Homework 5
                  MA/CS 375, Spring 2002 
                      Due April 26 


[i.] Use 4, 8, 16 and 32 equispaced points (+1!) and
the Matlab function spline to compute 
interpolants to the following functions:
(a) f(x) =  e^{-x^2}, -2 <= x <= 2.
(b) f(x) =  1/(1+x^2), -5 <= x <= 5.
(c) f(x) =  sqrt(x), 0 <= x <= 4.
Plot the function together with the four interpolants on one graph. Compute
the maximum error on one hundred equispaced points. (Do NOT interpolate on 
these.) Comment on the convergence.
[ii.] 3.3.10
[iii.-v.] To follow.
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INSTRUCTIONS:
   The following format is required of all work turned in:
(0) Be as brief as you can, but give all information required to
    resolve a question.
(1) Team names must appear on top left hand corner ON ALL PAGES
    turned in.
(2) Staple your papers together.
(3) All work must be typed (say in Word or Latex); you may handwrite
    math symbols if you do not have access to appropropriate software.
(4) Your reports must be structured as follows:
Problem # (each beginning on new page):
(  i) Problem statement
( ii) Theoretical analysis of question: if an algorithm must be written
      to solve the problem, give the mathematical/theoretical outline
      here and describe the method of solution.
(iii) Results: a coherent presentation of results. Include a minimum of
      numerical/graphical info. that is needed to answer the question.
      One graph, properly labeled, is preferable to lists of numbers.
( iv) Discussion: what you did, how your work answered the question.
(  v) Printouts of scripts and results.
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