COALITION MATH 152, SPRING 1998

              (S. A. Fulling, assisted by Vera Rice)

                             Day 18.T


    1.  The usual paper shuffling:  Old homework, CAPA, revised 
    new homework, lab sheet if ready.

    2.  Individual RAT:  The 4 basic calculus formulas for exp 
    and ln.

    3.  The bare minimum to know about exp and ln (prepared 
    transparency).

    4.  Team exercise:  Evaluate some derivatives and integrals 
    requiring chain rule, etc.  Rules for this type of exercise:

        A.  Every team puts an answer on plastic; graded for 1 or 
        2 points.                                

        B.  One person called on to present the answer on the 
        projector; team gets up to 4 points.  If your team needs 
        to bail you out, team loses a point.

        C.  Turn in plastic and tissue paper; keep the pens and 
        bring them to class henceforth.

        D.  Care of felt pens:  Keep capped!  Don't scrub or 
        stab.  Don't write on the tissue paper!
FOR LOGISTICAL REASONS AND TO PROVIDE A BREAK LATER, I POSTPONED 
THE EXERCISE TILL AFTER 5C.

    5.  More extended summary of the theory (more 
    transparencies). 

        A.  One definition:  ln as integral of 1/x, exp as 
        inverse.

        B.  Another definition:  exp as solution of y' = y.

        C.  The number e; exp and log with arbitrary base.

        D.  What questions do these functions answer?  (the basic 
        properties looked at from a more motivating angle)
MY LECTURE AND TRANSPARENCIES (INHERITED FROM LAST YEAR) NEED TO 
BE REVAMPED.  I FELT NEEDLESSLY REPETITIVE. 

    6.  Challenge problem for next time:  Explain the species-
    area rule,
    http://calclab.math.tamu.edu/~fulling/m152/species.html
  
    7.  Logarithmic differentiation:  Pose an example and the 
    basic theory.  Call on somebody to do the details.
STUDENTS HAVE SURPRISING TROUBLE IMPLEMENTING THIS PROCEDURE WHEN 
SIMPLY PRESENTED WITH THE FORMULA f' = f (ln f)' (NOTED THIS YEAR 
AND LAST).