity; Horizontal Asymptotes

(12)

1.7 Tangents, Velocities, and Other Rates of Change

102

(7)

Review

109

(3)

2 DERIVATIVES

112

(82)

2.1 Derivatives

112

(12)

2.2 Differentiation Formulas

124

(10)

2.3 Rates of Change in the Natural and Social Sciences

134

(9)

2.4 Derivatives of Trigonometric Functions

143

(7)

2.5 The Chain Rule

150

(8)

2.6 Implicit Differentiation

158

(6)

2.7 Higher Derivatives

164

(4)

2.8 Related Rates

168

(6)

2.9 Differentials; Linear and Quadratic Approximations

174

(8)

2.10 Newton's Method

182

(5)

Review

187

(3)

PROBLEMS PLUS

190

(4)

3 INVERSE FUNCTIONS: Exponential, Logarithmic, and Inverse Trigonometric Functions

194

(60)

3.1 Exponential Functions and Their Derivatives

194

(8)

3.2 Inverse Functions

202

(7)

3.3 Logarithmic Functions

209

(6)

3.4 Derivatives of Logarithmic Functions

215

(7)

3.5 Exponential Growth and Decay

222

(6)

3.6 Inverse Trigonometric Functions

228

(7)

3.7 Hyperbolic Functions

235

(6)

3.8 Indeterminate Forms and l'Hospital's Rule

241

(7)

Review

248

(4)

APPLICATIONS PLUS

252

(2)

4 THE MEAN VALUE THEOREM AND CURVE SKETCHING

254

(68)

4.1 Maximum and Minimum Values

254

(8)

4.2 The Mean Value Theorem

262

(6)

4.3 Monotonic Functions and the First Derivative Test

268

(5)

4.4 Concavity and Points of Inflection

273

(6)

4.5 Curve Sketching

279

(8)

4.6 Graphing with Calculus and Calculators

287

(7)

4.7 Applied Maximum and Minimum Problems

294

(9)

4.8 Applications to Economics

303

(4)

4.9 Antiderivatives

307

(8)

Review

315

(4)

PROBLEM PLUS

319

(3)

5 INTEGRALS

322

(58)

5.1 Sigma Notation

322

(6)

5.2 Area

328

(8)

5.3 The Definite Integral

336

(11)

5.4 The Fundamental Theorem of Calculus

347

(12)

5.5 The Substitution Rule

359

(7)

5.6 The Logarithm Defined as an Integral

366

(8)

Review

374

(3)

APPLICATIONS PLUS

377

(3)

6 APPLICATIONS OF INTEGRATION

380

(36)

6.1 Areas between Curves

380

(7)

6.2 Volume

387

(11)

6.3 Volumes by Cylindrical Shells

398

(5)

6.4 Work

403

(4)

6.5 Average Value of a Function

407

(3)

Review

410

(2)

PROBLEMS PLUS

412

(4)

7 TECHNIQUES OF INTEGRATION

416

(68)

7.1 Integration by Parts

417

(6)

7.2 Trigonometric Integrals

423

(6)

7.3 Trigonometric Substitution

429

(6)

7.4 Integration of Rational Functions by Partial Fractions

435

(9)

7.5 Rationalizing Substitutions

444

(3)

7.6 Strategy for Integration

447

(6)

7.7 Using Tables of Integrals and Computer Algebra Systems

453

(4)

7.8 Approximate Integration

457

(10)

7.9 Improper Integrals

467

(9)

Review

476

(3)

APPLICATIONS PLUS

479

(5)

8 FURTHER APPLICATIONS OF INTEGRATION

484

(44)

8.1 Differential Equations

484

(10)

8.2 Arc Length

494

(6)

8.3 Area of a Surface of Revolution

500

(5)

8.4 Moments and Centers of Mass

505

(7)

8.5 Hydrostatic Pressure and Force

512

(3)

8.6 Applications to Economics and Biology

515

(6)

Review

521

(3)

PROBLEMS PLUS

524

(4)

9 PARAMETRIC EQUATIONS AND POLAR COORDINATES

528

(50)

9.1 Curves Defined by Parametric Equations

528

(6)

