Homework #4 Due 11-8-2000

(1) Work p 121; 19

(2) You are to fit a natural spline s(x) to the function f(x) given the following information:

xk	0	1	2
f(xk)	1		0

(a) Find coefficients a0, b0,c0,d0,a1,b1,c1, and d1 using paper and pencil solutions using equations on p 146 and 147.

(b) Use maple as we done on handout (10-30-2000) to find the coefficients requested in (a).

(c) Using the spline s(x) from (a), approximate f(.3) and f(1.4)

(b) Evaluate .

(3) Work p 155, 7 (Hint: Use the conditions stated in Definition 3.10 on p 144)

(4) Work p 155, 11 (Hint: Use Theorem 3.11). You will set up a system of linear equations which you must solve. Since the number of unknowns are > 2, you might want to use an HP calculator, PC-Matlab (Read Matlab remarks below) or some other software to solve them. In any event, exhibit all the linear equations. To find f'(0.5), be sure to exhibit f'(x) for x's near 0.5 which will require using the coefficients you found earlier. The finding of f''(0.5) is similar.

Solving a system of linear equations via Matlab .

To solve 2x - 3y = -4, x + y = 3. This can be interpreted as ax = b. Use the following matlab code.

a=[2 -3; 1 1]

b=[-4;3]

x=a\b

(5) Redo p155,11 using either Matlab or Maple.

(6) Use dog1.dat, dog2.dat, dog3.dat from the following site

ftp://ftp.etsu.edu/pubdata/kerleyl/NA/

and get a graph similar to the one on p157. Use maple or matlab to accomplish this.At that same site resides

bird.m and bird.mws. You will need to study one of these 2 files depending on whether you use Maple or Matlab.