ECIV 301 Programming & Graphics Numerical Methods for Engineers Lecture 27 Numerical Integration &...
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ECIV 301 Programming & Graphics Numerical Methods for Engineers Lecture 27 Numerical Integration & Differentiation
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Transcript of ECIV 301 Programming & Graphics Numerical Methods for Engineers Lecture 27 Numerical Integration &...
ECIV 301
Programming & Graphics
Numerical Methods for Engineers
Lecture 27
Numerical Integration & Differentiation
Motivation
x
xfxxf
x
y ii
Motivation
x
xfxxf
x
y ii
Motivation
x
xfxxf
dx
dy ii
x
0lim
Motivation
b
a
dxxfI
AREA BETWEEN a AND b
Motivation
)()( tydt
dtv
Motivation
b
a
dxtvty
Motivation
Motivation
Calculate Derivative
Given
MotivationGiven
Calculate
Think as Engineers!
In Summary
INTERPOLATE
In SummaryNewton-Cotes Formulas
Replace a complicated function or tabulated data with an approximating
function that is easy to integrate
b
a
n
b
a
dxxfdxxfI
nn
nnon xaxaxaaxf
111
In Summary
Also by piecewise approximation
b
ax
x
x
n
b
a
i
i
i
dxxf
dxxfI
1
Closed/Open Forms
CLOSED OPEN
