AMSC 460 Homework Set 3 Due: 21.05.04

Note:
• Due: 2pm, May 4, 2021. Late submission is subject to automatic 20%
reduction.
• When submitting, make sure you upload your matlab or python codes, in
addition to your answer sheets to analytical questions.

Topic: Differentiation

Consider numerical differentiation schemes using
a. - f(x0-2h)+ 4 f(x0-h) -3 f(x0)
b. f(x0-h) - 2 f(x0) + f(x0+h)
c. f(x0-2h) - 8 f(x0-h) + 8 f(x0+h) - f(x0+2h)
d. -f(x0-2h) +16 f(x0-h) -30 f(x0) + 16 f(x0+h) - f(x0+2h)
These are the same as Quiz no.7

For each scheme,
1. [5pts] identify the order of derivative

2. [5pts] Identify the order of truncation error

3. [10pts] Write a matlab or python code that gives the corresponding derivative
at arbitrary x0 any h

4. [20pts] For f(x)=exp(2x),
a. obtain analytical form of corresponding derivative at arbitrary point x
b. At x0=0, obtain expected numerical value of the corresponding derivative
c. Generate a figure equivalent to Fig.14.2 in the text book
d. Comment on the figure.

Bonus Points: Quiz 6. Data Fitting Using Normal Equation

Indicate your choice:
A. Redo Quiz 6, and submit a new one
B. Keep original submission/points of Quiz.
Full points correspond to 2% towards final grade either way.


欢迎咨询51作业君