Applied calculus
Author(s)
Bibliographic Information
Applied calculus
John Wiley & Sons (Asia), c2011
4th ed
- : pbk
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Note
"International student version by Selin Kalaycioǧlu ; with the assistance of Otto K. Bretscher ... [et al.] ; coordinated by Elliot J. Marks"
Includes index
Description and Table of Contents
Description
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.
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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