Calculus, Early Transcendentals

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  • Edition: 7th
  • Format: Hardcover
  • Copyright: 2/27/2007
  • Publisher: Pearson

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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
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
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
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
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