A textbook of Computer Based Numerical and Statiscal Techniques part 32 pps
A textbook of Computer Based Numerical and Statiscal Techniques part 32 pps
... at equidistant and we want to find the value of y at x = 1.1. Therefore, we apply Newton’s forward difference formula. 304 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES Here we have to find ... 0.048 1.8 2. 4320 0. 432 1.5680 2.0 4.0000 298 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES 6.2.3 Derivatives Using Stirling’s Formula If we want to determine the...
Ngày tải lên: 04/07/2014, 15:20
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...
Ngày tải lên: 04/07/2014, 15:20
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...
Ngày tải lên: 04/07/2014, 15:20
A textbook of Computer Based Numerical and Statiscal Techniques part 5 ppsx
... 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 and biquadratic polynomial ... 26 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES The basic operations specified by IEEE arithmetic are first and foremost addition, subtraction, multiplication, and div...
Ngày tải lên: 04/07/2014, 15:20
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...
Ngày tải lên: 04/07/2014, 15:20
A textbook of Computer Based Numerical and Statiscal Techniques part 16 ppsx
... given a set of equidistant values of arguments and its corresponding value of f(x). Suppose for n + 1 equidistant argument values x = a, a + h, a + 2h, , a + nh, are given. 140 COMPUTER BASED NUMERICAL ... 22 1 2 n nn an bn c n a n b n a n − −++−∆+∆+∆ 142 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES 9. Evaluate the production of wool in t...
Ngày tải lên: 04/07/2014, 15:20
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+ ∆...
Ngày tải lên: 04/07/2014, 15:20
A textbook of Computer Based Numerical and Statiscal Techniques part 22 pps
... 0.25 = 32. 625 thousands Hence, the population in 1936 is 326 25 thousand. 196 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES Example 5. If f(x) is a polynomial of degree four find the value of ... 16.047 x x y [Ans. 19.704] 202 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES Example 4. Apply Stirling’s formula to find a polynomial of degree three whic...
Ngày tải lên: 04/07/2014, 15:20
A textbook of Computer Based Numerical and Statiscal Techniques part 25 ppsx
... f(x 2 ) = 13 and f(x 3 ) = 17.5 also, find the value of f(5) 232 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES Example 8. Prove that Lagrange’s formula can be expressed in the () () () () 2n n 2n 0000 2n 1111 2n nnnn P ... interpolation formula. Sol. We are given () :78910 :311 9 x fx 226 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES Example 1. Using Lagr...
Ngày tải lên: 04/07/2014, 15:20
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...
Ngày tải lên: 04/07/2014, 15:20