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
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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
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PROJECTS: ESTIMATING TEMPERATURE OF A YAM, TEMPERATURE AND ILLUMINATION
FOCUS ON THEORY
LIMITS, CONTINUITY, AND THE DEFINITION OF THE DERIVATIVE
3 SHORT뺺UTS 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
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PROJECTS: CORONER뭆 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
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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
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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
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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
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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
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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
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PROJECTS: A HEATER IN A ROOM, OPTIMIZING RELATIVE PRICES FOR ADULTS AND CHILDREN,
MAXIMIZING PRODUCTION AND MINIMIZING COST: QUALITY
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
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