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Calculus Concepts and Contexts

by: Stewart, James

Calculus Concepts and Contexts

by: Stewart, James

ISBN 13:
9780534410032
ISBN 10:
0534410030
Edition: 3rd
Format: Hardcover
Copyright: 11/04/2004
Publisher: Brooks Cole
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A Preview of Calculus

(8)

Functions and Models

(82)

Four Ways to Represent a Function

(14)

Mathematical Models: A Catalog of Essential Functions

(13)

New Functions from Old Functions

(11)

Graphing Calculators and Computers

(6)

Exponential Functions

(8)

Inverse Functions and Logarithms

(11)

Parametric Curves

(18)

Laboratory Project: Running Circles around Circles

(1)

Review

(3)

Principles of Problem Solving

(6)

Limits and Derivatives

(90)

The Tangent and Velocity Problems

(5)

The Limit of a Function

(10)

Calculating Limits Using the Limit Laws

108

(9)

Continuity

117

(11)

Limits Involving Infinity

128

(11)

Tangents, Velocities, and Other Rates of Change

139

(9)

Derivatives

148

(7)

Writing Project: Early Methods for Finding Tangents

155

(1)

The Derivative as a Function

155

(13)

What Does f' Say about f?

168

(14)

Review

175

(4)

Focus on Problem Solving

179

(3)

Differentiation Rules

182

(80)

Derivatives of Polynomials and Exponential Functions

183

(10)

Applied Project: Building a Better Roller Coaster

192

(1)

The Product and Quotient Rules

193

(7)

Rates of Change in the Natural and Social Sciences

200

(13)

Derivatives of Trigonometric Functions

213

(7)

The Chain Rule

220

(12)

Laboratory Project: Bezier Curves

231

(1)

Applied Project: Where Should a Pilot Start Descent?

232

(1)

Implicit Differentiation

232

(8)

Derivatives of Logarithmic Functions

240

(7)

Discovery Project: Hyperbolic Functions

246

(1)

Linear Approximations and Differentials

247

(15)

Laboratory Project: Taylor Polynomials

254

(1)

Review

255

(3)

Focus on Problem Solving

258

(4)

Applications of Differentiation

262

(80)

Related Rates

263

(6)

Maximum and Minimum Values

269

(9)

Applied Project: The Calculus of Rainbows

277

(1)

Derivatives and the Shapes of Curves

278

(11)

Graphing with Calculus and Calculators

289

(8)

Indeterminate Forms and I'Hospital's Rule

297

(9)

Writing Project: The Origins of I'Hospital's Rule

305

(1)

Optimization Problems

306

(11)

Applied Project: The Shape of a Can

316

(1)

Applications to Business and Economics

317

(5)

Newton's Method

322

(5)

Antiderivatives

327

(15)

Review

335

(4)

Focus on Problem Solving

339

(3)

Integrals

342

(98)

Areas and Distances

343

(11)

The Definite Integral

354

(12)

Evaluating Definite Integrals

366

(11)

Discovery Project: Area Functions

376

(1)

The Fundamental Theorem of Calculus

377

(9)

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

385

(1)

The Substitution Rule

386

(7)

Integration by Parts

393

(7)

Additional Techniques of Integration

400

(5)

Integration Using Tables and Computer Algebra Systems

405

(7)

Discovery Project: Patterns in Integrals

411

(1)

Approximate Integration

412

(11)

Improper Integrals

423

(17)

Review

433

(4)

Focus on Problem Solving

437

(3)

Applications of Integration

440

(58)

More about Areas

441

(6)

Volumes

447

(14)

Discovery Project: Rotating on a Slant

460

(1)

Arc Length

461

(6)

Discovery Project: Arc Length Contest

466

(1)

Average Value of a Function

467

(4)

Applied Project: Where to Sit at the Movies

470

(1)

Applications to Physics and Engineering

471

(11)

Applications to Economics and Biology

482

(4)

Probability

486

(12)

Review

493

(3)

Focus on Problem Solving

496

(2)

Differential Equations

498

(58)

Modeling with Differential Equations

499

(5)

Direction Fields and Euler's Method

504

(9)

Separable Equations

513

(11)

Applied Project: How Fast Does a Tank Drain?

