A textbook of Computer Based Numerical and Statiscal Techniques part 31 docx
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 4 ppt
... 32. In a ∆ABC, b = 9.5 cm, c = 8.5 cm and A = 45 o , 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 the ∆ABC be ... standards: IEEE 7 54 is for binary arithmetic, and IEEE 8 54 covers decimal arithmetic as well. The only IEEE 7 54, adopted almost universally by computer manufacturers. U...
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A textbook of Computer Based Numerical and Statiscal Techniques part 5 ppsx
... 0 .55 55e1, b = 0. 454 5e1, c = 0. 453 5e1 then (b – c) = 0.0010e1 = 0.1000e – l a( b – c) = (0 .55 55e1) × (0.1000e – 1) = (0. 055 5e0) = 0 .55 50e – 1 ab = (0 .55 55e1) × (0. 454 5e1) = 0. 252 4e2 ac = (0 .55 55e1) ... roots of the equation, obtained by x 1 = 2 22 44 and 22 bb ac bb ac aa −+ − −− − =x These are called closed form solution. Similar formulae are also available for cubic...
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A textbook of Computer Based Numerical and Statiscal Techniques part 6 pptx
... between 0 .65 7 and 0 .66 5. Eighth approximation: The eighth approximation to the root is given by 8 0 .65 7 0 .66 5 0 .66 1 2 x + == From last two approximations, i.e., 7 0 .6 65 x = and 8 0 .6 61 x = ... positive. Therefore f (0 .67 3) is positive and f(0 .65 7) is negative so the root lies between 0 .65 7 and 0 .67 3. ALGEBRAIC AND TRANSCENDENTAL EQUATION 41 Seventh approxi...
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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 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...
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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...
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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...
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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...
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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...
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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...
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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...
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