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Calculus of a Single Variable

by: Larson, Ron; Hostetler, Robert P.; Edwards, Bruce H.

Calculus of a Single Variable

by: Larson, Ron; Hostetler, Robert P.; Edwards, Bruce H.

ISBN 13:
9780395885789
ISBN 10:
0395885787
Edition: 6th
Format: Paperback
Copyright: 11/06/1997
Publisher: Brooks Cole
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Summary

This text combines the theoretical instruction of calculus with current best-practise strategies.

A Word from the Authors (Preface)

Index of Applications

xxxi

Preparation for Calculus

(38)

Graphs and Models

(8)

Linear Models and Rates of Change

(9)

Functions and Their Graphs

(11)

Fitting Models to Data

(8)

Review Exercises

(2)

Limits and Their Properties

(50)

A Preview of Calculus

(6)

Finding Limits Graphically and Numerically

(9)

Evaluating Limits Analytically

(11)

Continuity and One-Sided Limits

(12)

Infinite Limits

(10)

Review Exercises

(2)

Differentiation

(64)

The Derivative and the Tangent Line Problem

(11)

Basic Differentiation Rules and Rates of Change

102

(12)

The Product and Quotient Rules and Higher-Order Derivatives

114

(10)

The Chain Rule

124

(10)

Implicit Differentiation

134

(7)

Related Rates

141

(12)

Review Exercises

150

(3)

Applications of Differentiation

153

(86)

Extrema on an Interval

155

(8)

Rolle's Theorem and the Mean Value Theorem

163

(6)

Increasing and Decreasing Functions and the First Derivative Test

169

(10)

Concavity and the Second Derivative Test

179

(8)

Limits at Infinity

187

(9)

A Summary of Curve Sketching

196

(9)

Optimization Problems

205

(10)

Newton's Method

215

(6)

Differentials

221

(7)

Business and Economics Applications

228

(11)

Review Exercises

235

(4)

Integration

239

(70)

Antiderivatives and Indefinite Integration

241

(11)

Area

252

(12)

Riemann Sums and Definite Integrals

264

(10)

The Fundamental Theorem of Calculus

274

(13)

Integration by Substitution

287

(12)

Numerical Integration

299

(10)

Review Exercises

306

(3)

Logarithmic, Exponential, and Other Transcendental Functions

309

(96)

The Natural Logarithmic Function and Differentiation

311

(10)

The Natural Logarithmic Function and Integration

321

(8)

Inverse Functions

329

(9)

Exponential Functions: Differentiation and Integration

338

(10)

Bases Other than e and Applications

348

(10)

Differential Equations: Growth and Decay

358

(8)

Differential Equations: Separation of Variables

366

(11)

Inverse Trigonometric Functions and Differentiation

377

(8)

Inverse Trigonometric Functions and Integration

385

(7)

Hyperbolic Functions

392

(13)

Review Exercises

402

(3)

Applications of Integration

405

(68)

Area of a Region Between Two Curves

407

(9)

Volume: The Disc Method

416

(11)

Volume: The Shell Method

427

(8)

Arc Length and Surfaces of Revolution

435

(10)

Work

445

(9)

Moments, Centers of Mass, and Centroids

454

(11)

Fluid Pressure and Fluid Force

465

(8)

Review Exercises

471

(2)

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

473

(72)

Basic Integration Rules

475

(6)

Integration by Parts

481

(9)

Trigonometric Integrals

490

(9)

Trigonometric Substitution

499

(9)

Partial Fractions

508

(9)

Integration by Tables and Other Integration Techniques

517

(6)

Indeterminate Forms and L'Hopital's Rule

523

(10)

Improper Integrals

533

(12)

Review Exercises

542

(3)

Infinite Series

545

(90)

Sequences

547

(11)

Series and Convergence

558

(10)

The Integral Test and P-Series

568

(6)

Comparisons of Series

574

(7)

Alternating Series

581

(7)

The Ratio and Root Tests

588

(8)

Taylor Polynomials and Approximations

596

(10)

Power Series

606

(9)

Representation of Functions by Power Series

615

(7)

Taylor and Maclaurin Series

622

(13)

Review Exercises

632

(3)

Conics, Parametric Equations, and Polar Coordinates

635

(2)

Conics and Calculus

637

(15)

Plane Curves and Parametric Equations

652

(10)

Parametric Equations and Calculus

662

(9)

Polar Coordinates and Polar Graphs

671

(10)

Area and Arc Length in Polar Coordinates

681

(8)

Polar Equations of Conics and Kepler's Laws

689

(7)

Review Exercises

696

Appendix A Precalculus Review

A.1 Real Numbers and the Real Line

A.2 The Cartesian Plane

A10

A.3 Review of Trigonometric Functions

A17

Appendix B Proofs of Selected Theorems

A28

Appendix C Basic Differentiation Rules for Elementary Functions

A44

Appendix D Integration Tables

A45

Appendix E Rotation and the General Second-Degree Equation

A51

Appendix F Complex Numbers

A57

Answers to Odd-Numbered Exercises

A69

Index

A159

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Calculus of a Single Variable

Calculus of a Single Variable

9780395885789

0395885787

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

9780395885789

0395885787

Summary

Table of Contents

Supplemental Materials

Write a Review

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