Single Variable Calculus: STEWART;A/: 9780534355623: Book: : eCampus.com

Stewart's CALCULUS, FOURTH EDITION reflects the same dedication to excellence that characterized the first three editions. It has been revised with dedication, precision, and patient care to further emphasize conceptual understanding. A phenomenon of the Stewart success is the texts' use in such a wide variety of colleges and universities throughout the world. Just as he teaches to every student in his classes from the most unprepared to the most mathematically gifted, Stewart writes to a range of students - adding the explanations that make ideas come alive as well as the problems that challenge. Stewart's heuristic examples reveal calculus to students. His examples stand out because they are not just models for problem solving or a means of demonstrating techniques - they also encourage students to develop an analytic view of the subject.

A Preview of Calculus

(8)

1 Functions and Models

(56)

1.1 Four Ways to Represent a Function

(13)

1.2 Mathematical Models

(14)

1.3 New Functions from Old Functions

(12)

1.4 Graphing Calculators and Computers

(6)

Review

(3)

Principles of Problem Solving

(7)

2 Limits and Rates of Change

(62)

2.1 The Tangent and Velocity Problems

(5)

2.2 The Limit of a Function

(12)

2.3 Calculating Limits Using the Limit Laws

(10)

2.4 The Precise Definition of a Limit

(10)

2.5 Continuity

104

(10)

2.6 Tangents, Velocities, and Other Rates of Change

114

(10)

Review

124

(2)

Problems Plus

126

(2)

3 Derivatives

128

(94)

3.1 Derivatives

129

(7)

Writing Project Early Methods for Finding Tangents

135

(1)

3.2 The Derivative as a Function

136

(11)

3.3 Differentiation Formulas

147

(11)

3.4 Rates of Change in the Natural and Social Sciences

158

(12)

3.5 Derivatives of Trigonometric Functions

170

(7)

3.6 The Chain Rule

177

(8)

Applied Project Where Should a Pilot Start Descent?

199

3.7 Implicit Differentiation

185

(7)

3.8 Higher Derivatives

192

(7)

3.9 Related Rates

199

(6)

3.10 Linear Approximations and Differentials

205

(9)

Laboratory Project Taylor Polynomials

213

(1)

Review

214

(4)

Problems Plus

218

(4)

4 Applications of Differentiation

222

(90)

4.1 Maximum and Minimum Values

223

(11)

Applied Project The Calculus of Rainbows

232

(2)

4.2 The Mean Value Theorem

234

(6)

4.3 How Derivatives Affect the Shape of a Graph

240

(9)

4.4 Limits at Infinity; Horizontal Asymptotes

249

(14)

4.5 Summary of Curve Sketching

263

(8)

4.6 Graphing with Calculus and Calculators

271

(6)

4.7 Optimization Problems

277

(11)

Applied Project The Shape of a Can

287

(1)

4.8 Applications to Economics

288

(5)

4.9 Newton's Method

293

(6)

4.10 Antiderivatives

299

(7)

Review

306

(4)

Problems Plus

310

(2)

5 Integrals

312

(58)

5.1 Areas and Distances

313

(11)

5.2 The Definite Integral

324

(13)

Discovery Project Area Functions

336

(1)

5.3 The Fundamental Theorem of Calculus

337

(9)

5.4 Indefinite Integrals and the Total Change Theorem

346

(10)

Writing Project Newton, Leibniz, and the Invention of Calculus

355

(1)

5.5 The Substitution Rule

356

(7)

Review

363

(4)

Problems Plus

367

(3)

6 Applications of Integration

370

(36)

6.1 Areas between Curves

371

(7)

6.2 Volumes

378

(11)

6.3 Volumes by Cylindrical Shells

389

(5)

6.4 Work

394

(4)

6.5 Average Value of a Function

398

(3)

Review

401

(2)

Problems Plus

403

(3)

7 Inverse Functions: Exponential, Logarithmic, and Inverse Trigonometric Functions

406

(96)

7.1 Inverse Functions

407

(9)

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

7.2 Exponential Functions and Their Derivatives

416

(12)

7.3 Logarithmic Functions

428

(76)

