the appropriate application of computer aided design and manufacture techniques in silicone facial prosthetics
A study on the teachers' application of task-based method and the 10th form students' use of learning strategies in their listening lessons at Tran Phu High Sch
... the listening texts, and glance at the answers of the tasks in advance B Read the listening section in the textbook, guess the content of the listening text, look at the demand of the tasks in ... students to engage in various kinds of tasks; and (5) interesting, the contents of the listening texts are familiar with the students and succeed in drawing their interest As said in the previous chapter, ... challenged the theories in the 1960s and concluded that there was a very poor match between the kind of language found in the inputs learners received and the kind of language they themselves...
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A textbook of Computer Based Numerical and Statiscal Techniques part 62 docx
... Enter the value of x3 – 11 Enter the value of x4 – 13 Enter the value of x5 – 17 Enter the value in the form of y– Enter the value of y1 – 150 597 598 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES ... Step Start of the program for numerical integration Step Input the upper and lower limits a and b Step Step Obtain the number of subinterval by h = (b–a)/n Input the number of subintervals Step ... Step Start of the program for numerical integration Step Input the upper and lower limits a and b Step Obtain the number of subinterval by h = (b–a)/n Step Input the number of subintervals Step...
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A textbook of Computer Based Numerical and Statiscal Techniques part 1 ppt
... Preface The present book Computer 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 ... algorithm and computer program in Clanguage to understand the steps and methodology used in writing the program Thorough care has been taken to eradicate errors but perfection cannot be claimed The ... large number of examples in the best possible way have been discussed in detail and lucid manner so that the students should feel no difficulty to understand the subject A unique feature of this book...
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A textbook of Computer Based Numerical and Statiscal Techniques part 2 ppsx
... assumptions in the mathematical formulation of the problem or due to the errors in the physical measurements of the parameters of the problem Inherent error can be minimized by obtaining better ... data, by using high precision computing aids and by correcting obvious errors in the data Round-off Error: The round-off error is the quantity, which arises from the process of rounding off numbers ... are added then the magnitude of absolute error in the result is the sum of the magnitudes of the absolute errors in that numbers 1.4.2 Error in Subtraction of Numbers Let X = x1 – x2 then we have...
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A textbook of Computer Based Numerical and Statiscal Techniques part 3 ppsx
... significant figures Example 13 Find the relative error in the calculation of 3.724 × 4.312 and determine the interval in which true result lies Given that the numbers 3.724 and 4.312 are correct to ... places are 0.1429 and 0.0909 11 respectively Find the possible relative error and absolute error in the sum of 0.1429 and 0.0909 Example Approximate values of Sol The maximum error in each case = ... 0.004016=16.061904 Hence true value lies between 16.0539 and 16.0619 Example 14 Find the absolute error in calculating (768)1/5 and determine the interval in which true value lies 768 is correct its last...
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A textbook of Computer Based Numerical and Statiscal Techniques part 4 ppt
... FLOATING POINT The IEEE floating-point standards prescribe precisely how floating-point numbers should be represented, and the results of all operations on floating point numbers There are two standards: ... if all the 47 numerical quantities are rounded-off [Hint: on taking ea
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A textbook of Computer Based Numerical and Statiscal Techniques part 5 ppsx
... division of mantissa of the numerator by that of the denominator and denominator exponent is subtracted from the numerator exponent The resultant exponent is obtained by adjusting it appropriately and ... valid in case of normalized floatingpoint representation Give example to prove this statement Sol According to the consequence of the normalized floating-point representation the associative and the ... 0.1823e3] 33 ERRORS AND FLOATING POINT 10 Give example to show that most of the laws of arithmetic fail to hold for floating-point arithmetic 11 Find the root of smaller magnitude of the equation x2...
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A textbook of Computer Based Numerical and Statiscal Techniques part 6 pptx
... value of the roots x7 and x8, we observed that, up to two places of decimal, the root is 2.74 approximately Example Using Bisection Method, find the real root of the equation f(x) = 3x – Sol + sin ... Thus the Bisection Method is first order convergent or linearly convergent Example Find the root of the equation x3 – x – = lying between and by bisection method Sol Let f(x) = x3 – x – = Since and ... 0.14184 then, f ( x2 ) = (1.78125)3 − 1.78125 − = − 0.12960 Since f(1.78125) is negative and f(1.8125) is positive, therefore the root lies between 1.78125 and 1.8125 Repeating the process, the successive...
