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A textbook of Computer Based Numerical and Statiscal Techniques part 10 ppt

A textbook of Computer Based Numerical and Statiscal Techniques part 10 ppt

A textbook of Computer Based Numerical and Statiscal Techniques part 10 ppt

... next approximation can be obtained by using the values of x1 and x2 in Secantmethod. Similarly, other approximations can be obtained by using two recent values of approximations. These arex3= ... f(x5) = – 0.00002ALGEBRAIC AND TRANSCENDENTAL EQUATION77Since, imaginary roots occur in conjugate pairs roots are 1.915 ± 1.908i upto 3 places of decimal. Assuming other pair of roots to be α ... root can be taken as 2.0945 correct up to four decimals.ALGEBRAIC AND TRANSCENDENTAL EQUATION796. Using N–R method, obtain formula for N and find 20 correct to two decimal places.[Ans....
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A textbook of Computer Based Numerical and Statiscal Techniques part 1 ppt

A textbook of Computer Based Numerical and Statiscal Techniques part 1 ppt

... This pageintentionally leftblankThis pageintentionally leftblank A TEXTBOOK OF COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES Anju Khandelwal M.Sc., Ph.D.Department of MathematicsSRMS ... Based Numerical and Statistical Techniques is primarily writtenaccording to the unified syllabus of Mathematics for B. Tech. II year and M.C .A. I year students of all Engineering colleges affiliated ... affiliated to U.P. Technical University, Lucknow.The subject matter is presented in a very systematic and logical manner. In each chapter, allconcepts, definitions and large number of examples...
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A textbook of Computer Based Numerical and Statiscal Techniques part 4 ppt

A textbook of Computer Based Numerical and Statiscal Techniques part 4 ppt

... 0.10.0542ddd·Example 32. In a ∆ABC, b = 9.5 cm, c = 8.5 cm and A = 45o, find allowable errors in b, c, and A such that the area of ∆ABC may be determined nearest to a square centimeter.Sol. Let area of ... semantics are also specified in detail by the IEEE standards, are notalways handled the same way. It turns out that many manufacturers believe (sometimes rightly and sometimes wrongly) that ... Given δb = 2 mm = 0.2 cm a = 1 mm = 0.1 cmsin A = −⇒=1sin a a A bb∂∂ A a= 222211 11babab⋅=−−∂∂ A b= 2222211aababbab⋅− =−−− A < AAabaa∂∂δ+δ∂∂22 2212.30.1...
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A textbook of Computer Based Numerical and Statiscal Techniques part 6 pptx

A textbook of Computer Based Numerical and Statiscal Techniques part 6 pptx

... negative.Thus f(0.5) is negative and f(1) is positive. Then the root lies between 0.5 and 1.40 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES Second approximation: The second approximation to the root ... f(0) is negative and f(1) is positive, therefore, a root lies between 0 and 1.ALGEBRAIC AND TRANSCENDENTAL EQUATION37Here ei and ei + 1 are the errors in ith and (i + 1)th iterations respectively. ... Root of the Equation f(x) = 0Step 1: Choose two initial guess values (approximation) a and b (where (a > b)) such thatf (a) . f(b) < 0.Step 2: Evaluate the mid point x1 of a and...
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A textbook of Computer Based Numerical and Statiscal Techniques part 19 pptx

A textbook of Computer Based Numerical and Statiscal Techniques part 19 pptx

... the argument half waybetween the arguments at q and r is +B A, 24 where A is the arithmetic mean of q and r and B is arithmeticmean of 3q – 2p – s and 3r – 2s – p.Sol. Given A is the arithmetic ... 0.7880Example 7. Following are the marks obtained by 492 candidates in a certain examination:04040454550505555606065. 2104 354743279MarksNo of Candidates−−−−−−Find out (a) No. of candidates, ... r and s corresponds to argument a, a + h, a + 2h and a + 3h respectivelythen the value of the argument lying half way between a + h and a + 2h will be a + h + 2h i.e., a + 32hHence,a...
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A textbook of Computer Based Numerical and Statiscal Techniques part 20 pptx

