COALITION MATH 152, SPRING 1998

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

                             Day 25.T


    1.  The usual paper shuffling:  Old homework, CAPA, revised 
    new homework.  Announce test key and ODE class copies are on 
    sale.

    2.  Finish the exercise on undetermined coefficients.
THIS TOOK AT LEAST HALF THE PERIOD.

    3.  Introduction to Taylor expansions (see Web page for 
    elaboration)

        A.  Power series are your friends!  (Show transparency of 
        first few Taylor polynomials of sin x.)

        B.  Lessons from the crosswalk

        C.  Taylor's formula ("the key fact") and list of the 
        basic Maclaurin expansions

        D.  EXAMPLE:  Find Taylor expansion of e^x about 0.
        (Brief comment about sin, cos, sinh, cosh)

        E.  TEAM EXERCISE:  Find the Taylor expansion (the first 
        3 terms, at least) of \sqrt{x} about a = 1.