A textbook of Computer Based Numerical and Statiscal Techniques part 51 ppsx
A textbook of Computer Based Numerical and Statiscal Techniques part 51 ppsx
... cm = = = GGG 486 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES Negative LCL being taken as zero. Also for drawing the control chart we mark the sample No.’s along the horizontal axis and control ... statistical hypothesis, otherwise it is called a composite statistical hypothesis. Example: If X 1 , X 2 , , X n is a random sample of size n from a normal pop...
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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 ... significant figures at each step of computation. At each step of computations, retain at least one more significant figure than that given in the data, perform the last...
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A textbook of Computer Based Numerical and Statiscal Techniques part 3 ppsx
... 3 Hence maximum percentage error (E p ) max = 11.667%. Example 26. How accurately should the length and time of vibration of a pendulum should be measured in order that the computed value of g is ... 4008 and 30.4647 + 0.0639 = 30.5286. Example 12. Find the product of 346.1 and 865.2 and state how many figures of the result are trustworthy, given that the numbers are corr...
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A textbook of Computer Based Numerical and Statiscal Techniques part 5 ppsx
... 26 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES The basic operations specified by IEEE arithmetic are first and foremost addition, subtraction, multiplication, and division. Square roots ... + a n –1 x + a n where a s are constant (a 0 ≠ 0) and n is a positive integer, is called a polynomial in x of degree n, and the equation f (x) = 0 is called an algebr...
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A textbook of Computer Based Numerical and Statiscal Techniques part 14 ppsx
... 122 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES Example 22. Evaluate: ∆ n [sin (ax + b)] Sol. We know f∆ (x) = f(x + h) – f (x) therefore ∆ sin (ax + b) = sin [a (x + h)+b] – sin)(ax ... hD hD hD 116 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES Example 14. Evaluate the following: I. ∆ 2 (cos 2x) II. ∆ 2 (3e x ) III. ∆ tan –1 x IV. ∆(x + cos x) the inte...
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A textbook of Computer Based Numerical and Statiscal Techniques part 16 ppsx
... Suppose for n + 1 equidistant argument values x = a, a + h, a + 2h, , a + nh, are given. 140 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES Sol. For the given data, difference table is: ∆∆ ∆ ∆ − − − − − − ∆ ∆ ∆∆ ∆ ∆∆ ∆ ∆ 234 3 2 2 3 3 43 2 54 3 54 2 65 6 7 01 2 11 ... 0f−+×−×+= 138 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES i.e., 4f(3) = 124 i.e., f(3)...
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A textbook of Computer Based Numerical and Statiscal Techniques part 17 ppsx
... R.H.S. 3.9 FACTORIAL NOTATIONS The product of n consecutive factors each at a constant difference and the first factor being x is called a factorial function or a factorial polynomial of degree n and ... L.H.S. 150 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES CorCor CorCor Cor ollary:ollary: ollary:ollary: ollary: To show that, () n n x ∆ = n! h n and 1n+ ∆...
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A textbook of Computer Based Numerical and Statiscal Techniques part 25 ppsx
... interpolation formula. Sol. We are given () :78910 :311 9 x fx 226 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES Example 1. Using Lagrange’s formula, find the value of (i) y x if y 1 ... required polynomial. Example 4. Value of f(x) are given at a, b, c. Show that the maximum is obtained by x = () ( ) () ( ) () ( ) () () () () () () fa b c fb c a fc a b fa b c fb...
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A textbook of Computer Based Numerical and Statiscal Techniques part 26 ppsx
... differences where as the difference defined earlier are called ordinary differences. Lagrange’s interpolation formula has the disadvantage that if any other interpolation point were added, the interpolation co-efficient ... (5) 244 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES Example 10. Show that the sum of Lagrangian co-efficients is unity. Sol. Let () x ∏ = () () () 01...
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A textbook of Computer Based Numerical and Statiscal Techniques part 29 ppsx
... co-efficients a 1 , a 2 a n will produce little error for small x near zero. But probably substantial error near the ends of the interval 268 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES 7. Apply ... approximation to a given function. For evaluating a function f(x) on a computer it is generally more efficient of space and time to have an analytic approxi...
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