2nd Level
Numerical Analysis
Sheet No.: 1
Title: Interpolation 1
_____________________________________________________________________
Textbook: Numerical Methods for Engineers by: Steven C. Chapra, Raymond P.
Canal. McGraw-Hill.
_____________________________________________________________________
Solve the following examples by la Grange Interpolation
Method
(1) find f(2) for the data f(0)=1 ,f(1)=3 and f(3)=55
x 0 1 3
f 1 3 55
(2) The following data gives the percentage of criminals for different
age groups,
Age less than 25 30 40 50
Percentage of 52 67.3 84.1 94.4
criminals
Use Lagrange’s formula of third degree to find the percentage of criminals
under the age of 35.
(3) The following table gives the viscosity of a specific type of oil as a
function of temperature. Using Lagrange’s formula of third degree
to find the viscosity of this oil at a temperature of 140,
Temperature 110 130 160 190
Viscosity 10.8 8.1 5.5 4.8
(4) Find f(0.25) for
x 0.1 0.2 0.3 0.4 0.5
f 9.9833 4.9667 3.2836 2.4339 1.9177
1
Extra Problems:
Exercise of Chapter 18 p.522 numbers; 1, 4, 7.
2
Math 3 sheath lagrange
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71 1 4 2
To X X XX 2 1112 3
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9 1 4.1 414 s
3
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X 130
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4 XiXXo XX lx Xs
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56
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1532
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45
64
xoxo X x xxxx xx o s o 1 o s o2 10.3 0.4 o s o s
ki III Is
3128
Y it I 3 33
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tf faithfixletsfixleftfoxy 4 64 32
Math 3 sheet Neaten
Pix Fixo 1 fix X X Xo f Xo x x x Xo x Xi
X fix fix x fcxoixi.nl
1 212 03 812 0112 1 21
is
sq
3 8
355
Pextsfixoltfixoix X Xo fixoix x X Xo X X fix x Xz Xs X Rolex X lx Xe
X fix fixoix fcxoixiixzlfxoix.mx
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25 52
77.405
06
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30 67.3
40841 0.0325
5094.4
Pextsfixoltfixoix X Xo fixoix x X Xo X X fix x Xz 1 X Rolex X lx Xe
X fix fix x fcxoixiixzlfixo.x.mx
110 10.8
10.8 0.1351140 1107 9.6666661041140110111401301 1.111113338 150
imma
s
14011011140 13071140 160 7.0333
4
go g 9.666666 10
0.08666667
1605.5 1.055555 6
19048
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X fix twoX fo X Xz fixoixX2 Xs faux Xa x
0.1 9.9833 9.9833 50.16610 25 0.1
50.166
166.67510 25 0 1 0.25 0.2
0.2 4.9667 166.675
if 416.683333310250.116.250.226.240
16.831 416.6833333
833.41666661025 0.1 0.250.270.25 0.3
41.67 833.4166666
0.25 0.4 3.911598
8.497 83.31666667
0.4 2.4339 16.675
5.162
0.5 1.9177
