MAE 3210 Homework 1 Solved

Description

Monday’s class:

1. Read course syllabus in detail, including the Policies linked in syllabus. You do not need to submit anything for this problem.

Wednesday’s class:

2. Textbook problem 2.26.

(Textbook may have a typo labeling this as problem 20.26, see page 53)

Friday’s class:

3.a. The following infinite series can be used to approximate e^x:

• Prove that this Maclaurin series expansion is a special case of the Taylor series expansion(Eq. (4.7) in text) with x_i = 0 and h = x.
• Use a Taylor series to estimate f(x) = e^−x at x_i+1 = 2 for x_i = 1. Employ the zero-, first-, second-, and third-order versions and compute |ε_t| for each case. 3.b. Use zero- through third-order Taylor series expansions to predict f(1) for

f(x) = 20x³ − 5x² + 7x − 80

using a base point at x = −1. Compute the true percent relative error ε_t for each approximation.