Applied Calculus / Edition 4

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Overview

The fourth edition gives readers the skills to apply calculus on the job. It highlights the applications’ connection with real-world concerns. The problems take advantage of computers and graphing calculators to help them think mathematically.  The applied exercises challenge them to apply the math they have learned in new ways.  This develops their capacity for modeling in a way that the usual exercises patterned after similar solved examples cannot do. The material is also presented in a way to help business professionals decide when to use technology, which empowers them to learn what calculators/computers can and cannot do.

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Product Details

  • ISBN-13: 9780470170526
  • Publisher: Wiley
  • Publication date: 12/2/2009
  • Edition description: Older Edition
  • Edition number: 4
  • Pages: 560
  • Sales rank: 453,108
  • Product dimensions: 8.50 (w) x 10.40 (h) x 0.90 (d)

Table of Contents

Detailed TABLE of CONTENTS

1 FUNCTIONS AND CHANGE

1.1 WHAT IS A FUNCTION?

1.2 LINEAR FUNCTIONS

1.3 AVERAGE RATE OF CHANGE AND RELATIVE CHANGE

1.4 APPLICATIONS OF FUNCTIONS TO ECONOMICS

1.5 EXPONENTIAL FUNCTIONS

1.6 THE NATURAL LOGARITHM

1.7 EXPONENTIAL GROWTH AND DECAY

1.8 NEW FUNCTIONS FROM OLD

1.9 PROPORTIONALITY AND POWER FUNCTIONS

1.10 PERIODIC FUNCTIONS

REVIEW PROBLEMS

CHECK YOUR UNDERSTANDING

PROJECTS: COMPOUND INTEREST, POPULATION CENTER OF THE US

2 RATE OF CHANGE: THE DERIVATIVE

2.1 INSTANTANEOUS RATE OF CHANGE

2.2 THE DERIVATIVE FUNCTION

2.3 INTERPRETATIONS OF THE DERIVATIVE

2.4 THE SECOND DERIVATIVE

2.5 MARGINAL COST AND REVENUE

REVIEW PROBLEMS

CHECK YOUR UNDERSTANDING

PROJECTS: ESTIMATING TEMPERATURE OF A YAM, TEMPERATURE AND ILLUMINATION

FOCUS ON THEORY

LIMITS, CONTINUITY, AND THE DEFINITION OF THE DERIVATIVE

3 SHORT-CUTS TO DIFFERENTIATION

3.1 DERIVATIVE FORMULAS FOR POWERS AND POLYNOMIALS

3.2 EXPONENTIAL AND LOGARITHMIC FUNCTIONS

3.3 THE CHAIN RULE

3.4 THE PRODUCT AND QUOTIENT RULES

3.5 DERIVATIVES OF PERIODIC FUNCTIONS

REVIEW PROBLEMS

CHECK YOUR UNDERSTANDING

PROJECTS: CORONER’S RULE OF THUMB; AIR PRESSURE AND ALTITUDE; RELATIVE GROWTH

RATES: POPULATION, GDP, AND GDP PER CAPITA

FOCUS ON THEORY

ESTABLISHING THE DERIVATIVE FORMULAS

FOCUS ON PRACTICE

FOCUS ON PRACTICE

4 USING THE DERIVATIVE

4.1 LOCAL MAXIMA AND MINIMA

4.2 INFLECTION POINTS

4.3 GLOBAL MAXIMA AND MINIMA

4.4 PROFIT, COST, AND REVENUE

4.5 AVERAGE COST

4.6 ELASTICITY OF DEMAND

4.7 LOGISTIC GROWTH

4.8 THE SURGE FUNCTION AND DRUG CONCENTRATION

REVIEW PROBLEMS

CHECK YOUR UNDERSTANDING

PROJECTS: AVERAGE AND MARGINAL COSTS, FIREBREAKS, PRODUCTION AND THE PRICE OF

RAW MATERIALS

5 ACCUMULATED CHANGE: THE DEFINITE INTEGRAL

5.1 DISTANCE AND ACCUMULATED CHANGE

5.2 THE DEFINITE INTEGRAL

5.3 THE DEFINITE INTEGRAL AS AREA

