Root Finding
Determine the value of x that makes f(x)=0
Plot Your Function and see the general
behavior:
Use this plot to provide an initial guess orfor
potential problems.
Refine your Interval
1.
2.
3.
4.
How often will this function be evaluated?
How mu
Curve Fitting
1. Fitting a curve to a set of data points
2. Fitting a curve for the Extrapolation of the data points (Trend
Analysis).
3. Fitting a curve to a set of points to obtain a continuous
smooth curve
1
Mathematical Background
Arithmetic mean
Stan
Open Methods
*
*
Require a single starting point.
Convergence to a solution is not guarantied.
1
Fixed Point Iteration
A function f(x) can be converted
to a form:
x=g(x)
A guess on x (xi) can be refined
as:
xi+1=g(xi)
Converges if |g(x)|<1
in the region o
ME - 310
NUMERICAL METHODS
Fall 2007
Group 02
Instructor: Prof. Dr. Eres Sylemez (Rm C205, email:eres@metu.edu.tr )
Class Hours and Room:
Monday
13:40 - 15:30
Wendesday 12:40 - 13:30
Rm: B101
Rm: B103
Course TextBook: "Numerical Methods for Engineers" by
System of Nonlinear equations
N nonlinear equations in n unknowns
Sometimes you can use a fixed point iteration or an iteration
similar to Gauss Seidel Iteration for linear equations.
f1 ( x1 , x2 , x3 , x4 ,. xn )
f 2 ( x1 , x2 , x3 , x4 ,. xn )
Newton R
Fall 2007
ME-310 Numerical Methods
Homework Assignment 2
Program Due: 24 October 2007
Report Due: 25 October 2007 @ 13:30
Viscous frictional losses in pipe flow result in pressure drops that must be overcome.
These are expressed in terms of a friction fac
ME 310
NUMERICAL METHODS
Homework 3
Program Due: 07/11/2007 @ 24:00
Report Due: 08/11/2007 @ 13:30
Figure shows a six link mechanism used in textile machines. The link lengths are:
s 16
D
A0A = a2= 210 mm;
C0C = a5 = 600 mm;
CB = a4 = 350 mm;
BD = b4 = 60
ME-310 Numerical Methods
Fall 2007
Homework Assignment 1
Due: Wednesday, 10 October 2007
The value of can be calculated with the series
=4
(-1)
n-1
n=1
1
1 1 1
1
1
= 4 (1 + +
+ .)
2n - 1
3 5 7
9 11
Write a computer program that calculates the value of b