A textbook of Computer Based Numerical and Statiscal Techniques part 43 pot
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...
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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...
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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...
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A textbook of Computer Based Numerical and Statiscal Techniques part 3 ppsx
... Approximate value (x′) = 0 .33 3 Therefore, Absolute Error, 1 0 .33 3 0 .33 333 3 0 .33 3 0.00 033 3 3 a Exx ′ =− =− = − = Relative Error, E r = 0.00 033 3 0.000999 0 .33 333 3 a E x == and Percentage Error, E p = ... second decimal places. Example 4. If 0 .33 3 is the approximate value of 1 3 , then find its absolute, relative and percentage errors. Sol. Given that True val...
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A textbook of Computer Based Numerical and Statiscal Techniques part 7 potx
... 1.4036 0.10203 = Since, x 3 and x 4 are approximately the same upto four places of decimal, hence the required root of the given equation is 1.4036. 48 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES Using ... 4 .79 77 – 4.8446 = – 0.0469 Thus, the root lies between 1.6866 and 2. 50 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES and f(3) = (3...
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A textbook of Computer Based Numerical and Statiscal Techniques part 23 pot
... 206 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES 7. Apply Stirling’s formula to find a polynomial of degree four which takes the values of y as given below: x y −− 1234 5 11111 [Ans. 42 28 1 33 uu−+ ] 8. ... 1 – .25 = 0.75 214 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES 7. Apply Bessel’s interpolation formula, show that tan160° = 0.2867, Given that:...
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A textbook of Computer Based Numerical and Statiscal Techniques part 28 potx
... = 0.86742. Ans. Example 4. A switching path between parallel railroad tracks is to be a cubic polynomial joining positions (0,0) and (4,2) and tangent to the lines y = 0 and y = 2 as shown in ... Hermite’s interpolation formula. () () () () () () xfx fx afa fa bfb fb ′ ′ ′ INTERPOLATION WITH UNEQUAL INTERVAL 261 Example 1. Apply Hermite’s interpolation formula to obtain a polynomi...
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A textbook of Computer Based Numerical and Statiscal Techniques part 33 pot
... 32.98 33. 54 33. 97 33. 48 32.13 t x Evaluate dx dt at t = 0.1 and at t = 0.5 [Ans. 32.44166 cm/sec.; −24.05 833 cm/sec.] 9. A rod is rotating in a plane. The following table gives the angle θ (radians) ... a table, but no mathematical relationship between them is known as is often the case with experimental data. 6.4 GENERAL QUADRATURE FORMULA Let ()yfx= be a function, w...
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A textbook of Computer Based Numerical and Statiscal Techniques part 38 potx
... 1.3997 3 =+ ++ = 364 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES which is same as the predicted value. ∴ 60.30 1.3997 yy== and 6 1.6997 y ′ = The result can be put in the tabular form x 0.20 ... Methods Predictor-Corrector formulae are easily derived but require the previous evaluation of y and () 1 , yfxy = at a certain number of evenly spaced pivotal point (disc...
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A textbook of Computer Based Numerical and Statiscal Techniques part 39 potx
... value y i and the true value y(x i ) at any stage is known as the total error. The total error at any stage is comprised of truncation error and round-off error. The most important aspect of ... DIFFERENTIAL EQUATION 371 Inherent stability is determined by the mathematical formulations of the problem and is dependent on the eigen values of Jacobian Matrix of the differential...
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A textbook of Computer Based Numerical and Statiscal Techniques part 42 potx
... normal equations are given by 2 0 S ynab x a ∂ =⇒ = + ∂ ∑∑ (1) 224 0 S xy a x b x b ∂ =⇒ = + ∂ ∑∑∑ (2) 404 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES Here 6n = Normal equations are, 17.25573 ... = ∑ x 2 300 = ∑ xY ∑ Substituting the values of x ∑ , etc. and calculated by means of above table in the normal equations. We get, 5.7536 = 5A + 34B and 40.8862 = 3...
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A textbook of Computer Based Numerical and Statiscal Techniques part 43 pot
... n ≤≤ and 1}jn≤≤ be a bivariate distribution. If we plot the corresponding values of x and ,y taking the values of x along x-axis and the values of y along y-axis, we obtain a collection of ... [Ans. 2 13 22 yx=+ ] 410 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES Example 3. Prove that arithmetic mean of the coefficient of regression is greater t...
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A textbook of Computer Based Numerical and Statiscal Techniques part 54 potx
... that the sailors are on the average taller than soldiers? [Ans. Highly significant] 22. The yield of wheat in a random sample of 1000 farms in a certain area has a S.D. of 192 kg. Another random ... 516 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES where x 1 be the mean of a sample of size n 1 from a population with mean µ 1 and variance σ 1 2. x 2...
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A textbook of Computer Based Numerical and Statiscal Techniques part 55 potx
... E(c)= accd N ++ bgbg and E(d)= bdcd N ++ bgbg abab cdcd ac bd N + + ++ ∴ χ 2 = aEa Ea bEb Eb cEc Ec dEd Ed –––– af af af af af af af af 2222 +++ (2) a – E (a) =a – abac N ++ bgbg = a a b c d a ac ... expected frequencies of the accidents on each of the days would be: 528 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES Days Sun. Mon. Tues. Wed. Thus. Fri. Sat. Tot...
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A textbook of Computer Based Numerical and Statiscal Techniques part 56 potx
... sample size is less than equal to 30 (≤ 30) and the population standard deviation is unknown. Let X i , i = 1, 2, , n be a random sample of size n from a normal population with mean µ and variance ... highly significant. Hence we reject the null hypothesis. Example 16. A machinist is making engine parts with axle diameters of 0.700 inch. A random sample of 10 parts shows a...
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