A textbook of Computer Based Numerical and Statiscal Techniques part 37 doc
A textbook of Computer Based Numerical and Statiscal Techniques part 62 docx
... the Range
Lower limit a = 0
Upper limit b = 6
Enter the number of subintervals = 6
Value of the integral is: 1.3571
598
COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES
Enter the value of y2 ... ALGORITHM FOR TRAPEZOIDAL RULE
Step 1. Start of the program for numerical integration
Step 2. Input the upper and lower limits a and b
Step 3. Obtain the number of sub...
A textbook of Computer Based Numerical and Statiscal Techniques part 1 ppt
... This page
intentionally left
blank
This page
intentionally left
blank
A TEXTBOOK OF
COMPUTER BASED NUMERICAL
AND
STATISTICAL TECHNIQUES
Anju Khandelwal
M.Sc., Ph.D.
Department of Mathematics
SRMS ... Based Numerical and Statistical Techniques is primarily written
according to the unified syllabus of Mathematics for B. Tech. II year and M.C .A. I year students
of...
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 ... ()
22 2 2
22 2
12 12
22 2
12
12
1
2
2
n
n
XX x X
xx xxx
xx
xx x
∂∂ δ ∂
δ+δ++δ+δδ++
∂∂
∂∂ δ
Errors δx
1
, δx
2
, , δx
n
all are small so that th...
A textbook of Computer Based Numerical and Statiscal Techniques part 8 doc
... 1.796307
62
COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES
2.6.2 Rate of Convergence of Iteration Method
Let f(x) = 0 be the equation which is being expressed as x = g(x). The iterative formula for ... (3.7 781 5) = 3. 788 63
ALGEBRAIC AND TRANSCENDENTAL EQUATION
65
Example 5. Find the real root of equation f(x) = x
3
+ x
2
– 1 = 0 by using iteration method.
Sol. Here...
A textbook of Computer Based Numerical and Statiscal Techniques part 9 docx
... 66
COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES
Putting i = 2 in (1) x
3
= 0.024 39
Therefore reciprocal of 41 is 0.0244.
Example 8. Find the square root of 20 correct to 3 decimal places ... 1.22 39
x
2
= φ(x
1
) = 1 +
() () () ()
−+−
2345
2222
(1.22 39) (1.22 39) (1.22 39) (1.22 39)
2! 3! 4! 5!
+ = 1.3263
70
COMPUTER BASED NUMERICAL AND STATISTICAL TECHN...
A textbook of Computer Based Numerical and Statiscal Techniques part 13 doc
...
∇
and
4
log 50 = 0.0508
∇−
Example 10. Given that:
12345678
1 8 27 64 125 216 343 512
x
y
Construct backward difference table and obtain
4
()
f8∇
.
108
COMPUTER BASED NUMERICAL AND STATISTICAL ...
2
2
()
d
fx
dx
and so on.
The operator ∆ is an analogous to the operator D of differential calculus. In finite differences,
we deal with ratio of simultaneous increments o...
A textbook of Computer Based Numerical and Statiscal Techniques part 15 doc
... 12.
Similarly we have obtained
∆
3
u
0
= 6 and
∆
4
u
0,
∆
5
u
0
, are all zero as
u
r
=
r
3
is a polynomial
of third degree.
130
COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES
PROBLEM ... ax
−
−−
=
0
!
n
n
nhax
=
!
n
n
nha
132
COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES
Hence, we have nth difference of the polynomial is constant and so a...
A textbook of Computer Based Numerical and Statiscal Techniques part 21 docx
... = 0.047875
190
COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES
Example 4. Use Gauss’s forward formula to find a polynomial of degree four which takes the
following values of the function ... No. of Persons earning wages between Rs. 60 to 70 is 423.59375 – 370 = 53.59375 or
54000. (Approx.)
186
COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES
Take the mean o...
A textbook of Computer Based Numerical and Statiscal Techniques part 31 docx
... DIFFERENTIATION
The method of obtaining the derivatives of a function using a numerical technique is known as
numerical differentiation. There are essentially two situations where numerical differentiation ... Newton
forward formula, and if the same is required at a point near the end of the set of given tabular
294
INTERPOLATION WITH UNEQUAL INTERVAL
289
Example 1. Obta...
A textbook of Computer Based Numerical and Statiscal Techniques part 34 docx
... +6(0.3777)]
316
COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES
6.5 TRAPEZOIDAL RULE
Putting n =1 in equation (2) and taking the curve y = f(x) through (x
0
, y
0
) and (x
0
, y
0
) as a polynomial
of ... 1.3661 7341 3. Ans.
324
COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES
Example 6. Evaluate the integral
6
3
0
1
dx
x+
∫
by using Weddle’s rule.
Sol. Div...
A textbook of Computer Based Numerical and Statiscal Techniques part 36 docx
... 218295
13
afa f
or x ≤ .988.
340
COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES
Example 10. Obtain y when x = 0.1, x = 0.2 Given that
;
dy
xy
dx
=+
y(0) = 1, Check the result
with exact value.
Sol. ... integrate.
Thus, when,
()
1
0.1, 1 0.1 2log 1.1 0.9828
xy
==−+ =
. Ans.
Here in this example, only I approximation can be obtained and so it gives that approximate
value of...
A textbook of Computer Based Numerical and Statiscal Techniques part 37 doc
... Using Picard’d method, obtain the solution of
()
()
3
1;03
dy
xxyy
dx
=+ =
Compute the value of
()
0.1y
and
()
0.2y
.[Ans. 3.005, 3.020]
348
COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES
Now, ... simply replace
()
000
,,
xyz
by
()
111
,,
xyz
in the above formulae.
350
COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES
Since,
() ()
34
11
1.039473,
yy==...
A textbook of Computer Based Numerical and Statiscal Techniques part 45 doc
... 434
COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES
Sol. Calculation of 5 yearly moving averages
Year Value 5 Yearly 5 Yearly Moving
Moving Total Averages (trend value)
1971 105 ... of one year or shorter. The major factors
that cause seasonal variations are climate and weather conditions, customs and habits of
people, religious festivals, etc. For instance, the demand...
A textbook of Computer Based Numerical and Statiscal Techniques part 47 doc
... other hand graphs are more obvious, precise and
accurate than the diagrams and are quite helpful to the mathematician for the study of
slopes, rate of change and estimation i.e., interpolation and ... types:
(a) Qualitative Forecasting: Qualitative forecasting is used when past data is not available.
(b) Quantitative Forecasting: Quantitative forecasting is used if historical or...
A textbook of Computer Based Numerical and Statiscal Techniques part 60 docx
... INTERPOLATION
METHOD
Step 1. Start of the program to interpolate the given data
Step 2. Input the value of n (number of terms)
Step 3. Input the array ax for data of x
Step 4. Input the array ay for data of y
Step ... interpolate the given data
Step 2. Input the value of n (number of terms)
Step 3. Input the array ax for data of x
Step 4. Input the array ay for data of y
Ste...
Từ khóa: