Engineering BE Computer Engineering Sem 3 May 2019 2019 Applied Mathematics III Question Paper - Mumbai University | munotes

Questions asked in this paper

1. Q2 Attempt ANY 3 questions from Q.2 to Q.6
2. Q3 Use of scientific calculators allowed
3. Q4 Figures to right indicate marks
4. Q1 a) Find the Laplace transform of t e' sin2t cost. 5 marks
   • b) Find the inverse Laplace transform of 5
   • c) Determine whether the function f(z) = x? — y* + 2ixy is analytic and if so find its
   • d) Find the Fourier series for f(x) = in the interval 7). 5
5. Q2 a) Evaluate J dt 6 marks
   • b) Find the Z- Transf 06 ) Find the ransform of f(k) ok (06)
   • c) Show that the function u = 2x (1 — y) is a harmonic function. Find its harmonic conjugate and corresponding analytic function. (08)
6. Q3 a) Find the equation of the line of regression of y on x for the following data 6 marks
   • b) Find the bilinear transformation which maps ontow=1,0,1. 6
   • c) Obtain the expansion of f(x) =x x). ,0<x<a asahalf range cosine series Hence show that (08)
7. Q4 a) Find the inverse Laplace Transform by using convolution theorem
   • b) Calculate the coefficient of correlation between Price and Demand. 6
   • Q.P.Code: 21237
   • c) Find the inverse Z-transform for the following ; 8
8. Q5 a) Find the Laplace transform of sint H(t - 6 marks
   • b) Show that the set of functions { sinx , sin3x , orthogonal over [0, 2/2]. Hence construct orthonormal set of functions. (06)
9. Q6 a) Find the complex form of Fourier series for f(x) = 3x 27). 6 marks
   • b) If f(z) is an analytic function with constant modulus then , prove that f(z) is constant. (06)
   • c) Fit a curve of the form y = to the following data. 8

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