CBE 502 HW4

hw4.py

from math import exp, cos, sin

def print_answers(fs, fnames, W, tx=4.0):
    for (name, f) in zip(fnames, fs):
        print name+'(', tx, '):', f(tx)
    print " W(", tx, "):", W(tx)

def n32b():
    f1 = lambda t: exp(float(t)) * (3.0 / 4.0 - t / 2) - exp(-1.0 * t) / 4
    f1p = lambda t: exp(float(t))*(1./4-t/2)+exp(-t)/4
    f1pp = lambda t: -(1./4+t/2.)*exp(float(t)) - exp(-1.*t)/4.

    f2 = lambda t: exp(float(t)) / 2.0 - exp(-1.0 * t) / 2
    f2p = lambda t: exp(float(t))/2 + exp(-float(t))/2.
    f2pp = lambda t: exp(float(t))/2 - exp(-float(t))/2.

    f3 = lambda t: exp(float(t)) * (t / 2.0 - 0.25) + exp(-1.0 * t) / 4
    f3p = lambda t: exp(float(t))*(t/2.+1/4.) - exp(-float(t))/4.
    f3pp = lambda t: exp(float(t))*(t/2. + .75) + exp(-float(t))/4.

    def W(t):
        t = float(t)
        return f1(t)*f2p(t)*f3pp(t) + f2(t)*f3p(t)*f1pp(t) + f3(t)*f1p(t)*f2pp(t) \
              -f3(t)*f2p(t)*f1pp(t) - f2(t)*f1p(t)*f3pp(t) - f1(t)*f3p(t)*f2pp(t)
    return [[f1, f2, f3], W]

[[f1, f2, f3], W] = n32b()
print "3.2 (b)"
print_answers([f1, f2, f3], ['f1', 'f2', 'f3'], W)

def n32e():
    def f1(t):
        t = float(t)
        return exp(-t)*cos(t) + exp(-t)*sin(t)
    def f1p(t):
        t = float(t)
        return 0

    def f2(t):
        t = float(t)
        return exp(-t)*sin(t)
    def f2p(t):
        t = float(t)
        return exp(-t)*cos(t) - exp(-t)*sin(t)

    def W(t):
        return f1(t)*f2p(t) - f2(t)*f1p(t)
    return [[f1, f2], W]

print ""
print "3.2 (b)"
[[f1, f2], W] = n32e()
print_answers([f1, f2], ['f1', 'f2'], W)

print ""
print "3.3"
[[f1, f2, f3], W] = n32b()
print_answers([f1, f2], ['f1', 'f2'], W, tx=0.0)