eciv 301 programming & graphics numerical methods for engineers lecture 27 numerical integration...
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![Page 1: ECIV 301 Programming & Graphics Numerical Methods for Engineers Lecture 27 Numerical Integration & Differentiation](https://reader035.vdocument.in/reader035/viewer/2022062405/56649d815503460f94a65bd4/html5/thumbnails/1.jpg)
ECIV 301
Programming & Graphics
Numerical Methods for Engineers
Lecture 27
Numerical Integration & Differentiation
![Page 2: ECIV 301 Programming & Graphics Numerical Methods for Engineers Lecture 27 Numerical Integration & Differentiation](https://reader035.vdocument.in/reader035/viewer/2022062405/56649d815503460f94a65bd4/html5/thumbnails/2.jpg)
Motivation
x
xfxxf
x
y ii
![Page 3: ECIV 301 Programming & Graphics Numerical Methods for Engineers Lecture 27 Numerical Integration & Differentiation](https://reader035.vdocument.in/reader035/viewer/2022062405/56649d815503460f94a65bd4/html5/thumbnails/3.jpg)
Motivation
x
xfxxf
x
y ii
![Page 4: ECIV 301 Programming & Graphics Numerical Methods for Engineers Lecture 27 Numerical Integration & Differentiation](https://reader035.vdocument.in/reader035/viewer/2022062405/56649d815503460f94a65bd4/html5/thumbnails/4.jpg)
Motivation
x
xfxxf
dx
dy ii
x
0lim
![Page 5: ECIV 301 Programming & Graphics Numerical Methods for Engineers Lecture 27 Numerical Integration & Differentiation](https://reader035.vdocument.in/reader035/viewer/2022062405/56649d815503460f94a65bd4/html5/thumbnails/5.jpg)
Motivation
b
a
dxxfI
AREA BETWEEN a AND b
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Motivation
)()( tydt
dtv
![Page 7: ECIV 301 Programming & Graphics Numerical Methods for Engineers Lecture 27 Numerical Integration & Differentiation](https://reader035.vdocument.in/reader035/viewer/2022062405/56649d815503460f94a65bd4/html5/thumbnails/7.jpg)
Motivation
b
a
dxtvty
![Page 8: ECIV 301 Programming & Graphics Numerical Methods for Engineers Lecture 27 Numerical Integration & Differentiation](https://reader035.vdocument.in/reader035/viewer/2022062405/56649d815503460f94a65bd4/html5/thumbnails/8.jpg)
Motivation
![Page 9: ECIV 301 Programming & Graphics Numerical Methods for Engineers Lecture 27 Numerical Integration & Differentiation](https://reader035.vdocument.in/reader035/viewer/2022062405/56649d815503460f94a65bd4/html5/thumbnails/9.jpg)
Motivation
Calculate Derivative
Given
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MotivationGiven
Calculate
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Think as Engineers!
![Page 12: ECIV 301 Programming & Graphics Numerical Methods for Engineers Lecture 27 Numerical Integration & Differentiation](https://reader035.vdocument.in/reader035/viewer/2022062405/56649d815503460f94a65bd4/html5/thumbnails/12.jpg)
In Summary
INTERPOLATE
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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
![Page 14: ECIV 301 Programming & Graphics Numerical Methods for Engineers Lecture 27 Numerical Integration & Differentiation](https://reader035.vdocument.in/reader035/viewer/2022062405/56649d815503460f94a65bd4/html5/thumbnails/14.jpg)
In Summary
Also by piecewise approximation
b
ax
x
x
n
b
a
i
i
i
dxxf
dxxfI
1
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Closed/Open Forms
CLOSED OPEN