Engineering BE Electronics and Computer Science Sem 3 May 2023 2023 ETRX Engineering Mathematics III Question Paper - Mumbai University | munotes
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2023 - ETRX DSE3 Engineering Mathematics III
Semester-end · May 2023
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Q2 Attempt any 3 questions from Question 2 to Question 6 marks
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Q1 All questions Marks 5 find the eigen values for the matrix B Find Laplace transform of f(t) = sin(4t) 5 C Find the Fourier Series Expansion f(x) = x ,;where x 5 D Determine the constant a,b,c,d_ if 5 A Using Green’s theorem in a plane to evaluate the line integral 6 Where C is the triangle with vertices at (0,0), (2,0) and (2,2) and it is traversed in anticlockwise direction B Find the matrix A,,.2 whose eigen values are 4 and 1 and their 6 corresponding eigen vectors are = A and vz = 1 C Find the analytic function f(z) = u + iv such that 8 A Find the direction derivative of = sin(xy) + in the 6 direction of the vector v = i — 2j + 2K at the point P = 1) B Find an analytic function f(z) whose real part is given 6 C Find the Eigen values and Eigen vectors of 8 And show that it is diagonalizable matrix and find its transforming matrix and the diagonal form A Using Stokes theorem to evaluate F 6 Where F = (x y)k over the B Find the orthogonal trajectories of family of curves given by 6 C Using Convolution theorem, find the inverse Laplace transform of 8 B Consider the vector field F on R? defined by 6 Show that F is conservative and find its scalar potential C Find the Fourier Series for f(x) in 8 Hence deduce that Obtain half range sine series in (0, for f(x) = — x), Hence show that
- i) Find
- ii) Find L
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