Single Variable Calculus Early Transcendentals Version

by Edwards, C. Henry; Penney, David E.

• ISBN13: 9780130414076
• ISBN10: 0130414077
• Edition: 6th
• Format: Paperback
• Copyright: 2002-01-01
• Publisher: Pearson College Div

Summary

A mainstream calculus book with the most flexible and open approach to new ideas and calculator/computer technology. Solid coverage of the calculus of early transcendental functions is now fully integrated in Chapters 1 through 6. A new Chapter 8 on differential equations appears immediately after the chapter on techniques of integration. It includes both direction fields and Euler's method, together with the more symbolic elementary methods and applications for both first- and second-order equations. The CD-ROM accompanying the book contains a functional array of fully integrated learning resources linked to individual sections of the book. The user can view any desired book section in PDF format.

Table of Contents

Functions, Graphs, and Models

Functions and Mathematical Modeling

Graphs of Equations and Functions

Polynomials and Algebraic Functions

Transcendental Functions

Preview: What Is Calculus?

Prelude to Calculus

Tangent Lines and Slope Predictors

The Limit Concept

More About Limits

The Concept of Continuity

The Derivative

The Derivative and Rates of Change

Basic Differentiation Rules

The Chain Rule

Derivatives of Algebraic Functions

Maxima and Minima of Functions on Closed Intervals

Applied Optimization Problems

Derivatives of Trigonometric Functions

Exponential and Logarithmic Functions

Implicit Differentiation and Related Rates

Successive Approximations and Newton's Method

Additional Applications of the Derivative

Introduction

Increments, Differentials, and Linear Approximation

Increasing and Decreasing Functions and the Mean Value Theorem

The First Derivative Test and Applications

Simple Curve Sketching

Higher Derivatives and Concavity

Curve Sketching and Asymptotes

Indeterminate Forms and L'Hopitals' Rule

More Indeterminate Forms

The Integral

Introduction

Antiderivatives and Initial Value Problems

Elementary Area Computations

Riemann Sums and the Integral

Evaluation of Integrals

The Fundamental Theorem of Calculus

Integration by Substitution

Areas of Plane Regions

Numerical Integration

Applications of the Integral

Riemann Sum Approximations

Volumes by the Method of Cross Sections

Volumes by the Method of Cylindrical Shells

Arc Length and Surface Area of Revolution

Force and Work

Centroids of Plane Regions and Curves

The Natural Logarithm as an Integral

Inverse Trigonometric Functions

Hyperbolic Functions

Techniques of Integration

Introduction

Integral Tables and Simple Substitutions

Integration by Parts

Trigonometric Integrals

Rational Functions and Partial Fractions

Trigonometric Substitutions

Integrals Involving Quadratic Polynomials

Improper Integrals

Differential Equations

Simple Equations and Models

Slope Fields and Euler's Method

Separable Equations and Applications

Linear Equations and Applications

Population Models

Linear Second-Order Equations

Mechanical Vibrations

Polar Coordinates and Parametric Curves

Analytic Geometry and the Conic Sections

Polar Coordinates

Area Computations in Polar Coordinates

Parametric Curves

Integral Computations with Parametric Curves

Conic Sections and Applications

Infinite Series

Introduction

Infinite Sequences

Infinite Series and Convergence

Taylor Series and Taylor Polynomials

The Integral Test

Comparison Tests for Positive-Term Series

Alternating Series and Absolute Convergence

Power Series

Power Series Computations

Series Solutions of Differential Equations

Appendices

Real Numbers and Inequalities

The Coordinate Plane and Straight Lines

Review of Trigonometry

Proofs of the Limit Laws

The Completeness of the Real Number System

Existence of the Integral

Approximations and Riemann Sums

L'Hopital's Rule and Cauchy's Mean Value Theorem

Proof of Taylor's Formula

Conic Sections as Sections of a Cone

Proof of the Linear Approximation Theorem

Units of Measurement and Conversion Factors

Formulas from Algebra, Geometry, and Trigonometry

The Greek Alphabet

Answers to Odd-Numbered Problems

References for Further Study

Index

Table of Integrals

Table of Contents provided by Publisher. All Rights Reserved.

Excerpts

Contemporary calculus instructors and students face traditional challenges as well as new ones that result from changes in the role and practice of mathematics by scientists and engineers in the world at large. As a consequence, this sixth edition of our calculus textbook is its most extensive revision since the first edition appeared in 1982. Two entire chapters of the fifth edition have been replaced in the table of contents by two new ones; most of the remaining chapters have been extensively rewritten. Nearly 160 of the book's over 800 worked examples are new for this edition and the 1850 figures in the text include 250 new computer-generated graphics. Almost 800 of its 7250 problems are new, and these are augmented by over 330 new conceptual discussion questions that now precede the problem sets. Moreover, almost 1100 new true/false questions are included in the Study Guides on the new CD-ROM that accompanies this edition. In summary, almost 2200 of these 8650-plus problems and questions are new, and the text discussion and explanations have undergone corresponding alteration and improvement. PRINCIPAL NEW FEATURES The current revision of the text features Early transcendentalsfully integrated in Semester I. Differential equationsand applications in Semester II. Linear systems and matricesin Semester III. Complete coverage of the calculus of transcendental functions is now fully integrated in Chapters 1 through 6--with the result that the Chapter 7 and 8 titles in the 5th edition table of contents do not appear in this 6th edition. A new chapter on differential equations (Chapter 8) now appears immediately after Chapter 7 on techniques of integration. It includes both direction fields and Eider's method together with the more elementary symbolic methods (which exploit techniques from Chapter 7) and interesting applications of both first- and second-order equations. Chapter 10 (Infinite Series) now ends with a new section on power series solutions of differential equations, thus bringing full circle a unifying focus of second-semester calculus on elementary differential equations. Linear systems and matrices, ending with an elementary treatment of eigenvalues and eigenvectors, are now introduced in Chapter 11. The subsequent coverage of multivariable calculus now integrates matrix methods and terminology with the traditional notation and approach--including (for instance) introduction and extensive application of the chain rule in matrix-product form. NEW LEARNING RESOURCES CONCEPTUAL DISCUSSION QUESTIONS.The set of problems that concludes each section is now preceded by a briefConcepts: Questions and Discussionset consisting of several open-ended conceptual questions that can be used for either individual study or classroom discussion. THE TEXT CD-ROM.The content of the new CD-ROM that accompanies this text is fully integrated with the textbook material, and is designed specifically for use hand-in-hand with study of the book itself. This CD-ROM features the following resources to support learning and teaching: Interactive True/False Study Guidesthat reinforce and encourage student reading of the text. Ten author-written questions for each section carefully guide students through the section, and students can request individual hints suggesting where in the section to look for needed information. Live Examplesfeature dynamic multimedia and computer algebra presentations-many accompanied by audio explanations-which enhance student intuition and understanding. These interactive examples expand upon many of the textbook's principal examples; students can change input data and conditions and then observe the resulting changes in step-by-step solutions and accompanying graphs and figures.Walkthrough videosdemonstrate how students can inte