Efnisyfirlit

• Cover
• Title Page
• Copyright
• Dedication
• PREFACE
• Acknowledgments
• APPLICATIONS INDEX
• To Students: How to Learn from this Book
• Chapter 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
• Chapter 1: REVIEW EXERCISES AND PROBLEMS FOR CHAPTER 1
• Chapter 1: STRENGTHEN YOUR UNDERSTANDING
• Chapter 1: PROJECTS FOR CHAPTER ONE
• Chapter 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
• Chapter 2: REVIEW EXERCISES AND PROBLEMS FOR CHAPTER 2
• Chapter 2: STRENGTHEN YOUR UNDERSTANDING: Digital Only
• Chapter 2: PROJECTS FOR CHAPTER TWO
• Chapter 2: FOCUS ON THEORY: LIMITS, CONTINUITY, AND THE DEFINITION OF THE DERIVATIVE
• Chapter 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
• Chapter 3: REVIEW EXERCISES AND PROBLEMS FOR CHAPTER 3
• Chapter 3: STRENGTHEN YOUR UNDERSTANDING: Digital Only
• Chapter 3: PROJECTS FOR CHAPTER THREE
• Chapter 3: FOCUS ON THEORY: ESTABLISHING THE DERIVATIVE FORMULAS
• Chapter 3: FOCUS ON PRACTICE
• Chapter 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
• Chapter 4: REVIEW EXERCISES AND PROBLEMS FOR CHAPTER 4
• Chapter 4: STRENGTHEN YOUR UNDERSTANDING: Digital Only
• Chapter 4: PROJECTS FOR CHAPTER FOUR
• Chapter 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 TOTAL CHANGE AND THE FUNDAMENTAL THEOREM OF CALCULUS
• 5.6 AVERAGE VALUE
• Chapter 5: REVIEW EXERCISES AND PROBLEMS FOR CHAPTER 5
• Chapter 5: STRENGTHEN YOUR UNDERSTANDING: Digital Only
• Chapter 5: PROJECTS FOR CHAPTER FIVE
• Chapter 5: FOCUS ON THEORY: THEOREMS ABOUT DEFINITE INTEGRALS
• Chapter 6: 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
• Chapter 6: REVIEW EXERCISES AND PROBLEMS FOR CHAPTER 6
• Chapter 6: STRENGTHEN YOUR UNDERSTANDING: Digital Only
• Chapter 6: PROJECTS FOR CHAPTER SIX
• Chapter 6: FOCUS ON PRACTICE
• Chapter 7: PROBABILITY
• 7.1 DENSITY FUNCTIONS
• 7.2 CUMULATIVE DISTRIBUTION FUNCTIONS AND PROBABILITY
• 7.3 THE MEDIAN AND THE MEAN
• Chapter 7: REVIEW EXERCISES AND PROBLEMS FOR CHAPTER 7
• Chapter 7: STRENGTHEN YOUR UNDERSTANDING: Digital Only
• Chapter 7: PROJECTS FOR CHAPTER SEVEN
• Chapter 8: 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
• Chapter 8: REVIEW EXERCISES AND PROBLEMS FOR CHAPTER 8
• Chapter 8: STRENGTHEN YOUR UNDERSTANDING: Digital Only
• Chapter 8: PROJECTS FOR CHAPTER EIGHT
• Chapter 8: FOCUS ON THEORY: DERIVING THE FORMULA FOR A REGRESSION LINE
• Chapter 9: 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
• Chapter 9: REVIEW EXERCISES AND PROBLEMS FOR CHAPTER 9
• Chapter 9: STRENGTHEN YOUR UNDERSTANDING: Digital Only
• Chapter 9: PROJECTS FOR CHAPTER NINE
• Chapter 9: FOCUS ON THEORY: SEPARATION OF VARIABLES
• Chapter 10: GEOMETRIC SERIES
• 10.1 GEOMETRIC SERIES
• 10.2 APPLICATIONS TO BUSINESS AND ECONOMICS
• 10.3 APPLICATIONS TO THE NATURAL SCIENCES
• Chapter 10: REVIEW EXERCISES AND PROBLEMS FOR CHAPTER 10
• Chapter 10: STRENGTHEN YOUR UNDERSTANDING: Digital Only
• Chapter 10: 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
• INDEX
• GRAPHS OF FAMILIES OF FUNCTIONS
• End User License Agreement