521

(2)

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

523

(1)

Exponential Growth and Decay

524

(11)

Applied Project: Calculus and Baseball

534

(1)

The Logistic Equation

535

(9)

Predator-Prey Systems

544

(12)

Review

551

(3)

Focus on Problem Solving

554

(2)

Infinite Sequences and Series

556

(80)

Sequences

557

(10)

Laboratory Project: Logistic Sequences

567

(1)

Series

567

(10)

The Integral and Comparison Tests; Estimating Sums

577

(9)

Other Convergence Tests

586

(8)

Power Series

594

(5)

Representations of Functions as Power Series

599

(6)

Taylor and Maclaurin Series

605

(12)

Laboratory Project: An Elusive Limit

617

(1)

The Binomial Series

617

(4)

Writing Project: How Newton Discovered the Binomial Series

621

(1)

Applications of Taylor Polynomials

621

(15)

Applied Project: Radiation from the Stars

630

(1)

Review

631

(3)

Focus on Problem Solving

634

(2)

Vectors and the Geometry of Space

636

(58)

Three-Dimensional Coordinate Systems

637

(5)

Vectors

642

(9)

The Dot Product

651

(6)

The Cross Product

657

(9)

Discovery Project: The Geometry of a Tetrahedron

665

(1)

Equations of Lines and Planes

666

(10)

Laboratory Project: Putting 3D in Perspective

675

(1)

Functions and Surfaces

676

(9)

Cylindrical and Spherical Coordinates

685

(9)

Laboratory Project: Families of Surfaces

690

(1)

Review

690

(3)

Focus on Problem Solving

693

(1)

Vector Functions

694

(44)

Vector Functions and Space Curves

695

(7)

Derivatives and Integrals of Vector Functions

702

(6)

Are Length and Curvature

708

(8)

Motion in Space: Velocity and Acceleration

716

(12)

Applied Project: Kepler's Laws

727

(1)

Parametric Surfaces

728

(10)

Review

734

(2)

Focus on Problem Solving

736

(2)

Partial Derivatives

738

(90)

Functions of Several Variables

739

(11)

Limits and Continuity

750

(6)

Partial Derivatives

756

(13)

Tangent Planes and Linear Approximations

769

(11)

The Chain Rule

780

(8)

Directional Derivatives and the Gradient Vector

788

(13)

Maximum and Minimum Values

801

(12)

Applied Project: Designing a Dumpster

811

(1)

Discovery Project: Quadratic Approximations and Critical Points

812

(1)

Lagrange Multipliers

813

(15)

Applied Project: Rocket Science

820

(1)

Applied Project: Hydro-Turbine Optimization

821

(1)

Review

822

(4)

Focus on Problem Solving

826

(2)

Multiple Integrals

828

(76)

Double Integrals over Rectangles

829

(8)

Iterated Integrals

837

(6)

Double Integrals over General Regions

843

(8)

Double Integrals in Polar Coordinates

851

(6)

Applications of Double Integrals

857

(10)

Surface Area

867

(5)

Triple Integrals

872

(10)

Discovery Project: Volumes of Hyperspheres

881

(1)

Triple Integrals in Cylindrical and Spherical Coordinates

882

(7)

Applied Project: Roller Derby

888

(1)

Discovery Project: The Intersection of Three Cylinders

889

(1)

Change of Variables in Multiple Integrals

889

(15)

Review

898

(4)

Focus on Problem Solving

902

(2)

Vector Calculus

904

Vector Fields

905

(7)

Line Integrals

912

(12)

The Fundamental Theorem for Line Integrals

924

(9)

Green's Theorem

933

(7)

Curl and Divergence

940

(8)

Surface Integrals

948

(11)

Stokes' Theorem

959

(7)

Writing Project: Three Men and Two Theorems

965

(1)

The Divergence Theorem

966

(7)

Summary

973

Review

974

(3)

Focus on Problem Solving

977

Appendixes

(134)

A Intervals, Inequalities, and Absolute Values

(5)

B Coordinate Geometry

(11)

C Trigonometry

(11)

D Precise Definitions of Limits

(10)

E A Few Proofs

(5)

F Sigma Notation

(6)

G Integration of Rational Functions by Partial Fractions

(8)

H Polar Coordinates

(16)

I Complex Numbers

(9)

J Answers to Odd-Numbered Exercises

(52)

Index

135

Amazon no longer offers textbook rentals. We do!

Calculus Concepts and Contexts

Calculus Concepts and Contexts

9780534410032

0534410030

Table of Contents

Supplemental Materials

Write a Review

Amazon no longer offers textbook rentals. We do!

Calculus Concepts and Contexts

Calculus Concepts and Contexts

9780534410032

0534410030

Table of Contents

Supplemental Materials

Write a Review

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