Calculus: Single Variable / Edition 6

by Deborah Hughes-Hallett, Andrew M. Gleason, William G. McCallum, Daniel E. Flath, Patti Frazer Lock

Overview

An innovative text that emphasizes the graphical, numerical and analytical aspects of calculus throughout and often asks students to explain ideas using words. This problem driven text introduces topics with a real-world problem and derives the general results from it. It can be used with any technology that can graph and find definite integrals numerically. The derivative, the integral, differentiation, and differential equations are among the topics covered.

Product Details

ISBN-13:	9780470888643
Publisher:	Wiley
Publication date:	11/06/2012
Edition description:	Older Edition
Pages:	768
Product dimensions:	8.50(w) x 10.40(h) x 1.00(d)

About the Author

Deborah Hughes-Hallett is Adjunct Professor of Public Policy and Professor of Mathematics at the University of Arizona. She graduated from Cambridge University in England and has taught at Middle East Technical University in Ankara, Turkey. Her work is on strategies to improve the teaching of mathematics, and she is interested in promoting international cooperation between mathematicians. She has served on committees for the National Academy of Sciences and organized three international conferences on the teaching of mathematics. She is a fellow of the American Advancement of Science and the author or coauthor of seven books, which have been translated into several languages. Her work has been recognized by prizes from Harvard, Arizona, the Association for Women in Mathematics, and the Mathematical Association of America.

Table of Contents

1 A LIBRARY OF FUNCTIONS

1.1 FUNCTIONS AND CHANGE

1.2 EXPONENTIAL FUNCTIONS

1.3 NEW FUNCTIONS FROM OLD

1.4 LOGARITHMIC FUNCTIONS

1.5 TRIGONOMETRIC FUNCTIONS

1.6 POWERS, POLYNOMIALS, AND RATIONAL FUNCTIONS

1.7 INTRODUCTION TO CONTINUITY

1.8 LIMITS

REVIEW PROBLEMS

PROJECTS

2 KEY CONCEPT: THE DERIVATIVE

2.1 HOW DO WE MEASURE SPEED?

2.2 THE DERIVATIVE AT A POINT

2.3 THE DERIVATIVE FUNCTION

2.4 INTERPRETATIONS OF THE DERIVATIVE

2.5 THE SECOND DERIVATIVE

2.6 DIFFERENTIABILITY

REVIEW PROBLEMS

PROJECTS

3 SHORT-CUTS TO DIFFERENTIATION

3.1 POWERS AND POLYNOMIALS

3.2 THE EXPONENTIAL FUNCTION

3.3 THE PRODUCT AND QUOTIENT RULES

3.4 THE CHAIN RULE

3.5 THE TRIGONOMETRIC FUNCTIONS

3.6 THE CHAIN RULE AND INVERSE FUNCTIONS

3.7 IMPLICIT FUNCTIONS

3.8 HYPERBOLIC FUNCTIONS

3.9 LINEAR APPROXIMATION AND THE DERIVATIVE

3.10 THEOREMS ABOUT DIFFERENTIABLE FUNCTIONS

REVIEW PROBLEMS

PROJECTS

4 USING THE DERIVATIVE

4.1 USING FIRST AND SECOND DERIVATIVES

4.2 OPTIMIZATION

4.3 OPTIMIZATION AND MODELING

4.4 FAMILIES OF FUNCTIONS AND MODELING

4.5 APPLICATIONS TO MARGINALITY

4.6 RATES AND RELATED RATES

4.7 L’HOPITAL’S RULE, GROWTH, AND DOMINANCE

4.8 PARAMETRIC EQUATIONS

REVIEW PROBLEMS

PROJECTS

5 KEY CONCEPT: THE DEFINITE INTEGRAL

5.1 HOW DO WE MEASURE DISTANCE TRAVELED?

5.2 THE DEFINITE INTEGRAL

5.3 THE FUNDAMENTAL THEOREM AND INTERPRETATIONS

5.4 THEOREMS ABOUT DEFINITE INTEGRALS

REVIEW PROBLEMS

PROJECTS

6 CONSTRUCTING ANTIDERIVATIVES

6.1 ANTIDERIVATIVES GRAPHICALLY AND NUMERICALLY

6.2 CONSTRUCTING ANTIDERIVATIVES ANALYTICALLY

6.3 DIFFERENTIAL EQUATIONS AND MOTION

6.4 SECOND FUNDAMENTAL THEOREM OF CALCULUS

REVIEW PROBLEMS

PROJECTS

7 INTEGRATION

7.1 INTEGRATION BY SUBSTITUTION

7.2 INTEGRATION BY PARTS

7.3 TABLES OF INTEGRALS

7.4 ALGEBRAIC IDENTITIES AND TRIGONOMETRIC SUBSTITUTIONS

7.5 NUMERICAL METHODS FOR DEFINITE INTEGRALS

7.6 IMPROPER INTEGRALS

7.7 COMPARISON OF IMPROPER INTEGRALS

REVIEW PROBLEMS

PROJECTS

8 USING THE DEFINITE INTEGRAL

8.1 AREAS AND VOLUMES

8.2 APPLICATIONS TO GEOMETRY

8.3 AREA AND ARC LENGTH IN POLAR COORDINATES

8.4 DENSITY AND CENTER OF MASS

8.5 APPLICATIONS TO PHYSICS

8.6 APPLICATIONS TO ECONOMICS

8.7 DISTRIBUTION FUNCTIONS

8.8 PROBABILITY, MEAN, AND MEDIAN

REVIEW PROBLEMS

PROJECTS

9 SEQUENCES AND SERIES

9.1 SEQUENCES

9.2 GEOMETRIC SERIES

9.3 CONVERGENCE OF SERIES

9.4 TESTS FOR CONVERGENCE

9.5 POWER SERIES AND INTERVAL OF CONVERGENCE

REVIEW PROBLEMS

PROJECTS

10 APPROXIMATING FUNCTIONS USING SERIES

10.1 TAYLOR POLYNOMIALS

10.2 TAYLOR SERIES

10.3 FINDING AND USING TAYLOR SERIES

10.4 THE ERROR IN TAYLOR POLYNOMIAL APPROXIMATIONS

10.5 FOURIER SERIES

REVIEW PROBLEMS

PROJECTS

11 DIFFERENTIAL EQUATIONS

11.1 WHAT IS A DIFFERENTIAL EQUATION?

11.2 SLOPE FIELDS

11.3 EULER’S METHOD

11.4 SEPARATION OF VARIABLES

11.5 GROWTH AND DECAY

11.6 APPLICATIONS AND MODELING

11.7 THE LOGISTIC MODEL

11.8 SYSTEMS OF DIFFERENTIAL EQUATIONS

11.9 ANALYZING THE PHASE PLANE

REVIEW PROBLEMS

PROJECTS

APPENDICES

A ROOTS, ACCURACY, AND BOUNDS

B COMPLEX NUMBERS

C NEWTON’S METHOD

D VECTORS IN THE PLANE

READY REFERENCE

ANSWERS TO ODD-NUMBERED PROBLEMS

INDEX

Editorial Reviews

Calculus can be taught as nothing but rules and procedures--losing sight of both the mathematics and its inherent practical value. In 1989, the Calculus Consortium based at Harvard was formed to create a completely new calculus curriculum. A part of their endeavor is this textbook, which presents a radically different approach to the teaching and learning of the subject. The two guiding principles: 1) every topic should be presented geometrically, numerically, and algebraically; and 2) formal definitions and procedures evolve from the investigation of practical problems (the way of Archimedes). Annotation c. Book News, Inc., Portland, OR (booknews.com)

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