1
MATH 348 - Homework III
Hand in by November 2.
He can compress the most words into the smallest
idea of any man I know. - Abraham Lincoln
dy
y
1. #4 page 5 and #11 and #12 page 6. In #12 note that the solution to
= is
dx
x
y
y = κx or κ = .
x
2. Exercise #10 page 14 (If need be, see #9 for guidance).
3. Exercise #15 page 15.
4. Fourier series and even and odd parts.
(
(a) Find the Fourier series of the function f (x) =
p, −p < x < 0
x, 0 < x < p
(b) Apply problem #20(a) and (b) to f (x) in (a).
(c) Find the Fourier series of fe (x) and fo (x).Apply the problem #20(a) and (b).
∞
X
1
is
2
k=0 (2k − 1)
convergent. This means that S is a finite real number. It is a much harder
problem to find the actual number S represents. This is the the domain of
numerical analysis. This led one pundit to assert that analysists carry the
light loads and numericist do the heavy lifting. Make an adroit choice for x
in the Fourier series for fe (x) or fo (x) and find S.
(d) It’s a problem in real analysis to show that the series S =
Hand in #12 page 6 (5 points), #4 (20 points).