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Applied Calculus 5th Edition by Brad G. Osgood, Brigitte Lahme, Adam H. Speigler, William G. McCallum, Selin Kalaycýoðlu, Karen R. Rhea, Guadalupe I. Lonzano, Eric Connally, Douglas Quinney, David Lovelock, Daniel E. Flath, Andrew M. Gleason, Patti Frazer Lock, Deborah Hughes-Hallett

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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

STRENGTHEN YOUR UNDERSTANDING

PROJECTS: COMPOUND INTEREST, POPULATION CENTER OF THE US, MEDICAL CASE STUDY: ANAPHYLAXIS

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

STRENGTHEN YOUR UNDERSTANDING

PROJECTS: ESTIMATING TEMPERATURE OF A YAM; TEMPERATURE AND ILLUMINATION; CHLOROFLUOROCARBONS IN THE ATMOSPHERE

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

STRENGTHEN YOUR UNDERSTANDING

PROJECTS: CORONER'S RULE OF THUMB; AIR PRESSURE AND ALTITUDE; RELATIVE GROWTH RATES: POPULATION, GDP, AND GDP PER CAPITA; KEELING CURVE: ATMOSPHERIC CARBON DIOXIDE

FOCUS ON THEORY

ESTABLISHING THE DERIVATIVE FORMULAS

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, ...

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