5.4 INTERPRETATIONS OF THE DEFINITE INTEGRAL

5.5 THE FUNDAMENTAL THEOREM OF CALCULUS

REVIEW PROBLEMS

CHECK YOUR UNDERSTANDING

PROJECTS: CARBON DIOXIDE IN POND WATER, FLOODING IN THE GRAND CANYON

FOCUS ON THEORY

THEOREMS ABOUT DEFINITE INTEGRALS

6 USING THE DEFINITE INTEGRAL

6.1 AVERAGE VALUE

6.2 CONSUMER AND PRODUCER SURPLUS

6.3 PRESENT AND FUTURE VALUE

6.4 INTEGRATING RELATIVE GROWTH RATES

REVIEW PROBLEMS

CHECK YOUR UNDERSTANDING

PROJECTS: DISTRIBUTION OF RESOURCES, YIELD FROM AN APPLE ORCHARD

7 ANTIDERIVATIVES

7.1 CONSTRUCTING ANTIDERIVATIVES ANALYTICALLY

7.2 INTEGRATION BY SUBSTITUTION

7.3 USING THE FUNDAMENTAL THEOREM TO FIND DEFINITE INTEGRALS

7.4 INTEGRATION BY PARTS

7.5 ANALYZING ANTIDERIVATIVES GRAPHICALLY AND NUMERICALLY

REVIEW PROBLEMS

CHECK YOUR UNDERSTANDING

PROJECTS: QUABBIN RESERVOIR

FOCUS ON PRACTICE

FOCUS ON PRACTICE

8 PROBABILITY

8.1 DENSITY FUNCTIONS

8.2 CUMULATIVE DISTRIBUTION FUNCTIONS AND PROBABILITY

8.3 THE MEDIAN AND THE MEAN

REVIEW PROBLEMS

CHECK YOUR UNDERSTANDING

PROJECTS: TRIANGULAR PROBABILITY DISTRIBUTION

9 FUNCTIONS OF SEVERAL VARIABLES

9.1 UNDERSTANDING FUNCTIONS OF TWO VARIABLES

9.2 CONTOUR DIAGRAMS

9.3 PARTIAL DERIVATIVES

9.4 COMPUTING PARTIAL DERIVATIVES ALGEBRAICALLY

9.5 CRITICAL POINTS AND OPTIMIZATION

9.6 CONSTRAINED OPTIMIZATION

REVIEW PROBLEMS

CHECK YOUR UNDERSTANDING

PROJECTS: A HEATER IN A ROOM, OPTIMIZING RELATIVE PRICES FOR ADULTS AND CHILDREN,

MAXIMIZING PRODUCTION AND MINIMIZING COST: “DUALITY”

FOCUS ON THEORY

DERIVING THE FORMULA FOR A REGRESSION LINE

10 MATHEMATICAL MODELING USING DIFFERENTIAL EQUATIONS

10.1 MATHEMATICAL MODELING: SETTING UP A DIFFERENTIAL EQUATION

10.2 SOLUTIONS OF DIFFERENTIAL EQUATIONS

10.3 SLOPE FIELDS

10.4 EXPONENTIAL GROWTH AND DECAY

10.5 APPLICATIONS AND MODELING

10.6 MODELING THE INTERACTION OF TWO POPULATIONS

10.7 MODELING THE SPREAD OF A DISEASE

REVIEW PROBLEMS

CHECK YOUR UNDERSTANDING

PROJECTS: HARVESTING AND LOGISTIC GROWTH, POPULATION GENETICS, THE SPREAD OF

SARS

FOCUS ON THEORY

SEPARATION OF VARIABLES

11 GEOMETRIC SERIES

11.1 GEOMETRIC SERIES

11.2 APPLICATIONS TO BUSINESS AND ECONOMICS

11.3 APPLICATIONS TO THE NATURAL SCIENCES

REVIEW PROBLEMS

CHECK YOUR UNDERSTANDING

PROJECTS: DO YOU HAVE ANY COMMON ANCESTORS?, HARROD-HICKS MODEL OF AN EXPANDING

NATIONAL ECONOMY, PROBABILITY OF WINNING IN SPORTS

APPENDICES 471

A FITTING FORMULAS TO DATA

B COMPOUND INTEREST AND THE NUMBER

C SPREADSHEET PROJECTS

1. MALTHUS: POPULATION OUTSTRIPS FOOD SUPPLY

2. CREDIT CARD DEBT

3. CHOOSING A BANK LOAN

4. COMPARING HOME MORTGAGES

5. PRESENT VALUE OF LOTTERYWINNINGS

6. COMPARING INVESTMENTS

7. INVESTING FOR THE FUTURE: TUITION PAYMENTS

8. NEW OR USED?

9. VERHULST: THE LOGISTIC MODEL

10. THE SPREAD OF INFORMATION: A COMPARISON OF TWO MODELS

11. THE FLU IN WORLD WAR I

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