Read sections 1.1-1.3, 1.5-1.9, and examples 1-4 in 1.13.
Do problems 1a-1d, 3a, pp. 38-39.
Due Thursday, 1/28/99
Week of 1/24.
Tolstov
Read sections 1.4, 1.10-1.13, 1.15.
Do problems 4b, 4c, 5a, 6, 9, 12, pp. 38-39.
Due Thursday, 2/4/99
Week of 1/31.
Tolstov
Read sections 1.14, 2.1-2.5
Find the complex form of the Fourier series in 1a, 1d, pp. 38-39
Do problems 10a, 10b, 11a, pp. 38-39.
Do problem 4, pp. 63-65.
Due Thursday, 2/11/99
Week of 2/7.
Powers
Read sections 2.1 & 2.2.
Section 2.1. Do problem 4, p. 119.
Section 2.2. Do problems 3, 6c, pp. 124-125.
Tolstov
Read sections 2.7, 2.10.
Show that the polynomials
P0(x)=1
P1(x)=x
P2(x)=3x2 - 1
are orthogonal in the inner product < f, g > :=
-1S1 f(x) g(x)dx.
From first principles (i.e., minimize the error directly; don't
just quote the answer), use these polynomials to find the best
least-squares fit to exp(-x) on the interval [-1, 1].
On the same set of axes, sketch exp(-x), the least-squares fit
you've found, and the quadratic Taylor polynomial about x=0 for
exp(-x) .