CS/MATH 3414 Assignment #5

1. (10 points) Exercise 5.2.6 (page 206) from your textbook. If you would like to refresh your memory about what lower sums and upper sums mean, see Example 1 (page 187) in your textbook. This example was partially worked out in class.
   
   
2. (5 points) Exercise 5.2.8 (page 206) from your textbook.
   
   
3. (10 points) QUADDEMO is a MATLAB function that claims to "demonstrate adaptive numerical quadrature." It is written in terms of the MATLAB function QUAD. QUAD appears to be based on the recursive adaptive Simpson's rule that we studied in class. Experiment with the QUAD and QUADDEMO functions (type help; lookup the manual; try it out with different integration problems; type "quaddemo" on the MATLAB prompt, etc.) and write a short paragraph on whether you think QUAD is faithful to the method, as described in the book (and covered in class). If it is not, identify and explain the differences.
   
   
4. (10 points) Computer Problem 5.4.1 (page 228) from your textbook. Use the MATLAB QUAD function to determine the integrals (i.e., you do not have to write your own code to do them). For full credit, submit the MATLAB code (to call QUAD), your results, and a list of observations.
   
   
5. (5 points) Exercise 5.5.5 (page 236) from your textbook.
   
   
6. (10 points) Exercise 5.5.12 (page 237) from your textbook. The "method of undetermined coefficients" merely refers to trying out different polynomials (1, x, x^2, etc.) in order to setup a set of constraints on the coefficients (in this case, A, B, and C).