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Calculus of a Single Variable

by: Larson, Ron

Calculus of a Single Variable

by: Larson, Ron

ISBN 13:
9780618149162
ISBN 10:
0618149163
Edition: 7th
Format: Hardcover
Copyright: 07/13/2001
Publisher: CENGAGE Learning
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Summary

Ideal for the single-variable, one-, or two-semester calculus course, "Calculus of a Single Variable, 7/e, contains the first 9 chapers of "Calculus with Analytic Geometry, 7/e. For a description, see Larson et al., "Calculus with Analytic Geometry, 7/e.

A Word from the Authors (Preface)

Features

Preparation for Calculus

(39)

Eruptions of Old Faithful

(1)

Graphs and Models

(8)

Linear Models and Rates of Change

(9)

Functions and Their Graphs

(11)

Fitting Models to Data

(10)

Review Exercises

(2)

Problem Solving

(2)

Limits and Their Properties

(52)

Swimming Speed: Taking It to the Limit

(2)

A Preview of Calculus

(6)

Finding Limits Graphically and Numerically

(9)

Evaluating Limits Analytically

(11)

Continuity and One-Sided Limits

(12)

Infinite Limits

(12)

Section Project: Graphs and Limits of Trigonometric Functions

(1)

Review Exercises

(2)

Problem Solving

(2)

Differentiation

(66)

Gravity: Finding It Experimentally

(2)

The Derivative and the Tangent Line Problem

(11)

Basic Differentiation Rules and Rates of Change

105

(12)

The Product and Quotient Rules and Higher-Order Derivatives

117

(10)

The Chain Rule

127

(10)

Implicit Differentiation

137

(7)

Section Project: Optical Illusions

143

(1)

Related Rates

144

(14)

Review Exercises

153

(3)

Problem Solving

156

(2)

Applications of Differentiation

158

(82)

Packaging: The Optimal Form

158

(2)

Extrema on an Interval

160

(8)

Rolle's Theorem and the Mean Value Theorem

168

(6)

Increasing and Decreasing Functions and the First Derivative Test

174

(10)

Section Project: Rainbows

183

(1)

Concavity and the Second Derivative Test

184

(8)

Limits at Infinity

192

(10)

A Summary of Curve Sketching

202

(9)

Optimization Problems

211

(11)

Section Project: Connecticut River

211

(11)

Newton's Method

222

(6)

Differentials

228

(12)

Review Exercises

235

(3)

Problem Solving

238

(2)

Integration

240

(72)

The Wankel Rotary Engine and Area

240

(2)

Antiderivatives and Indefinite Integration

242

(11)

Area

253

(12)

Reimann Sums and Definite Integrals

265

(10)

The Fundamental Theorem of Calculus

275

(13)

Section Project: Demonstrating the Fundamental Theorem

287

(1)

Integration by Substitution

288

(12)

Numerical Integration

300

(12)

Review Exercises

307

(3)

Problem Solving

310

(2)

Logarithmic, Exponential, and Other Transcendental Functions

312

(98)

Plastics and Cooling

312

(2)

The Natural Logarithmic Function: Differentiation

314

(10)

The Natural Logarithmic Function: Integration

324

(8)

Inverse Functions

332

(9)

Exponential Functions: Differentiation and Integration

341

(10)

Bases Other Than e and Applications

351

(10)

Section Project: Using Graphing Utilities to Estimate Slope

360

(1)

Differential Equations: Growth and Decay

361

(8)

Differential Equations: Separation of Variables

369

(11)

Inverse Trigonometric Functions: Differentiation

380

(8)

Inverse Trigonometric Functions: Integration

388

(7)

Hyperbolic Functions

395

(15)

Section Project: St. Louis Arch

405

(1)

Review Exercises

405

(3)

Problem Solving

408

(2)

Applications of Integration

410

(70)

Constructing an Arch Dam

410

(2)

Area of a Region Between Two Curves

412

(9)

Volume: The Disk Method

421

(11)

Volume: The Shell Method

432

(8)

Section Project: Saturn

439

(1)

Arc Length and Surfaces of Revolution

440

(10)

Work

450

(9)

Section Project: Tidal Energy

458

(1)

Moments, Centers of Mass, and Centroids

459

(11)

Fluid Pressure and Fluid Force

470

(10)

Review Exercises

476

(2)

Problem Solving

478

(2)

Integration Techniques, L'Hopital's Rule, and Improper Integrals

480

(74)

Making a Mercator Map

480

(2)

Basic Integration Rules

482

(6)

Integration by Parts

488

(9)

Trigonometric Integrals

497

(9)

Section Project: Power Lines

505

(1)

Trigonometric Substitution

506

(9)

Partial Fractions

515

(9)

Integration by Tables and Other Integration Techniques

524

(6)

Indeterminate Forms and L'Hopital's Rule

530

(10)

Improper Integrals

540

(14)

Review Exercises

550

(2)

Problem Solving

552

(2)

Infinite Series

554

(94)

The Koch Snowflake: Infinite Perimeter?

554

(2)

Sequences

556

(11)

Series and Convergence

567

(10)

Section Project: Cantor's Disappearing Table

576

(1)

The Integral Test and p-Series

577

(6)

Section Project: The Harmonic Series

582

(1)

Comparisons of Series

583

(7)

Section Project: Solera Method

589

(1)

Alternating Series

590

(7)

The Ratio and Root Tests

597

(8)

Taylor Polynomials and Approximations

605

(11)

Power Series

616

(9)

Representation of Functions by Power Series

625

(7)

Taylor and Maclaurin Series

632

(16)

Review Exercises

643

(3)

Problem Solving

646

(2)

Conics, Parametric Equations, and Polar Coordinates

648

(1)

Exploring New Planets

648

(2)

Conics and Calculus

650

(15)

Plane Curves and Parametric Equations

665

(9)

Section Project: Cycloids

674

(1)

Parametric Equations and Calculus

675

(9)

Polar Coordinates and Polar Graphs

684

(9)

Section Project: Anamorphic Art

693

(1)

Area and Arc Length in Polar Coordinates

694

(8)

Polar Equations of Conics and Kepler's Laws

702

(7)

Review Exercises

709

(3)

Problem Solving

712

Appendices

(1)

Appendix A Additional Topics in Differential Equations

(7)

Appendix B Proofs of Selected Theorems

(18)

Appendix C Integration Tables

(6)

Appendix D Precalculus Review

Appendix E Rotation and the General Second-Degree Equation

Appendix F Complex Numbers

Appendix G Business and Economic Applications

Answers to Odd-Numbered Exercises

(96)

Index of Applications

129

(4)

Index

133

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Calculus of a Single Variable

Calculus of a Single Variable

9780618149162

0618149163

Summary

Table of Contents

Supplemental Materials

Write a Review

Amazon no longer offers textbook rentals. We do!

Calculus of a Single Variable

Calculus of a Single Variable

9780618149162

0618149163

Summary

Table of Contents

Supplemental Materials

Write a Review

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