Num_Diff-Example_Error_in_Data.xls

	A	B	C	D	E	F	G	H	I	J
1	Example of Num Differentiation (With and without errors in data points):
2
3	S. No.	x	y=f(x)= x2 (w/o error)	y'=f '(x)	y''=f ''(x)	Random error in y	Random error in y	y=f(x)= x2 (with error)	y'=f '(x) (with error)	y''=f ''(x) (with error)
4	1	0	0				0.09238744728	0.09238744728
5	2	0.5	0.25	0.5			0.6965364441	0.9465364441	1.708297994
6	3	1	1	1.5	2		0.8825528068	1.882552807	1.872032725	0.3274694632
7	4	1.5	2.25	2.5	2		0.6931785156	2.943178516	2.121251418	0.4984373845
8	5	2	4	3.5	2		0.8390549266	4.839054927	3.791752822	3.341002809
9	6	2.5	6.25	4.5	2		0.1188465671	6.368846567	3.059583281	-1.464339082
10	7	3	9	5.5	2		0.004194963141	9.004194963	5.270696792	4.422227022
11	8	3.5	12.25	6.5	2		0.2522935233	12.50229352	6.99619712	3.451000656
12	9	4	16	7.5	2		0.6236073295	16.62360733	8.242627612	2.492860984
13	10	4.5	20.25	8.5	2		0.5301348526	20.78013485	8.313055046	0.1408548674
14	11	5	25	9.5	2		0.4208564502	25.42085645	9.281443195	1.936776298
15	12	5.5	30.25	10.5	2		0.6474715211	30.89747152	10.95323014	3.343573894
16	13	6	36	11.5	2		0.373684731	36.37368473	10.95242642	-0.001607444757
17	14	6.5	42.25	12.5	2		0.5725351468	42.82253515	12.89770083	3.890548824
18	15	7	49	13.5	2		0.9197009002	49.9197009	14.19433151	2.59326135
19	16	7.5	56.25	14.5	2		0.5741304665	56.82413047	13.80885913	-0.7709447486
20	17	8	64	15.5	2		0.6408774166	64.64087742	15.6334939	3.649269535
21	18	8.5	72.25	16.5	2		0.7159418759	72.96594188	16.65012892	2.033270036
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