9.2 Tangents and Areas

534

(6)

9.3 Arc Length and Surface Area

540

(4)

9.4 Polar Coordinates

544

(10)

9.5 Areas and Lengths in Polar Coordinates

554

(5)

9.6 Conic Sections

559

(7)

9.7 Conic Sections in Polar Coordinates

566

(5)

Review

571

(2)

APPLICATIONS PLUS

573

(5)

10 INFINITE SEQUENCES AND SERIES

578

(86)

10.1 Sequences

578

(11)

10.2 Series

589

(9)

10.3 The Integral Test and Estimates of Sums

598

(6)

10.4 The Comparison Tests

604

(5)

10.5 Alternating Series

609

(5)

10.6 Absolute Convergence and the Ratio and Root Tests

614

(7)

10.7 Strategy for Testing Series

621

(2)

10.8 Power Series

623

(5)

10.9 Representation of Functions as Power Series

628

(5)

10.10 Taylor and Maclaurin Series

633

(11)

10.11 The Binomial Series

644

(4)

10.12 Applications of Taylor Polynomials

648

(7)

Review

655

(3)

PROBLEMS PLUS

658

(6)

11 THREE-DIMENSIONAL ANALYTIC GEOMETRY AND VECTORS

664

(76)

11.1 Three-Dimensional Coordinate Systems

664

(5)

11.2 Vectors

669

(7)

11.3 The Dot Product

676

(6)

11.4 The Cross Product

682

(7)

11.5 Equations of Lines and Planes

689

(9)

11.6 Quadric Surfaces

698

(6)

11.7 Vector Functions and Space Curves

704

(9)

11.8 Arc Length and Curvature

713

(8)

11.9 Motion in Space: Velocity and Acceleration

721

(8)

11.10 Cylindrical and Spherical Coordinates

729

(4)

Review

733

(4)

APPLICATIONS PLUS

737

(3)

12 PARTIAL DERIVATIVES

740

(72)

12.1 Functions of Several Variables

740

(10)

12.2 Limits and Continuity

750

(8)

12.3 Partial Derivatives

758

(9)

12.4 Tangent Planes and Differentials

767

(7)

12.5 The Chain Rule

774

(8)

12.6 Directional Derivatives and the Gradient Vector

782

(10)

12.7 Maximum and Minimum Values

792

(9)

12.8 Lagrange Multipliers

801

(6)

Review

807

(3)

PROBLEMS PLUS

810

(2)

13 MULTIPLE INTEGRALS

812

(60)

13.1 Double Integrals over Rectangles

812

(5)

13.2 Iterated Integrals

817

(6)

13.3 Double Integrals over General Regions

823

(8)

13.4 Double Integrals in Polar Coordinates

831

(6)

13.5 Applications of Double Integrals

837

(6)

13.6 Surface Area

843

(2)

13.7 Triple Integrals

845

(9)

13.8 Triple Integrals in Cylindrical and Spherical Coordinates

854

(6)

13.9 Change of Variables in Multiple Integrals

860

(7)

Review

867

(3)

APPLICATIONS PLUS

870

(2)

14 VECTOR CALCULUS

872

14.1 Vector Fields

872

(4)

14.2 Line Integrals

876

(11)

14.3 The Fundamental Theorem for Line Integrals

887

(9)

14.4 Green's Theorem

896

(7)

14.5 Curl and Divergence

903

(8)

14.6 Parametric Surfaces and Their Areas

911

(7)

14.7 Surface Integrals

918

(12)

14.8 Stokes' Theorem

930

(6)

14.9 The Divergence Theorem

936

(5)

14.10 Summary

941

(1)

Review

942

(3)

PROBLEMS PLUS

945

Amazon no longer offers textbook rentals. We do!

Calculus : Early Transcendentals

Calculus : Early Transcendentals

9780534251581

0534251587

Summary

Table of Contents

Supplemental Materials

Write a Review

Amazon no longer offers textbook rentals. We do!

Calculus : Early Transcendentals

Calculus : Early Transcendentals

9780534251581

0534251587

Summary

Table of Contents

Supplemental Materials

Write a Review

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