Math 170B HW #7 Partial Solutions
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1a.  The smallest d can be is 5.

1b.  We can prescribe 4 more conditions so that there will be a 
     unique solution.


2. S_0(0) = 3    (S_0)'(2)  = (S_1)'(2)
   S_0(2) = 4    (S_0)''(2) = (S_1)''(2)
   S_1(2) = 4    (S_0)''(0) = 0 
   S_1(4) = 2    (S_1)''(4) = 0

   The last two second-order conditions are since S is a natural cubic spline.
   Hence we have 8 equations in 8 unknowns. The directions say not to solve 
   this system, so I did not solve.


3. b = -1, c = -3, d = 1.


4. a = 1, b = -1, c = 1, d = 0.


5. We need n >= 672.


(For the following, come to office hours or section for explanations.) 

6a. False.

6b. True.

6c. False.

6d. True.

6e. False.

6f. True.


7.  MATLAB.