
The fourth edition gives readers the skills to apply calculus on the job. It highlights the applications' connection with realworld 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.
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 SHORTCUTS 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?, HARRODHICKS 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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