Math 414 - Spring 2000
Homework
Assignment 1
- Read sections 1.1, 1.2, 8.1-8.3.1.
- Problems
- §1.4: 1-4, 8, 13, 28
- §8.8: 1, 4.
- Due Thursday, 1/27/00
Assignment 2
- Read sections 1.3, 8.3-8.5.
- Problems
- §1.4: 16, 17(a,c), 18(a,d,e), 20, 25(a,c,d)
- §8.8: 6, 7, 13
- Due Thursday, 2/8/00
Assignment 3
- Read sections 2.1 and 2.2.1.
- Problems
- Use Parseval's theorem and the Fourier series for x2
(exercise 1, §1.4) to find the sum
S = 1 + 2-4 + 3-4 + 4-4 ...
- For the function f(t) and its Fourier series in exercise 25,
§1.4, plot EN(t) = | f(t) - SN
|2 on [-pi,pi] for N=1,2,3. Numerically integrate
EN(t) for these values of N. Compare this with what we
derived in class:
|| EN(t) || 2 =|| f(t) ||2 - 4*pi*(1
+ 2-2 + 3-2 + 4-2 + ... +
N-2 )
- §2.6: 1, 2, 7 (second half of problem).
- Due Tuesday, 2/22/00
Assignment 4
- Read sections 2.3 and 2.4. Think about projects.
- Problems
- §2.6: 6, 8, 9, 11, 13
- Due Thursday, 3/9/00
Assignment 5
- Read sections 3.1 & 3.2. Think about projects.
- Problems
- §3.3: 3, 4, 6, 7, 10, 12, 13 (See Errata)
- Due Thursday, 3/30/00
Assignment 6
- Read sections 4.1-4.4. Think about projects.
- Problems
- §4.5: 1-7
- Due Thursday, 4/13/00
Updated: 4/6/00