Engineering BE Electronics and Computer Science Sem 3 December 2018 2018 Applied Mathematics III Question Paper - Mumbai University | munotes
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Questions asked in this paper
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Q2 Attempt any three questions from the remaining five questions
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Q3 Figures to the right indicate full marks
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Q1 Evaluate e dt. 5 marks
- b) an analytic function f(z) = u + iv where 05 Obtain Fourier series of x cosx in (—7, 7). 05 along the parabola y? = x
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Q2 Find half-range cosine series for f(x) = e*, 0< <1. 6 marks
- b) that 06 is solenoidal and determine the constants a, b,c if F is irrotational ) Prove that w = (=) maps upper half of the Z —plane into the 08 interior of the unit circle in the w —plane
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Q3 a). Prove that is an even function if is even integer and is an odd function if is odd integer Find the inverse Laplace transform of 06 6 marks
- c) Obtain the complex form of Fourier series for f (x) = in (0, a). 08 prove that = and hence, find f if Vf = 06
- b) Prove that (x) = ~ (x) + (x). 06
- (i) Find the Laplace transform of e* 04
- (ii) Find the Laplace transform of t + sint. 04 Prove that fx (x2) dx = x (x2)
- b) Find p if f(z) = is analytic. 06 If f(x) = 1<x<2 with period 2, show that
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Q6 a) Show that the set of functions cosnx, n = . is orthogonal 6 marks
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Q5 Stoke’s theorem to evaluate f é F where F y?zk is the surface of hemisphere x? + + = a? lying above the xy —plane 6 marks
- c) Laplace transform to solve 08
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