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Applied Calculus 5th Edition

Book Description

Applied Calculus is praised for the creative and varied conceptual and modeling problems which motivate and challenge students. The 5th Edition of this market leading text exhibits the same strengths from earlier editions including the "Rule of Four," an emphasis on concepts and modeling, exposition that students can read and understand and a flexible approach to technology. Updated data and fresh applications throughout the book are designed to build student confidence with basic concepts and to reinforce skills. As in the previous edition, a Pre-test is included for students whose skills may need a refresher prior to taking the course.

Table of Contents

  1. Cover Page
  2. Title Page
  3. Copyright
  4. Dedication
  5. PREFACE
    1. APPLICATIONS INDEX
  6. CONTENTS
  7. Chapter One: FUNCTIONS AND CHANGE
    1. 1.1 WHAT IS A FUNCTION?
    2. 1.2 LINEAR FUNCTIONS
    3. 1.3 AVERAGE RATE OF CHANGE AND RELATIVE CHANGE
    4. 1.4 APPLICATIONS OF FUNCTIONS TO ECONOMICS
    5. 1.5 EXPONENTIAL FUNCTIONS
    6. 1.6 THE NATURAL LOGARITHM
    7. 1.7 EXPONENTIAL GROWTH AND DECAY
    8. 1.8 NEW FUNCTIONS FROM OLD
    9. 1.9 PROPORTIONALITY AND POWER FUNCTIONS
    10. 1.10 PERIODIC FUNCTIONS
    11. REVIEW PROBLEMS FOR CHAPTER ONE
    12. STRENGTHEN YOUR UNDERSTANDING
    13. PROJECTS FOR CHAPTER ONE
  8. Chapter Two: RATE OF CHANGE: THE DERIVATIVE
    1. 2.1 INSTANTANEOUS RATE OF CHANGE
    2. 2.2 THE DERIVATIVE FUNCTION
    3. 2.3 INTERPRETATIONS OF THE DERIVATIVE
    4. 2.4 THE SECOND DERIVATIVE
    5. 2.5 MARGINAL COST AND REVENUE
    6. REVIEW PROBLEMS FOR CHAPTER TWO
    7. STRENGTHEN YOUR UNDERSTANDING
    8. PROJECTS FOR CHAPTER TWO
    9. FOCUS ON THEORY
    10. LIMITS, CONTINUITY, AND THE DEFINITION OF THE DERIVATIVE
  9. Chapter Three: SHORTCUTS TO DIFFERENTATION
    1. 3.1 DERIVATIVE FORMULAS FOR POWERS AND POLYNOMIALS
    2. 3.2 EXPONENTIAL AND LOGARITHMIC FUNCTIONS
    3. 3.3 THE CHAIN RULE
    4. 3.4 THE PRODUCT AND QUOTIENT RULES
    5. 3.5 DERIVATIVES OF PERIODIC FUNCTIONS
    6. REVIEW PROBLEMS FOR CHAPTER THREE
    7. STRENGTHEN YOUR UNDERSTANDING
    8. PROJECTS FOR CHAPTER THREE
    9. FOCUS ON THEORY
    10. ESTABLISHING THE DERIVATIVE FORMULAS
    11. FOCUS ON PRACTICE
  10. Chapter Four: USING THE DERIVATIVE
    1. 4.1 LOCAL MAXIMA AND MINIMA
    2. 4.2 INFLECTION POINTS
    3. 4.3 GLOBAL MAXIMA AND MINIMA
    4. 4.4 PROFIT, COST, AND REVENUE
    5. 4.5 AVERAGE COST
    6. 4.6 ELASTICITY OF DEMAND
    7. 4.7 LOGISTIC GROWTH
    8. 4.8 THE SURGE FUNCTION AND DRUG CONCENTRATION
    9. REVIEW PROBLEMS FOR CHAPTER FOUR
    10. STRENGTHEN YOUR UNDERSTANDING
    11. PROJECTS FOR CHAPTER FOUR
  11. Chapter Five: ACCUMULATED CHANGE: THE DEFINITE INTEGRAL
    1. 5.1 DISTANCE AND ACCUMULATED CHANGE
    2. 5.2 THE DEFINITE INTEGRAL
    3. 5.3 THE DEFINITE INTEGRAL AS AREA
    4. 5.4 INTERPRETATIONS OF THE DEFINITE INTEGRAL
