My summary of principal subject matter for the first exam in Math 151, fall 2007

  1. Analytic geometry: coordinates, points, distance, lines, circles. Functions: domains; ranges; graphs.
  2. Common sorts of functions: polynomial, rational, algebraic (roots), trig, inverse trig, exp, ln, with corresponding domain restrictions.
  3. Limits
    1. Plugging in (cite "Continuity").
    2. Algebraic transformation to a form which is recognized by a).
    3. Use of one of the complicated results or special limits (such as sin(theta)/theta).
  4. Continuity: no breaks, etc.: its specific definition. Recognition of the graph of a continuous function.
  5. Intermediate Value Theorem (bisection for location of a root).
  6. The derivative
    1. Instantaneous rate of change using approximation by average rate of change.
    2. Slope of a tangent line.
    3. The actual definition with a limit.
  7. Computation of derivative from the definition using limit properties.
  8. Computation of derivative formulas or values for functions defined by formulas or tabular information using the differentiation algorithms.
  9. Graph of a derivative from graphical information (or the reverse).

Maintained by and last modified 10/10/2007.