CS3331: 數值方法 (Numerical Methods)

Homework 4

Instructor: Roger Jang

For the following questions, you need to submit hardcopies of your programs, together with the results returned by MATLAB.

1. (20%) Exercise P7.2 (page 201)
   Note that:
   • "n=2ⁿ" should be changed to "n=2^k".
   • Test your function on all five given functions, with k = 10.

2. (20%) Exercise P7.5 (page 201)

3. (20%) Exercise P7.6 (page 201)

4. (20%) Write a MATLAB script to generate the coefficients of the Newton-Cotes formula when the polynomial order is 4.
   Note that:
   • You should know what Lagrange interpolation polynomials are before attempting this question. (If you don't, then it means that you've been skipping classes!)
   • You should use the "polyfit" function to find Lagrange interpolation polynomials.
   • The correct answer is at the footnote of page 189.