Applied Calculus
5th Edition

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

© 2014

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Features

Read, Study, Practice

• A complete online version of the text (eBook)
• Student Solutions Manual
• Student Study Guide
• Web Quizzes
• Alg & Trig Refreshers

Prepare and Present

• Concept Tests
• Instructor Lecture Notes
• Instructor Solution Manual
• Instructor Manual
• Printed Test Bank
• Computerised Test Bank

Assignment

• A "Link-to-text" feature that allows students to access specific portions of their online text for immediate, contextual help as they are working
• Correlated End-of-section algorithmic questions, approximately 700 questions
• Instructor Diagnostic Assignments
• Learning Objectives associated with every chapter
• WileyPLUS/Quickstart assignments and presentations for the entire course created by a subject expert.

Topics covered

1 FUNCTIONS AND CHANGE

  1. What is a Function?
  2. Linear Functions
  3. Average Rate of Change and Relative Change
  4. Applications of Functions to Economics
  5. Exponential Functions
  6. The Natural Logarithm
  7. Exponential Growth and Decay
  8. New Functions from Old
  9. Proportionality and Power Functions
  10. Periodic Functions
  11. Review Problems
  12. Strengthen your Understanding
  13. Projects: Compound Interest, Population Center of the US, Medical Case Study: Anaphylaxis

2 RATE OF CHANGE: THE DERIVATIVE

  1. Instantaneous Rate of Change
  2. The Derivative Function
  3. Interpretations of the Derivative
  4. The Second Derivative
  5. Marginal Cost and Revenue
  6. Review Problems
  7. Strengthen your Understanding
  8. Projects: Estimating Temperature of a Yam; Temperature and Illumination; Chlorofluorocarbons in the Atmosphere
  9. Focus on Theory
  10. Limits, Continuity, and the Definition of the Derivative

3 SHORTCUTS TO DIFFERENTIATION

  1. Derivative Formulas for Powers and Polynomials
  2. Exponential and Logarithmic Functions
  3. The Chain Rule
  4. The Product and Quotient Rules
  5. Derivatives of Periodic Functions
  6. Review Problems
  7. Strengthen your Understanding
  8. Projects: Coroner’s Rule of Thumb; Air Pressure and Altitude; Relative Growth Rates: Population, GDP, and GDP per Capita; Keeling Curve: Atmospheric Carbon Dioxide
  9. Focus on Theory
  10. Establishing the Derivative Formulas
  11. Focus on Practice
  12. Focus on Practice

4 USING THE DERIVATIVE

  1. Local Maxima and Minima
  2. Inflection Points
  3. Global Maxima and Minima
  4. Profit, Cost, and Revenue
  5. Average Cost
  6. Elasticity of Demand
  7. Logistic Growth
  8. The Surge Function and Drug Concentration
  9. Review Problems
  10. Strengthen your Understanding
  11. Projects: Average and Marginal Costs, Firebreaks, Production and the Price of Raw Materials, Medical Case Study: Impact of Asthma on Breathing 

5 ACCUMULATED CHANGE: THE DEFINITE INTEGRAL

  1. Distance and Accumulated Change
  2. The Definite Integral
  3. The Definite Integral as Area
  4. Interpretations of the Definite Integral
  5. Total Change and the Fundamental Theorem of Calculus
  6. Average Value
  7. Review Problems
  8. Strengthen Your Understanding
  9. Projects: Carbon Dioxide i Pond Water, Flooding in the Grand Canyon
  10. Focus on Theory
  11. Focus on Theory
  12. Theorems about Definite Integrals

6 ANTIDERIVATIVES AND APPLICATIONS

  1. Analysing Antiderivatives Graphically and Numerically
  2. Antiderivatives and the Indefinite Integral
  3. Using the Fundamental Theorem to find Definite Integrals
  4. Application: Consumer and Producer Surplus
  5. Application: Present and Future Value
  6. Integration by Substitution
  7. Integration by Parts
  8. Review Problems
  9. Strengthen your Understanding
  10. Projects: Quabbin Reservoir, Distribution of Resources, Yield from an Apple Orchard
  11. Focus on Practice

7 PROBABILITY

  1. Density Functions
  2. Cumulative Distribution Functions and Probability
  3. The Median and the Mean
  4. Review Problems
  5. Strengthen your Understanding
  6. Projects: Triangular Probability Distribution

8 FUNCTIONS OF SEVERAL VARIABLES

  1. Understanding Functions of Two Variables
  2. Contour Diagrams
  3. Partial Derivatives
  4. Computing Partial Derivatives Algebraically
  5. Critical Points and Optimisation
  6. Constrained Optimisation
  7. Review Problems
  8. Strengthen your Understanding
  9. Projects: A Heater in a Room, Optimising Relative Prices for Adults and Children,
  10. Maximising Production and Minimising Cost: “Duality”
  11. Focus on Theory
  12. Deriving the formula for a Regression Line 

9 MATHEMATICAL MODELING USING DIFFERENTIAL EQUATIONS

  1. Mathematical Modeling: Setting up a Differential Equation
  2. Solutions of Differential Equations
  3. Slope Fields
  4. Exponential Growth and Decay
  5. Applications and Modeling
  6. Modeling the Interaction of Two Populations
  7. Modeling the Spread of a Disease
  8. Review Problems
  9. Strengthen your Understanding
  10. Projects: Harvesting and Logistic Growth, Population Genetics, the Spread of Sars
  11. Focus on Theory
  12. Separation of Variables

10 GEOMETRIC SERIES

  1. Geometric Series
  2. Applications to Business and Economics
  3. Applications to the Natural Sciences
  4. Review Problems
  5. Strengthen your Understanding
  6. Projects: Do you have any Common Ancestors?, Harrod-Hicks Model of an Expanding National Economy, Probability of winning in Sports, Medical Case Study: Drug Desensitisation Schedule

Appendix

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