    5. 5.5 TOTAL CHANGE AND THE FUNDAMENTAL THEOREM OF CALCULUS
    6. 5.6 AVERAGE VALUE
    7. REVIEW PROBLEMS FOR CHAPTER FIVE
    8. STRENGTHEN YOUR UNDERSTANDING
    9. PROJECTS FOR CHAPTER FIVE
    10. FOCUS ON THEORY
    11. THEOREMS ABOUT DEFINITE INTEGRALS
  12. Chapter Six: ANTIDERIVATIVES AND APPLICATIONS
    1. 6.1 ANALYZING ANTIDERIVATIVES GRAPHICALLY AND NUMERICALLY
    2. 6.2 ANTIDERIVATIVES AND THE INDEFINITE INTEGRAL
    3. 6.3 USING THE FUNDAMENTAL THEOREM TO FIND DEFINITE INTEGRALS
    4. 6.4 APPLICATION: CONSUMER AND PRODUCER SURPLUS
    5. 6.5 APPLICATION: PRESENT AND FUTURE VALUE
    6. 6.6 INTEGRATION BY SUBSTITUTION
    7. 6.7 INTEGRATION BY PARTS
    8. REVIEW PROBLEMS FOR CHAPTER SIX
    9. STRENGTHEN YOUR UNDERSTANDING
    10. PROJECTS FOR CHAPTER SIX
    11. FOCUS ON PRACTICE
  13. Chapter Seven: PROBABILITY
    1. 7.1 DENSITY FUNCTIONS
    2. 7.2 CUMULATIVE DISTRIBUTION FUNCTIONS AND PROBABILITY
    3. 7.3 THE MEDIAN AND THE MEAN
    4. REVIEW PROBLEMS FOR CHAPTER SEVEN
    5. STRENGTHEN YOUR UNDERSTANDING
    6. PROJECTS FOR CHAPTER SEVEN
  14. Chapter Eight: FUNCTIONS OF SEVERAL VARIABLES
    1. 8.1 UNDERSTANDING FUNCTIONS OF TWO VARIABLES
    2. 8.2 CONTOUR DIAGRAMS
    3. 8.3 PARTIAL DERIVATIVES
    4. 8.4 COMPUTING PARTIAL DERIVATIVES ALGEBRAICALLY
    5. 8.5 CRITICAL POINTS AND OPTIMIZATION
    6. 8.6 CONSTRAINED OPTIMIZATION
    7. REVIEW PROBLEMS FOR CHAPTER EIGHT
    8. STRENGTHEN YOUR UNDERSTANDING
    9. PROJECTS FOR CHAPTER EIGHT
    10. FOCUS ON THEORY
    11. DERIVING THE FORMULA FOR A REGRESSION LINE
  15. Chapter Nine: MATHEMATICAL MODELING USING DIFFERENTIAL EQUATIONS
    1. 9.1 MATHEMATICAL MODELING: SETTING UP A DIFFERENTIAL EQUATION
    2. 9.2 SOLUTIONS OF DIFFERENTIAL EQUATIONS
    3. 9.3 SLOPE FIELDS
    4. 9.4 EXPONENTIAL GROWTH AND DECAY
    5. 9.5 APPLICATIONS AND MODELING
    6. 9.6 MODELING THE INTERACTION OF TWO POPULATIONS
    7. 9.7 MODELING THE SPREAD OF A DISEASE
    8. REVIEW PROBLEMS FOR CHAPTER NINE
    9. STRENGTHEN YOUR UNDERSTANDING
    10. PROJECTS FOR CHAPTER NINE
    11. FOCUS ON THEORY
    12. SEPARATION OF VARIABLES
  16. Chapter Ten: GEOMETRIC SERIES
    1. 10.1 GEOMETRIC SERIES
    2. 10.2 APPLICATIONS TO BUSINESS AND ECONOMICS
    3. 10.3 APPLICATIONS TO THE NATURAL SCIENCES
    4. REVIEW PROBLEMS FOR CHAPTER TEN
    5. STRENGTHEN YOUR UNDERSTANDING
    6. PROJECTS FOR CHAPTER TEN
  17. APPENDICES
    1. A FITTING FORMULAS TO DATA
    2. B COMPOUND INTEREST AND THE NUMBER e
    3. C SPREADSHEET PROJECTS
      1. 1. MALTHUS: POPULATION OUTSTRIPS FOOD SUPPLY
      2. 2. CREDIT CARD DEBT
      3. 3. CHOOSING A BANK LOAN
      4. 4. COMPARING HOME MORTGAGES
      5. 5. PRESENT VALUE OF LOTTERY WINNINGS
      6. 6. COMPARING INVESTMENTS
      7. 7. INVESTING FOR THE FUTURE: TUITION PAYMENTS
      8. 8. NEW OR USED?
      9. 9. VERHULST: THE LOGISTIC MODEL
      10. 10. THE SPREAD OF INFORMATION: A COMPARISON OF TWO MODELS
      11. 11. THE FLU IN WORLD WAR I
  18. ANSWERS TO ODD NUMBERED PROBLEMS
  19. PRETEST
  20. INDEX