Calculus Early Transcendentals

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

• ISBN13: 9780131569898
• ISBN10: 0131569899
• Edition: 7th
• Format: Hardcover
• Copyright: 2007-02-27
• Publisher: Pearson

Summary

The Seventh Edition of this highly dependable book retains its best featuresit keeps the accuracy, mathematical precision, and rigor appropriate that it is known for.This book contains an entire six chapters on early transcendental calculus and a chapter on differential equations and their applications.For professionals who want to brush up on their calculus skills.

Author Biography

C. Henry Edwards is emeritus professor of mathematics at the University of Georgia.  He earned his Ph.D. at the University of Tennessee in 1960, and recently retired after 40 years of classroom teaching (including calculus or differential equations almost every term) at the universities of Tennessee, Wisconsin, and Georgia, with a brief interlude at the Institute for Advanced Study (Princeton) as an Alfred P. Sloan Research Fellow.  He has received numerous teaching awards, including the University of Georgia’s honoratus medal in 1983 (for sustained excellence in honors teaching), its Josiah Meigs award in 1991 (the institution’s highest award for teaching), and the 1997 statewide Georgia Regents award for research university faculty teaching excellence.  His scholarly career has ranged from research and dissertation direction in topology to the history of mathematics to computing and technology in the teaching and applications of mathematics.  In addition to being author or co-author of calculus, advanced calculus, linear algebra, and differential equations textbooks, he is well-known to calculus instructors as author of The Historical Development of the Calculus (Springer-Verlag, 1979).  During the 1990s, he served as a principal investigator on three NSF-supported projects: (1) A school mathematics project including Maple for beginning algebra students, (2) A Calculus-with-Mathematica program, and (3) A MATLAB-based computer lab project for numerical analysis and differential equations students.

 

David E. Penney, University of Georgia, completed his Ph.D. at Tulane University in 1965 (under the direction of Prof. L. Bruce Treybig) while teaching at the University of New Orleans.  Earlier he had worked in experimental biophysics at Tulane University and the Veteran’s Administration Hospital in New Orleans under the direction of Robert Dixon McAfee, where Dr. McAfee’s research team’s primary focus was on the active transport of sodium ions by biological membranes.  Penney’s primary contribution here was the development of a mathematical model (using simultaneous ordinary differential equations) for the metabolic phenomena regulating such transport, with potential future applications in kidney physiology, management of hypertension, and treatment of congestive heart failure.  He also designed and constructed servomechanisms for the accurate monitoring of ion transport, a phenomenon involving the measurement of potentials in microvolts at impedances of millions of megohms.  Penney began teaching calculus at Tulane in 1957 and taught that course almost every term with enthusiasm and distinction until his retirement at the end of the last millennium.  During his tenure at the University of Georgia, he received numerous University-wide teaching awards as well as directing several doctoral dissertations and seven undergraduate research projects.  He is the author or co-author of textbooks on calculus, computer programming, differential equations, linear algebra, and liberal arts mathematics.

Table of Contents

About the Authors

Preface

Functions, Graphs, and Models

Functions and Mathematical ModelingInvestigation: Designing a Wading Pool

Graphs of Equations and Functions

Polynomials and Algebraic Functions

Transcendental Functions

Preview: What Is Calculus?

Review - Understanding: Concepts and Definitions

Objectives: Methods and Techniques

Prelude to Calculus

Tangent Lines and Slope Predictors

Investigation: Numerical Slope Investigations

The Limit ConceptInvestigation: Limits, Slopes, and Logarithms

More About LimitsInvestigation: Numerical Epsilon-Delta Limits

The Concept of Continuity

Review - Understanding: Concepts and Definitions

Objectives: Methods and Techniques

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

Investigation: When Is Your Coffee Cup Stablest?

Applied Optimization Problems

Derivatives of Trigonometric Functions

Exponential and Logarithmic Functions

Investigation: Discovering the Number e for Yourself

Implicit Differentiation and Related Rates

Investigation: Constructing the Folium of Descartes

Successive Approximations and Newton's Method

Investigation: How Deep Does a Floating Ball Sink?

Review - Understanding: Concepts, Definitions, and Formulas

Objectives: Methods and Techniques

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

Investigation: Constructing a Candy Box With Lid

Simple Curve Sketching

Higher Derivatives and Concavity

Curve Sketching and Asymptotes

Investigation: Locating Special Points on Exotic Graphs

Indeterminate Forms and L'Hapital's Rule

More Indeterminate Forms

Review - Understanding: Concepts, Definitions, and Results

Objectives: Methods and Techniques

The Integral

Introduction

Antiderivatives and Initial Value Problems

Elementary Area Computations

Riemann Sums and the Integral

Investigation: Calculator/Computer Riemann Sums

Evaluation of Integrals

The Fundamental Theorem of Calculus

Integration by Substitution

Areas of Plane Regions

Numerical IntegrationInvestigation: Trapezoidal and Simpson Approximations

Review - Understanding: Concepts, Definitions, and Results

Objectives: Methods and Techniques

Applications of the Integral

Riemann Sum Approximations

Volumes by the Method of Cross Sections

Volumes by the Method of Cylindrical Shells

Investigation: Design Your Own Ring!

Arc Length and Surface Area of Revolution

Force and Work

Centroids of Plane Regions and Curves

The Natural Logarithm as an Integral

Investigation: Natural Functional Equations

Inverse Trigonometric Functions

Hyperbolic Functions

Review - Understanding: Concepts, Definitions, and Formulas

Objectives: Methods and Techniques

Techniques of Integration

Introduction<

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