COALITION MATH 152, SPRING 1998

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

                             Day 24.R


    1.  Finish the homogeneous problems from the previous day.
WE LOOKED AT CASE v (DAMPED OSCILLATIONS) IN DETAIL AND RAN 
THROUGH THE REMAINING CASES QUICKLY.

    2.  RAT:  Find a solution (ANY solution) of y" + y = e^{2x}
I DID THIS MYSELF AS AN EXAMPLE.  THE THREAT OF A RAT WAS ONLY TO 
SERVE WARNING THAT NEXT WEEK, ADVANCE STUDY OF THE TAYLOR 
POLYNOMIAL WEB MATERIAL IS MANDATORY.

    3.  Construct a nonhomogeneous team problem:  Subtract 4 from 
    each digit in 2 ID numbers getting (b1,b2,b3,b4,c1,c2,c3,c4).
    Define  T = b1 + b2, D = b1 b2.  Your problem is
        y" + Ty' + Dy = c1 e^{b3 x} + g(b4 x), where
        g = sin  if b4 > 0,  
            cos  otherwise,
    with initial data  y(c2 \pi) = c3,  y'(c2 \pi) = c4.
    
    4.  A minilecture on nonhomogeneous 2nd order ODEs before 
    starting the class exercise:

        A.  The basic principle:  general solution = particular 
        solution + homogeneous solution.  Emphasize that IC are 
        applied to the whole general solution, not just the 
        homogeneous piece.

        B.  Examples of method of undetermined coefficients.
        Resonance:  If y_p overlaps y_h, multiply the offending 
        term of y_p by x.  Superposition applies to compound 
        source terms.

    5.  TEAM EXERCISE:  Solve your problem.  Lottery:  Extra 
    points for those who demonstrate a resonance.
TEAMS WILL REPORT RESULTS AT NEXT CLASS.