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...

Ngày tải lên: 04/07/2014, 15:20

... 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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... = 0.86742. 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 ... shown in the figure. Apply Hermite’s interpolation formula to obtain this polynomial Sol. Since tangents are parallel to X-axis, y′ = 0 in both the cases. ∴ We have the table of values....

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... 1.6997 1 .399 7 3 =+ ++ = 364 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES which is same as the predicted value. ∴ 60.30 1 .399 7 yy== and 6 1.6997 y ′ = The result can be put in the tabular form x 0.20 ... 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 1...

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... 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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... 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. Tot...

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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 ... 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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... 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 ... 13.28 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 o...

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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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