7.4 Derivatives of Logarithmic Functions

435

(10)

7.2(*) The Natural Logarithmic Function

445

(8)

7.3(*) The Natural Exponential Function

453

(7)

7.4(*) General Logarithmic and Exponential Functions

460

(9)

7.5 Inverse Trigonometric Functions

469

(9)

Applied Project Where To Sit at the Movies

478

(1)

7.6 Hyperbolic Functions

478

(7)

7.7 Indeterminate Forms and L'Hospital's Rule

485

(11)

Writing Project The Origins of L'Hospital's Rule

496

(1)

Review

496

(4)

Problems Plus

500

(2)

8 Techniques of Integration

502

(72)

8.1 Integration by Parts

503

(7)

8.2 Trigonometric Integrals

510

(7)

8.3 Trigonometric Substitution

517

(7)

8.4 Integration of Rational Functions by Partial Fractions

524

(9)

8.5 Strategy for Integration

533

(6)

8.6 Integration Using Tables and Computer Algebra Systems

539

(7)

Discovery Project Patterns in Integrals

545

(1)

8.7 Approximate Integration

546

(11)

8.8 Improper Integrals

557

(11)

Review

568

(2)

Problems Plus

571

(3)

9 Further Applications of Integration

574

(40)

9.1 Arc Length

575

(7)

9.2 Area of a Surface of Revolution

582

(7)

Discovery Project Rotating on a Slant

588

(1)

9.3 Applications to Physics and Engineering

589

(9)

9.4 Applications to Economics and Biology

598

(5)

9.5 Probability

603

(7)

Review

610

(2)

Problems Plus

612

(2)

10 Differential Equations

614

(60)

10.1 Modeling with Differential Equations

615

(5)

10.2 Direction Fields and Euler's Method

620

(9)

10.3 Separable Equations

629

(8)

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

636

(1)

10.4 Exponential Growth and Decay

637

(10)

Applied Project Calculus and Baseball

646

(1)

10.5 The Logistic Equation

647

(9)

10.6 Linear Equations

656

(6)

10.7 Predator-Prey Systems

662

(6)

Review

668

(4)

Problems Plus

672

(2)

11 Parametric Equations and Polar Coordinates

674

(52)

11.1 Curves Defined by Parametric Equations

675

(7)

Laboratory Project Families of Hypocycloids

682

(1)

11.2 Tangents and Areas

682

(7)

Laboratory Project Bezier Curves

689

(1)

11.3 Arc Length and Surface Area

689

(5)

11.4 Polar Coordinates

694

(10)

11.5 Areas and Lengths in Polar Coordinates

704

(5)

11.6 Conic Sections

709

(7)

11.7 Conic Sections in Polar Coordinates

716

(6)

Review

722

(2)

Problems Plus

724

(2)

12 Infinite Sequences and Series

726

12.1 Sequences

727

(11)

Laboratory Project Logistic Sequences

738

(1)

12.2 Series

738

(10)

12.3 The Integral Test and Estimates of Sums

748

(7)

12.4 The Comparison Tests

755

(5)

12.5 Alternating Series

760

(5)

12.6 Absolute Convergence and the Ratio and Root Tests

765

(7)

12.7 Strategy for Testing Series

772

(2)

12.8 Power Series

774

(5)

12.9 Representations of Functions as Power Series

779

(6)

12.10 Taylor and Maclaurin Series

785

(11)

12.11 The Binomial Series

796

(4)

Writing Project How Newton Discovered the Binomial Series

799

(1)

12.12 Applications of Taylor Polynomials

800

(10)

Applied Project Radiation from the Stars

808

(2)

Review

810

(2)

Problems Plus

812

Appendixes

(104)

A Intervals, Inequalities, and Absolute Values

(8)

B Coordinate Geometry and Lines

A10

(6)

C Graphs of Second-Degree Equations

A16

(8)

D Trigonometry

A24

(10)

E Sigma Notation

A34

(5)

F Proofs of Theorems

A39

(7)

G Complex Numbers

A46

(8)

H Answers to Odd-Numbered Exercises

A54

(51)

Index

A105


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