COALITION MATH 151, FALL 1997

        Group II (S. A. Fulling, assisted by Cary Lasher)

                              Day 5.1


    1.  Questions?  Announce review session and pretest office 
    hour.

    2.  Individual RAT on product and quotient rules.  "Extra 
    points for tasteful simplification."  Show answers and 
    emphasize that those who did not get basic points should 
    study for the test. 

    3.  Remarks on Sec. 2.3, "Rates of change in the .. sciences"

        A.  Of the 8 examples, the most important for the future 
        is the second one (density in a wire).  We will be 
        reversing it when we study integration.  (summarize)
    
        B.  Examples 6 and 8 (population and marginal cost) 
        demonstrate the use of derivatives with inherently 
        discrete data.

        C.  Example 4 (chemical reactions):  All the terms in the 
        last equation are separately equal (book's version is an 
        understatement):

        - d[A]/dt/a = - d[B]/dt/b = + d[C]/dt/c = + d[D]/dt/c

        D.  Example 5 (compressibility):  - dV/dP /V.  Why do we 
        divide by V?  (want intensive quantity)  Invite response;
        hint with samples of different sizes.

    4.  Calculus of trigonometric functions

        A.  Review derivative formulas for sine and cosine.  
        (Return to limits and proofs later.)

        B.  Derivatives of the other 4 functions by quotient or 
        reciprocal rule.  (Call on teams.)
GOT THIS FAR.  RETURNED TO THE REMAINDER AT THE END OF THE NEXT 
DAY (AND AT THE REVIEW SESSION ON THE PREVIOUS EVENING).

        C.  Antiderivative formulas.  Many natural functions 
        still missing from our trigonometric integral table, such 
        as tan x, sec x, sin^2 x; integration is more of an art 
        than differentiation.