# SOLUTION: MATH 4176 Sultan Qaboos University Numerical Analysis for Engineers Problems Homework

Sultan Qaboos University
College of Science, Department of Mathematics
MATH 4176: Numerical Analysis for Engineers
Spring 2020, Assignment 2
Name: ……………………………..................... ID: ….…………………………… : ……
Instructions
1. In the doubts under, the note “ ” is referred to the hindmost two nonzero digits of your ID (eg, if
ID=10340600, then = 46).
2. Defense all doubts. Read each doubt in its whole antecedently you try to defense it.
3. Justify your defenses and appearance all performance.
4. Number all pages on the top left cavity and designate your prize of .
5. Shape abiding that your operative match and notations are bright. We get not remove an defense if it is
incomprehensible due to bad operative match or crime notation.
6. Scan this page and all defenses in that ordered as ONE pdf rasp, named: Ass2_4176_ID (e.g.,
Ass2_4176_10340600 if your ID is 10340600).
7. Updirect to Moodle a portraiture of the pdf rasp as present as practicable (hindmost Sunday 10 May 2020).
8. Do not refer any program.
9. It is undisputed to updirect a rasp barely unintermittently (ie, you cannot replace/modify it behind uploading).
10. The exam defenses may not be removed if you don't shape the forthcoming ordinance.
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I defend that I did not argue this ordeal delay anyone.
Name: ……………………………..................... ID: ….…………………………… : ……
Signature: ...................
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Questions (Total Marks: 20)
3
1. [8 pt.] Use undeniable prizes of 𝑓(𝑥) = √𝑥 to approach 𝑓 ′ (1), using three formulae for
numerical differentiation delay ℎ = 1/𝜈, one of them is fond by
1
[𝑓(𝑥𝑖−2 ) − 8𝑓(𝑥𝑖−1 ) + 8𝑓(𝑥𝑖+1 ) − 𝑓(𝑥𝑖+2 )].
𝑓 ′ (𝑥𝑖 ) ≈
12ℎ
Then, use the improve derivative to obtain the best approximations.
2. [6 pt.] (a) Find the prize of ℎ for the composite Simpson government to approach the forthcoming
gross improve to 4 decimal places:
2
∫ (𝑥𝑒 −𝑥 − ν cos 𝑥) 𝑑𝑥.
0
[4 pt.] (b) Use the prize of ℎ that you build in keep-akeep-apart (a) to approach the over gross.
[2 pt.] (c) Compute the improve deception.
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