Lecture 7
●
MEEN 357 Engineering Analysis for Mechanical Engineers
1
Lecture07MEEN3572009.doc
RMB
Lecture 7
Possible Exam 1 Rules
:
EXAM 1
MEEN 357
February 17, 2009
Dr. Bowen
Section:
502
Name:
____________________________________________
"Aggies do not lie, cheat, or steal, nor do they tolerate those who do."
Aggie Code of Honor
By my signature below I pledge that my conduct on this exam is consistent in every way
with the Aggie Code of Honor:
Signature:
____________________________________________
1.
This exam consists of
???? (?)
problems that are weighted as shown below.
2.
This is a
open textbook (
Applied Numerical Methods with MATLAB
) open
lecture note
exam.
a)
The lecture notes are those posted on Vista Blackboard.
1.
It is understood that you add incidental comments to your copies of
these notes.
b)
You may also use graded homework solutions and the solutions posted on
Vista Blackboard
c)
You may not use individual notes that you have created other than what
you have added to the pages of the posted and printed class notes.
3.
You may use
handheld calculators unless the problem dictates otherwise.
a)
You may not use other computing devices.
4.
Be sure to read the question carefully.
5.
Be sure to show all work and calculations
, and organize
your solution procedure
as clearly and systematically as possible.
a)
Example:
Do not simply enter a string of numbers in your calculators and
write down the answer.
Write out the numbers in a mathematical formula
and then show the answers obtained from doing the mathematical
operations on your calculators.
6.
Work problems in the space provided on the exam sheets. Clearly indicate
continuation of the problem if you need extra pages.
GRADE
Problem ?:
________
/ ??
%
Problem ?:
________
/ ??%
Problem ?:
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/ ??%
Problem ?:
________
/ ??%
TOTAL
:
___________
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View Full DocumentLecture 7
●
MEEN 357 Engineering Analysis for Mechanical Engineers
2
Lecture07MEEN3572009.doc
RMB
Roots to Nonlinear Equations
Chapter 5 and 6 of the textbook.
We are looking at various ways to find the roots of the equation
( )
0
fx
=
(7.1)
in some given interval of the real axis.
As explained during Lectures 5 and 6, there are
two methods that are used to find the roots of the function
( )
yfx
=
.
•
Bracketing method:
This method involves first establishing that the root lies
within some interval and the use of an iteration scheme to find the root.
o
We discussed
±
Bisection Method
±
False Position Method
•
Open method:
An open method utilizes formulas that only require a single
starting value or two
starting values that do not necessarily bracket the root.
o
We discussed
±
NewtonRaphson method
±
Secant Method
MATLAB Resources:
1.
For the bisection method, the textbook provided,
bisect.m.
2.
For the false position method, we modified the
bisect.m
file and named
it
falsepos.m
3.
For the NewtonRaphson method, the textbook provided
newtraph.m
.
4.
The built in MATLAB command
fzero
can also be used.
This
command was discussed in Lecture 5.
It is also discussed in Section 6.4 of
the textbook.
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 Fall '07
 ANAMALAI
 Matrices, Mechanical Engineers

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