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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... 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 ... between 1.6866 and 2. 50 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES and f(3) = (3) 3 – 2(3) – 5 = 16 Therefore, a root lies betw...

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... () [] 0.05 1.2 428 1.4 428 6.2724 1.6997 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 ... differential equation () , dy yfxy dx ′ == by this method we first obtain the approximate value of 1n y + by Predictor formula and then improve the value of 1n...

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... 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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... method of least squares a parabola of the type 2 yabx=+ . Sol. Error of estimate for i th point (,) ii xy is () 2 ii i eyabx =−− By the principle of least squares, the values of a and b are ... = ∑ 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 4A...

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... 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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... 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. T...

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... 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 ... 151.29 538 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES (A 1 B 1 ) 0 = AB N 12 bgbg = 285 0 1000 2985 afaf × = 954.77; (A 1 B 2 ) 0 = AB N 12 bgbg = 285 0 990...

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... 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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... 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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