A textbook of Computer Based Numerical and Statiscal Techniques part 57 pps
A textbook of Computer Based Numerical and Statiscal Techniques part 57 pps
... the mean length of the
consignment can be taken as 46. [Ans. Accepted]
18. A sample of 18 items has a mean 24 units and standard deviation 3 units. Test the
hypothesis that it is a random sample ... (also called an object) is a place where computer can
store a value. So that they can refer to it unambiguously, a variable needs a name. A declaration
tells the compiler t...
A textbook of Computer Based Numerical and Statiscal Techniques part 2 ppsx
... problems. A major
advantage for numerical technique is that a numerical answer can be obtained even when a
problem has no analytical solution. However, result from numerical analysis is an approximation,
in ... significant figures at each step of
computation. At each step of computations, retain at least one more significant figure
than that given in the data, perform the last...
A textbook of Computer Based Numerical and Statiscal Techniques part 3 ppsx
... 3
Hence maximum percentage error (E
p
)
max
= 11.667%.
Example 26. How accurately should the length and time of vibration of a pendulum should be
measured in order that the computed value of g is ... 4008 and 30.4647 + 0.0639 =
30.5286.
Example 12. Find the product of 346.1 and 865.2 and state how many figures of the result are
trustworthy, given that the numbers are corr...
A textbook of Computer Based Numerical and Statiscal Techniques part 5 ppsx
... roots of the equation, obtained by
x
1
=
2
22
44
and
22
bb ac bb ac
aa
−+ − −− −
=x
These are called closed form solution. Similar formulae are also available for cubic and
biquadratic polynomial ... 26
COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES
The basic operations specified by IEEE arithmetic are first and foremost addition, subtraction,
multiplication, and div...
A textbook of Computer Based Numerical and Statiscal Techniques part 14 ppsx
... 122
COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES
Example 22. Evaluate: ∆
n
[sin (ax + b)]
Sol. We know
f∆
(x) = f(x + h) – f (x) therefore
∆
sin (ax + b) = sin [a (x + h)+b] – sin)(ax ... hD hD
hD
116
COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES
Example 14. Evaluate the following:
I. ∆
2
(cos 2x)
II. ∆
2
(3e
x
)
III. ∆ tan
–1
x
IV. ∆(x + cos x)
the inte...
A textbook of Computer Based Numerical and Statiscal Techniques part 16 ppsx
... given a set of equidistant values of arguments and its corresponding value of f(x). Suppose
for n + 1 equidistant argument values x = a, a + h, a + 2h, , a + nh, are given.
140
COMPUTER BASED NUMERICAL ... 0f−+×−×+=
138
COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES
i.e., 4f(3) = 124
i.e., f(3) = 31
(function values are 3
n
type and this is not a pol...
A textbook of Computer Based Numerical and Statiscal Techniques part 17 ppsx
... R.H.S.
3.9 FACTORIAL NOTATIONS
The product of n consecutive factors each at a constant difference and the first factor being x is
called a factorial function or a factorial polynomial of degree n and ... L.H.S.
150
COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES
CorCor
CorCor
Cor
ollary:ollary:
ollary:ollary:
ollary:
To show that,
()
n
n
x
∆
= n! h
n
and
1n+
∆...
A textbook of Computer Based Numerical and Statiscal Techniques part 22 pps
... 16.047
x
x
y
[Ans. 19.704]
202
COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES
Example 4. Apply Stirling’s formula to find a polynomial of degree three which takes the following
values of x and y:
x
y ... 32.625 thousands
Hence, the population in 1936 is 32625 thousand.
196
COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES
Example 5. If f(x) is a polynomial...
A textbook of Computer Based Numerical and Statiscal Techniques part 25 ppsx
... interpolation formula.
Sol. We are given
()
:78910
:311 9
x
fx
226
COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES
Example 1. Using Lagrange’s formula, find the value of
(i) y
x
if y
1
... required polynomial.
Example 4. Value of f(x) are given at a, b, c. Show that the maximum is obtained by
x =
()
(
)
()
(
)
()
(
)
()
()
()
()
()
()
fa b c fb c a fc a b
fa b c fb...
A textbook of Computer Based Numerical and Statiscal Techniques part 26 ppsx
... differences
where as the difference defined earlier are called ordinary differences. Lagrange’s interpolation
formula has the disadvantage that if any other interpolation point were added, the interpolation
co-efficient ... (5)
244
COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES
Example 10. Show that the sum of Lagrangian co-efficients is unity.
Sol. Let
()
x
∏
=
()
()
()
01...
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