By A.K. Jaiswal, Anju Khandelwal
Salient positive aspects of this paintings comprise: mathematical derivation of every strategy is given to construct the scholars knowing of numerical research; a number of solved examples are given; desktop courses for the majority numerical tools mentioned were offered in 'C' language; mistakes research for the majority equipment are offered; every one bankruptcy starts with an creation of involved subject; and, workout questions provide a chance to the scholars to check their knowing of the techniques.
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018%] 12. 001. [Ans. 006] 1 , x ∈ [1, 2] using 1 + x2 Taylor’s series expansion about x = 1. Find a bound on the truncation error. [Ans. 25] 13. Obtain a second-degree polynomial approximation to the function f(x) = 14. Find the number of terms in the series expansion of the function f(x) = cos x , such that their sum gives the value of cos x correct to five decimal places for all values of x in the range − π π ≤ x ≤ + . Find also the truncation error. 2 2 [Ans. n = 6, Trun. 6 SOME IMPORTANT MATHEMATICAL PRELIMINARIES There are some important mathematical preliminaries given below which would be useful in numerical computation.
Digit normalized form of Sol. 6666666; Result after chopping 3 In computers, each location called word in memory stores only a finite numbers of digits. If we assume computer memory store 6 digits in each location and also store one or more signs then to represent real number, computer assumed a fixed position for the decimal point and all numbers are stored after appropriate shifting with an assumed decimal point. 01. These maximum and minimum limits for numbers are in magnitude. For this purpose, preserve the maximum number of significant digits in a real number and increase the range of values for that real number.
Sol. Let d is the diameter of a circle, and then its area is given by A = πd 2 . 05 · πd 4d 2 Example 32. 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. 055 cm. 049 cm. 006 radians. 5 × 3 2 2 2 ∂A Example 33. 7 cm and ∠ B = 90o. If possible errors in the computed value of b and a are 2 mm and 1 mm respectively, find the possible error in the measurement of angle A. Sol. 7276 Example 34. In a triangle ∆ABC, a = 30 cm, b = 80 cm and ∠ B = 90o.
A Textbook of Computer Based Numerical and Statistical Techniques by A.K. Jaiswal, Anju Khandelwal