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Complex Analysis and General Transform — Minor 1 2023 question paper

MMMUT Mechanical Engineering previous year question paper for Complex Analysis and General Transform (BSM-153), semester 2, Minor 1 2023. All 8 questions are listed below, each with a written answer on Nexsus.

Paper details

  • Subject: Complex Analysis and General Transform (BSM-153)
  • Branch: Mechanical Engineering
  • Semester: 2
  • Exam: Minor 1 2023
  • Questions: 8

Questions asked in Complex Analysis and General Transform Minor 1 2023

  1. Q1. Attempt any two parts of the following. Q1 (a) is compulsory.
  2. Q1(a). Show that the function f(z) (given below) is differentiable or not and also show that Cauchy-Riemann equation satisfies or not. [5 marks]
  3. Q1(b). If f(z) = u(r, θ) + i*v(r, θ) is analytic and u(r, θ) = -r^3 sin 3θ then find f(z). [3 marks]
  4. Q1(c). Evaluate, using Cauchy Integral formula ∮ (sin π z^2 + cos π z^2) / ((z - 1)(z - 2)) dz Where C is the circle |z|=3 [3 marks]
  5. Q2. Attempt any two parts of the following. Q2 (a) is compulsory.
  6. Q2(a). Determine the poles of the function f(z) = z^2 / ((z - 1)^2 (z + 2)) and the residue at each point. Hence evaluate ∮ f(z) dz, where C: |z| = 2.5 [4 marks]
  7. Q2(b). Evaluate ∫_0^2π (cos 3θ) / (5 -4cos θ) dθ [3 marks]
  8. Q2(c). Expand f(z) = 1 / ((z - 1)(z - 2)) in the region (i) 1 < |z| < 2 (ii) |z| < 1 [3 marks]