Engineering B.E. (Computer Engineering) Sem 3 Engineering Mathematics III Dec 2019 R16 Question Paper - Mumbai University | munotes
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Questions asked in this paper
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Q2 Attempt any three from the remaining six questions
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Q3 Figures to the right indicate full marks
- b. If f(z) = (x* + axy + + i(cx* + dxy + is analytic find a,b,c and d
- c. Find the Fourier series expansion of f(x) = x* (—7,7)
- d. If the two regression equations are 4x — 5y + 33 = 0,20x — 9y — 107 = 0 find i) the mean values of x and y 1i) the Correlation Coefficient 111) Standard deviation of y if variance of x is 9
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Q2 a. Show that the function is Harmonic and find the Harmonic Conjugate
- c. Find Fourier Series expansion of f(x) = x -1<x<0
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Q3 a. Find the Analytic function ifu—v — siny) 6 marks
- b. Find Inverse Z transform of <3 6
- c. Solve the Differential Equation using Laplace transform
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Q4 a. Find the Complex Form of Fourier Series for f(x) = cosax 6 marks
- b. Find the Spearman’s Rank correlation coefficient between X and Y. 6
- c. Find the inverse Laplace transform of 8
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Q5 a. Find the Z{f(k)} where f(k) = ,k <0 6 marks
- b. Show that {cosx is orthogonal set over the interval Construct the corresponding orthonormal set. [6]
- c. Find the bilinear transformation which maps the points z = —1 into the points w Hence find the image of |z| <1. [8]
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Q6 a. Fit a straight line to the given data 6 marks
- c. Find Half Range Cosine Series for = sinx in (0,2) and hence deduce that
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