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A textbook of Computer Based Numerical and Statiscal Techniques part 7 potx
... constant (5) f ′ (α ) In order to find the order of convergence, it is necessary to find a formula of the type ei + = Ae k with an appropriate value of k i .(6) With the help of (6), we can write ... 52 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES Since f(2) and f(3) are of opposite signs, therefore the root lies between and 3, so taking x0 = 2, x1 = 3, f(x0) = – 9, f(x1) = 1, then ... 0.10203 Since, x3 and x4 are approximately the same upto four places of decimal, hence the required root of the given equation is 1.4036 54 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES...
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A textbook of Computer Based Numerical and Statiscal Techniques part 8 doc
... Which of these, if any, would succeed and which would fall to give root in the neighbourhood of 0.5 Example The equation sin x = 5x – can be put as x = sin–1 (5x – 2) and also as x = Sol In First ... 1.796321 Since x2 and x3 are same up to decimal places hence the required root is 1.7963 correct up to four decimal places Example Find the root of the equation tan x + tan h x = which lies in the interval ... = g(xi) If a is the root of the equation x = g(x) lying in the interval ]a,b[, α = g (α) The iterative formula may also be written as ( xi + = g x + xi − α ) Then by mean value theorem xi + =...
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A textbook of Computer Based Numerical and Statiscal Techniques part 9 docx
... Similarly, PROBLEM SET 2.3 Use the method of Iteration to find a positive root between and of the equation xex – [Ans 0.5671477] Find the Iterative method, the real root of the equation 3x – log10 x ... Method to Find the Root of the Equation f (x) = Step 1: Take a trial solution (initial approximation) as x0 Find f(x0) and f ′(x0) Step 2: Find next (first) approximation x1 by using the formula ... each step is proportional to the square of the previous error and as such the convergence is quadratic Example Find the real root of the equation x2 – 5x + = between and by NewtonRaphson’s method...
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A textbook of Computer Based Numerical and Statiscal Techniques part 10 ppt
... Geometrically, in Secant method we replace the function f ( x) by a straight line passing through the points ( xn , f ( x n )) and ( xn −1 , f ( xn −1 )) and take the point of intersection of the straight ... method to find a root of the equation x3 – 3x – = (U.P.T.U 2005) [Ans 2.279] Find the four places of decimal, the smallest root of the equation e–x = sin x [Ans 0.5885] Find the cube root of 10 [Ans ... On comparing the powers of εn , we have p= or 1+ p p p2 – p – = 1+ 1− 1+ and Taking, p = = 1.618 and neglecting 2 the other, we obtain from equation (4), the rate of convergence for the Secant...
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A textbook of Computer Based Numerical and Statiscal Techniques part 11 pdf
... then the remainder terms must vanish, therefore the problem is then to find p and q such that R(p, q) = and S (p, q) = .(3) If we regularly change the values of p and q, we can make the remainder ... Find the quadratic factor of the equation x4 – 6x3 + 18x2 – 24x + 16 = using Bairstow’s method where p0 = – 1.5 and q0 = Also, find all the roots of the equation Sol Let the quadratic factor of ... of the equation be x2 + px + q Using Bairstow’s method we find the values of p and q First approximation: Let p0 and q0 be the initial approximations, then the first approximation can be obtained...
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A textbook of Computer Based Numerical and Statiscal Techniques part 12 pdf
... find the complex roots and multiple roots of polynomials and also for determining the Eigen values of a matrix An important feature of the method is that it gives approximate values of all the ... Calculus of Finite Differences 3.1 INTRODUCTION Finite differences: The calculus of finite differences deals with the changes that take place in the value of the dependent variable due to finite ... ∆1(2) can be computed since the other quantities are known (2) If a q-element is at the top, then the sum of one pair is equal to that of the other pair For example, in the rhombus ∆(1) q(0) q(1)...
