CSE541 Homework #3

Answers

Due:

• Hardcopy written or typed answers are due at the beginning of class, Tuesday, Jan. 24 in class

GENERAL INSTRUCTIONS

• Homework is due in lecture when I ask for it.
• All work must be your own. You are not allowed to work in groups or use third party sources.
• All make-ups for homework must be accompanied by a documented and verifiable excuse well before the deadline. Given the severity of the emergency please inform me as soon as possible.
• Please make sure your homework answers are legible, otherwise they will be marked wrong.
• Staple your pages.
• Homework submissions will NOT be accepted via email to me or the grader. No late homework will be accepted.
• For each problem, SHOW ALL WORK in order to receive full credit. Just giving a final answer (correct or incorrect) will receive NO CREDIT. Thus, you will be graded on the work shown.
• Each problem is worth the same amount
• Similarly, each of the n homework assignments will be worth 1/nth of the total for Assignments. 'n' is yet to be determined, but should be around 8.

ASSIGNMENT

Consider the following function in the problems below

f(x) = x^3 - 2*x^2 + 2x - 3

1. Write table of values for x = 0, 1, 2, 3, 4; also write value for x = 0.5

2. Write the equations of each of the first 4 derivatives of f(x)

3. Evaluate each of the derivatives at x=0

4. Write each of the first 4 Taylor Series expansions of f(x=0) using: one term, two terms, three terms, four terms

5. For each of the 4 Taylor Series expansions, give the estimation for Δx=0.5. Explain the results - the trend in the values as well as the specific value for the four term Taylor Series expansion.

6. For Newton polynomial interpolation, using the table of values from Step #1, write the matrix (sideways pyramid) of divided differences

7. Write the progression of estimates for Newton polynomial interpolation using the table of divided differences using one term, two terms, three terms, four terms.

8. For each of the four Newton polynomials, write the estimate for x = 0.5. Explain the results - the trend in the values as well as the specific value for the four term Newton polynomial.