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by Brad G. Osgood, Brigitte Lahme, Adam H. Speigler, William G. McCallum, Selin Kal
Applied Calculus 5th Edition
Cover Page
Title Page
Copyright
Dedication
PREFACE
APPLICATIONS INDEX
CONTENTS
Chapter One: 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 FOR CHAPTER ONE
STRENGTHEN YOUR UNDERSTANDING
PROJECTS FOR CHAPTER ONE
Chapter Two: 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 FOR CHAPTER TWO
STRENGTHEN YOUR UNDERSTANDING
PROJECTS FOR CHAPTER TWO
FOCUS ON THEORY
LIMITS, CONTINUITY, AND THE DEFINITION OF THE DERIVATIVE
Chapter Three: SHORTCUTS TO DIFFERENTATION
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 FOR CHAPTER THREE
STRENGTHEN YOUR UNDERSTANDING
PROJECTS FOR CHAPTER THREE
FOCUS ON THEORY
ESTABLISHING THE DERIVATIVE FORMULAS
FOCUS ON PRACTICE
Chapter Four: 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 FOR CHAPTER FOUR
STRENGTHEN YOUR UNDERSTANDING
PROJECTS FOR CHAPTER FOUR
Chapter Five: 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 TOTAL CHANGE AND THE FUNDAMENTAL THEOREM OF CALCULUS
5.6 AVERAGE VALUE
REVIEW PROBLEMS FOR CHAPTER FIVE
STRENGTHEN YOUR UNDERSTANDING
PROJECTS FOR CHAPTER FIVE
FOCUS ON THEORY
THEOREMS ABOUT DEFINITE INTEGRALS
Chapter Six: ANTIDERIVATIVES AND APPLICATIONS
6.1 ANALYZING ANTIDERIVATIVES GRAPHICALLY AND NUMERICALLY
6.2 ANTIDERIVATIVES AND THE INDEFINITE INTEGRAL
6.3 USING THE FUNDAMENTAL THEOREM TO FIND DEFINITE INTEGRALS
6.4 APPLICATION: CONSUMER AND PRODUCER SURPLUS
6.5 APPLICATION: PRESENT AND FUTURE VALUE
6.6 INTEGRATION BY SUBSTITUTION
6.7 INTEGRATION BY PARTS
REVIEW PROBLEMS FOR CHAPTER SIX
STRENGTHEN YOUR UNDERSTANDING
PROJECTS FOR CHAPTER SIX
FOCUS ON PRACTICE
Chapter Seven: PROBABILITY
7.1 DENSITY FUNCTIONS
7.2 CUMULATIVE DISTRIBUTION FUNCTIONS AND PROBABILITY
7.3 THE MEDIAN AND THE MEAN
REVIEW PROBLEMS FOR CHAPTER SEVEN
STRENGTHEN YOUR UNDERSTANDING
PROJECTS FOR CHAPTER SEVEN
Chapter Eight: FUNCTIONS OF SEVERAL VARIABLES
8.1 UNDERSTANDING FUNCTIONS OF TWO VARIABLES
8.2 CONTOUR DIAGRAMS
8.3 PARTIAL DERIVATIVES
8.4 COMPUTING PARTIAL DERIVATIVES ALGEBRAICALLY
8.5 CRITICAL POINTS AND OPTIMIZATION
8.6 CONSTRAINED OPTIMIZATION
REVIEW PROBLEMS FOR CHAPTER EIGHT
STRENGTHEN YOUR UNDERSTANDING
PROJECTS FOR CHAPTER EIGHT
FOCUS ON THEORY
DERIVING THE FORMULA FOR A REGRESSION LINE
Chapter Nine: MATHEMATICAL MODELING USING DIFFERENTIAL EQUATIONS
9.1 MATHEMATICAL MODELING: SETTING UP A DIFFERENTIAL EQUATION
9.2 SOLUTIONS OF DIFFERENTIAL EQUATIONS
9.3 SLOPE FIELDS
9.4 EXPONENTIAL GROWTH AND DECAY
9.5 APPLICATIONS AND MODELING
9.6 MODELING THE INTERACTION OF TWO POPULATIONS
9.7 MODELING THE SPREAD OF A DISEASE
REVIEW PROBLEMS FOR CHAPTER NINE
STRENGTHEN YOUR UNDERSTANDING
PROJECTS FOR CHAPTER NINE
FOCUS ON THEORY
SEPARATION OF VARIABLES
Chapter Ten: GEOMETRIC SERIES
10.1 GEOMETRIC SERIES
10.2 APPLICATIONS TO BUSINESS AND ECONOMICS
10.3 APPLICATIONS TO THE NATURAL SCIENCES
REVIEW PROBLEMS FOR CHAPTER TEN
STRENGTHEN YOUR UNDERSTANDING
PROJECTS FOR CHAPTER TEN
APPENDICES
A FITTING FORMULAS TO DATA
B COMPOUND INTEREST AND THE NUMBER e
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 LOTTERY WINNINGS
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
ANSWERS TO ODD NUMBERED PROBLEMS
PRETEST
INDEX
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