Assignment #1
(Sep. 27, 2012)
ME3905 Numerical Methods
(Deadline for submission: Oct. 11, 2012, 6:30 pm)
Find the root(s) of the equations f(x)=0
(i)
f ( x) =
1 .5 x
1 0.65 x
0.65 tan 1 ( ) +
=0
22
x 1+ x2
(1 + x )
by using the bisection method with a =
ME3905
Chapter 1: Tutorial questions
ote: (i) Work on the following questions;
(ii) You may discuss with each other or with the TA;
(iii) Submission of your solutions to the TA is not compulsory, or if you wish, the TA
will correct your solutions in 2-3 w
ME3905
Chapter 3/4: Tutorial questions
ote: (i) Work on the following questions;
(ii) You may discuss with each other or with the TA;
(iii) Submission of your solutions to the TA is not compulsory, or if you wish, the TA
will correct your solutions in 2-3
ME3905
Chapter 2: Tutorial questions
ote: (i) Work on the following questions;
(ii) You may discuss with each other or with the TA;
(iii) Submission of your solutions to the TA is not compulsory, or if you wish, the TA
will correct your solutions in 2-3 w
Midterm Test: umerical Methods (ME 3905)
Student ame _
Student ID _
Question 1.
(a) Determine the root of an equation f ( x ) = 0.1 -
[3 - sin(x)]ln( 1 + x)
=0 .
(x + 2) 2
using bisection method with two initial guesses of a=0 and b=0.5. Perform the
compu
Exercise /Question EX1
For a set of 4 data points,
i
0
1
2
3
xi
1.5
2.5
3.5
4.5
yi
3
5
3
7
Employ the Newtons divided difference interpolating
polynomial to fit the data. Determine the coefficients of
the interpolating formulas.
2
solutiom
Question EX2
Gi
ME3905 Revision Questions
Chapter 1
1.
2.
3.
4.
5.
6.
7.
What is the bi-section method for solving equation?
Tutorial question #1(a).
What are the drawbacks of bi-section methods?
What is Newton-Raphson method for solving equation?
Tutorial question #1(c)
Example /exercise question EX1
1. Problem 5.15 of textbook [1] (Chapra & Canale)
bisection method.
(see No.11-12 PPT slides for solution)
Example /exercise question EX2
EX3.
Locate the first nontrivial root of sin(x)=x3, where x is in radians. Use a
graph
Question #1.
(i) Use central difference approximations to estimate the 1st derivative of
y=ex at x=2 for h=0.1.
(ii) Employ the following formulas to estimate the 1st derivative of y=f(x)=ex
at x=2 for h=0.1.
f ( x) =
'
f ( x 2h ) 8 f ( x h ) + 8 f ( x +
Assignment #3
(Nov.22, 2012)
ME3905 Numerical Methods
(Deadline for submission: 14 Dec 2012, 6:30pm)
Question 1. For a set of 5 data points,
x
y
1
0
3
-2
6
3
8
1
14
9
Employ the Newtons divided difference interpolating polynomial to fit the data.
Determin
ME46002 Chapter 1: Exercise questions
EX1:
Given
f (x ) = 2x 6 1.5x 4 + 10x + 2=0
Use bisection to determine the maximum of this function. Employ initial guesses of xl = 0 and xu
= 1, and perform iterations until the approximate relative error falls below