A textbook of Computer Based Numerical and Statiscal Techniques part 20 pptx

... gives bestestimation when 11.44u−< This formula is obtained by taken mean of Gauss forward and Gaussbackward difference formula.Gauss forward formula for interpolating central difference ... 4!−− −−+−+ = 147.2251 Approx.Example 5. In an examination, the number of candidates who obtained marks between certain limitsare as follows:MarksNo of candidates−−−−−0192039405960798099. ... ×−= 235 – 24.65 – 10. 76625 – 1.076625= 235 – 36.492875= 198.507 { 198∴ Total no. of candidates who obtained fewer than 70 marks are 198.Example 6. The area A of a circle of diameter d is given...
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A textbook of Computer Based Numerical and Statiscal Techniques part 27 ppt

A textbook of Computer Based Numerical and Statiscal Techniques part 27 ppt

... result.Example 7. The following are the mean temperatures (°F) on three days, 30 days apart round the pds. of summer and winter. Estimate the app. dates and values of max. and min. temperature.INTERPOLATION ... differences of a polynomial of nth degree are constant.Let f(x) = A 0xn + A 1xn–1 + + A n–1 x + A n by a polynomial of degree n provided A 0 ≠ 0 and arguments be equally spaced so thatx1 ... of 20th Jan. and its value can be obtained similarly.[f(x)]min = [f(x)]1.184 = 63.647 °F approximately.Example 8. The mode of a certain frequency Curve y = f (x) is very near to x = 9 and...
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A textbook of Computer Based Numerical and Statiscal Techniques part 30 pptx

A textbook of Computer Based Numerical and Statiscal Techniques part 30 pptx

... BASED NUMERICAL AND STATISTICAL TECHNIQUES after simplication, we get() () () () ()+++ =∫∫ ∫∫01 bb b bnnaa a a a wxdx a xwxdx a xwxdx wxfxdx() () () () ()2101 bb b bnnaa a a a xw ... dxa xdxa xdxa xdx 111135/2 2 40120000x dxa xdxa xdxa xdx=++∫∫∫∫or Simplifying above equations, we get12001201222332234523457aa a aaaaaa++=++ =++=284 COMPUTER BASED NUMERICAL ... NUMERICAL AND STATISTICAL TECHNIQUES Minimax polynomial approximation: Let f(x) be continuous on [a, b] and it isapproximated by the polynomial Pn (x) = a 0 + a 1x + +a nxn , then the minimax...
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A textbook of Computer Based Numerical and Statiscal Techniques part 35 pptx

A textbook of Computer Based Numerical and Statiscal Techniques part 35 pptx

... numerical solutions of differential equations. In researches,especially after the advent of computer, the numerical solutions of the differential equations havebecome easy for manipulations. Hence, ... the values of 1y and its derivativies in Taylor series expansion, we obtain ()()()()23 10 10 1101 1 1 2! 3!xx xxyx y x x y y y−−′ ′′ ′′′=+ − + + +330 COMPUTER BASED NUMERICAL AND ... below some of the methods of numerical solutions of the ordinary differential equations. No doubt, such numerical solutions are approxi-mate solutions. But, in many cases approximate solutions...
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A textbook of Computer Based Numerical and Statiscal Techniques part 40 pptx

A textbook of Computer Based Numerical and Statiscal Techniques part 40 pptx

... sensitiveto small changes in A and B i.e., small change in A or B causes a large change in the solution of the system. On the other hand if small changes in A and B give small changes in the solution,the ... find that 12 iteration are necessary in Gauss-Jacobi Method to get the same accuracyas achieved by 7 iterations in Gauss-Seidel method.SOLUTION OF SIMULTANEOUS LINEAR EQUATION385Example 8. ... coefficient matrix are diagonally dominant.10x + y – 2z = 7.74x + 12y + 3z = 39.663x + 4y + 15z = 54.8376 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES largest coefficient of y. We continue...
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