Day 01 in MAT227

Today:

• Announcements/Welcome:
  • Introductions (3x5 cards)
    1. Name
    2. Hometown
    3. What is your calling? ("a calling has to do with one's larger purpose, personhood, deepest values, and the gift one wishes to give the world.... A calling is about the use one makes of a career." David Orr, Earth in Mind)
    4. What is your dream job?
    5. What is something special about you?

  • Some course details:
    • The course website will be useful: http://www.nku.edu/~longa/classes/mat227
    • Syllabus (logistics, etc.)
    • Departmental Syllabus (the fine print)
    • Schedule and Assignments (tentative)
    • You should do the reading in advance of our discussion of that section in class.
    • Calculators (especially TI 89, 92, titanium, or comparable) -- are encouraged in class.
    • Other than calculators, you are not to use any other electronics in this class (without my explicit permission) -- no phones. These must be stowed before class.

      Furthermore, In fact, I need you to sign my agreement....

    • Calculus lab: A Calculus Lab, run by the Math/Stat Dept. and staffed by upper level students, will provide tutoring to Calculus students in MEP 457 (hours are 9-3, M-R, and 9-12 on F).

  • Your first assignment (you'll find these on the assignment page of our website)

• Examples of the general problems we'll consider in this course:
  • How do we calculate
    • the area under a curve?
    • the length of a curve?
    • the volume of a solid?

  • What are some new functions that can help us as modellers?
    • Some that serve as "Undoers" (e.g. logs, which undo exponentials);
    • Some that satisfy neat and important properties (e.g. logs!).

  • How do we create mathematical descriptions of "space curves" (e.g. a suspended cable, or the trajectory of a rocket)?
  • How can we use calculus to characterize important facets of these space curves?

  • How do we relate rates of change and areas (derivatives and integrals)?

• Some fundamental things to recall from your earlier calc days:
  • classes of important functions (e.g. linear, quadratic, general polynomials, rational functions, trig functions)
  • limits
  • "linearization": tangent lines, secant lines
  • rates of change (instantaneous and average)
  • derivatives and differentiation (algebraic, basic rules, the limit definition, how reflected in curves, higher order)

    Hopefully you remember some of the applications of derivatives (or higher derivatives): for example, derivatives become the central issue in this article on sea level rise, and, in particular, this image:

    

• So let's think about a specific problem: How do we calculate the area under a known curve?
  • In order to make the question more concrete, how about answering this question in the context of these curves: what is the area under the graph of "urine fertilized cabbage".
    

  • What could this area mean?
  • What special challenge(s) does this graph and problem present?