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Table of Contents (6/9/11 PDF)

Proposal for Reviewers (6/8/11 PDF)

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Chapter 10 - Functions and Limits

  1. Functions
    1. What is a function?
    2. What is function notation?
    3. What is a piecewise defined function?
  2. Basic Concepts of Limits
    1. How do you evaluate a limit from a table?
    2. How do you evaluate a limit from a graph?
  3. Computing Limits Algebraically
    1. How can a limit be computed algebraically?
    2. How do you evaluate limits involving difference quotients?
  4. Computing Limits at Infinity
    1. How do you evaluate a limit at infinity using a table or graph?
    2. How do you evaluate limits at infinity using algebra?
  5. Continuous Functions
    1. What does a continuous function look like?
    2. How is a limit related to a continuous function?

Chapter 11 - Calculating Change

  1. Average Rate of Change
    1. How do you calculate the average rate of change from a table?
    2. How do you calculate the average rate of change from a function?
  2. Instantaneous Rate of Change
    1. How do you estimate the instantaneous rate of change?
    2. How do you compute the instantaneous rate of change using a limit?
  3. The Derivative at a Point
    1. What is a derivative?
    2. How do you compute the derivative at a point using a limit?
    3. How can you use a tangent line to forecast function values?
    4. What does the derivative at a point tell you about a function?
  4. The Derivative Function
    1. What is a derivative function?
    2. How do you calculate the derivative of a function from the definition?
    3. What are the derivatives of some basic functions (linear, polynomial,
      power, exponential, and logarithmic)?
  5. Economic Applications of the Derivative
    1. What does the term marginal mean?
    2. How are derivatives used to compute elasticity?
  6. Derivatives of Products and Quotients
    1. How do you find the derivative of a product of two functions?
    2. How do you find the derivative of a quotient of two functions?
    3. What is an average cost function?
  7. The Chain Rule
    1. What is a composition of two functions?
    2. How do you write a function as a composition of two functions?
    3. How do you apply the chain rule to take a derivative?
    4. How do you combine derivative rules to take more complicated
      derivatives?

Chapter 12 - Applying Derivatives

  1. Extrema of a Function
    1. What is the difference between a relative extremum and an absolute
      extremum?
    2. What is a critical point of a function?
    3. How do you find the relative extrema of a function?
    4. How do you find the absolute extrema of a function?
  2. Higher Derivatives
    1. How is the second derivative calculated?
    2. How are other higher derivatives calculated?
    3. What does the second derivative of a function tell you about a function?
    4. What is the point of diminishing returns?
  3. Optimizing Business Functions
    1. How do you maximize the revenue or profit for a business?
    2. How do you minimize the average cost for a business?
  4. Business Applications of Extrema
    1. How do you find the optimal dimensions of a product?
    2. How do we make decisions about inventory?

Chapter 13 - Calculating Area

  1. Antiderivatives
    1. What is an antiderivative?
    2. What are the antiderivatives of some basic functions?
    3. How do we find the antiderivative of functions that are combinations of
      basic functions?
    4. How do we find the value of the arbitrary constant?
  2. Approximating Area
    1. Why is area important?
    2. How is the area under a function approximated?
  3. The Definite Integral
    1. What is a definite integral?
    2. How is the definite integral related to the approximate area?
  4. The Fundamental Theorem of Calculus
    1. How do you calculate the total change of a quantity exactly?
    2. What is the Fundamental Theorem of Calculus?

Chapter 14 - Integration Techniques

  1. The Substitution Method
    1. How do we find the antiderivative of functions involving compositions?
    2. How is the exact area under a function involving compositions computed?
  2. Integration by Parts
    1. How do we find the antiderivative of functions involving products?
    2. How is the exact area under a function involving products computed?
  3. Area Between Curves
    1. How is the area between two functions calculated?
    2. What are consumers’ and producers’ surplus?

Chapter 15 - Multivariable Calculus

  1. Functions of Several Variables
  2. Partial Derivatives
  3. Extrema of Multivariable Functions

 

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