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A textbook of Computer Based Numerical and Statiscal Techniques part 13 doc
... function is given by h Example Find the first term of the series whose second and subsequent terms are 8, 3, 0, –1, and Sol If the interval of differencing is unity, then f(1) = E–1f(2) = (1+ ∆)–1 ... Construct the backward difference table from the data: sin 30o = 0.5, sin 35o = 0.5736, sin 40o = 0.6428, sin 45o = 0.7071 Assuming third difference to be constant, find the value of sin 25° Sol ... CALCULUS OF FINITE DIFFERENCES Example Find the function whose first difference is ex Sol We know that ∆e x = e x −h − e x = e x (e h − 1) , where h is the interval of differencing Therefore,...
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A textbook of Computer Based Numerical and Statiscal Techniques part 14 ppsx
... CALCULUS OF FINITE DIFFERENCES (E − 2E + 1) sin( x + h ) sin( x + h ) = (E – + E–1) sin (x + h) + sin( x + h) − sin( x + h ) + sin( x + h ) = [sin (x + 2h) – sin (x + h) + sin x] + sin( x ... (2 sin ) sin [ax + b + + ] 2 2 ah + π ah = 2sin sin ax + b + On continuing in the same manner, we get 3( ah + π ) ah ∆ sin (ax + b) = 2sin sin ... COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES ∆2 Ee x Example 17 Show that ex = ex x ; the interval of differencing being h E ∆ e Sol Let f(x) = ex, then Ef (x) = f(x + h), therefore...
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A textbook of Computer Based Numerical and Statiscal Techniques part 15 doc
... zero., The errors in the column ∆iy are given by the coefficients of the binomial expansion (1 –δ)i In even differences columns of ∆2y, ∆4y, ., the maximum error occurs in a horizontal line in which ... which incorrct value of y lies In odd difference columns of ∆1y, ∆3y, , the maximum error lies in the two middle terms and the incorrect value of y lies between these two middle terms Example Find ... 50 Here the sum of all the third differences is zero and the adjacent values –3, are equal in magnitude Also horizontal line between –3 and points out the incorrect functional value 18 Therefore...
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A textbook of Computer Based Numerical and Statiscal Techniques part 16 ppsx
... 2.0170 find log 102 [Ans log 102 = 2.0086] Estimate the missing term in the following: x y ? 32 64 128 Explain why the result differs from 16 [Ans f(4) = 16.1] Find the first term of the series ... 30 ⇒ Again, y5 = 31 ∆4y2 = 16 then after solving, we get y6 = 129 and ∆4y3 = 16 gives y7 = 351 141 CALCULUS OF FINITE DIFFERENCES PROBLEM SET 3.2 Locate the error in the following table and correct ... ) = 0, ∀x (on taking interval of differencing being 1) On putting x = 0, we get f (4) − f (3) + f (2) − f (1) + f (0) = .(1) Substituting the value of f(0), f(1), f(2), f(4) in (1), we get 37...
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A textbook of Computer Based Numerical and Statiscal Techniques part 17 ppsx
... 2=A The following steps are to be followed in the method of synthetic division: Put the coefficients of different powers of x in order beginning with the coefficients of higher power of x Put in ... A and the remainder are = B Hence the required polynomial will be 2x(3) + 3x(2) + 2x − 10 We can also simplify the above in the following way: Taking the coefficients of various powers of x in ... get the sum 2, put below –3 as given in (a) Now multiply –3 by and by and add them to get the sum –1 which is to be written below The remainder –10 is the value of D Add the terms of corresponding...
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A textbook of Computer Based Numerical and Statiscal Techniques part 19 pptx
... + 0.000024 = 0.14959 Example In the following table, values of y are consecutive terms of a series of which 23.6 is the 6th term Find the first and tenth terms of the series x y 4.8 8.4 14.5 23.6 ... where A is the arithmetic mean of q and r and B is arithmetic between the arguments at q and r is A + 24 mean of 3q – 2p – s and 3r – 2s – p Sol Given A is the arithmetic mean of q and r q+r q ... formula to find (1) the number of students who got more than 55 marks (2) the number of students who secured marks in the range from 36 to 45 [Ans (i) 28, (ii) 36] From the following table of half-yearly...
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