Day 01 in MAT227

Today:

• Announcements:
  • Introductions (3x5 cards)
    1. Name
    2. Year (Freshman, etc.)
    3. Major
    4. Where are you from?
    5. Something special about yourself.

  • 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. Your colleagues are counting on you!
    • Calculators (TI 89, 92) -- you need one!
    • Other than calculators, you are not to use any other electronics in this class (without my explicit permission) -- and the penalty for doing so is that you will have to leave class for the day if you do.

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

    • Calculus lab: A Calculus Lab, run by the Mathematics Dept. and staffed by upper level students, will provide tutoring to Calculus students in ST 343. Hours (to start -- subject to change):

         Monday: 12:00-3:00pm
        Tuesday:  8:30am-2:00pm and 5:00-7:30pm
      Wednesday: 12:00-3:00pm
       Thursday:  8:30am-2:00pm and 5:00-7:30pm
      

  • My philosophy regarding this course
    • A calculus survey of some 20 textbook authors suggests that we're not succeeding in calculus instruction using lecture: reiterating what is said in the text (and said fairly well, in general) is not working. What I do should complement the text.

    • My philosophy accords well with comments Keith Devlin made in his MAA column Devlin's Angle: quoting from that article, "...there seems to be a wide (though not universal) consensus over three main causes:
      • Our mathematics curriculum (actually, it's curricula, since each state has its own, but the complaint applies to all) contains far too many required topics, each of which can be taught only to a shallow degree - often referred to as the "mile wide, inch deep" problem;
      • Far too many math teachers do not have a good understanding of the subject they teach;
      • In the majority of classrooms, mathematics is taught in a rigid, rule-based fashion.
      Devlin asserts this: "Mathematics is a way of thinking about problems and issues in the world. Get the thinking right and the skills come largely for free." I agree.

    • I plan to spend the first 30 minutes of each class session answering your questions. These may have everything to do with particular skills. Your homework problems may ask you to work on those skills, so you will have questions about them.

    • The final 45 minutes is for discussion of new ideas. This will generally involve small group work as you work as a team to solve a problem. You will need a notebook (worth 5% of your grade) in which you will take notes on this process. For each entry you should have the following:
      1. Date
      2. Question
      3. Group member names
      4. Solution strategy or strategies proposed.
      5. Analysis of the process.
      We'll spend about 20 minutes on this phase. Then, for the final 25 minutes, we'll switch to a class discussion of the proposed solutions.

  • Questions?

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

  • What are some new functions that can help us as modellers?
    • "Undoers"
    • That satisfy certain neat properties.

  • 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?

• 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.

• 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 could this area mean?
  • What special challenge does this special case present?
  • More generally now, what are some special cases of curves that would make the solution easy?
  • What problems would throw serious monkey wrenches into this process?