Engineering Mathematics-II Unit 5 Notes AKTU (BAS203)

AKTU · BTECH · Semester 2 · Engineering Mathematics-II · Unit 5 · Notes

AKTU Engineering Mathematics-II (BAS203) Unit 5 notes for B.Tech Semester 2 – Complex Variable – Integration. Topics: Complex Integration, Taylor and…

Open the interactive reader to study this resource on AcademicArk.

Unit 5: Complex Variable – Integration – AKTU syllabus topics

  • Complex Integration: Cauchy Integral Theorem, Cauchy Integral Formula
  • Taylor and Laurent Series: Singularities and Classification, Zeros of Analytic Functions
  • Residues and Residue Theorem: Applications of Residue Theorem

Most asked AKTU PYQ questions from Unit 5

  1. Q7b. Apply residue theorem to evaluate ∫₋∞^∞ x² dx / [(x² + 1)(x² + 4)] (10 marks, 2018-19)
  2. Q7a. Using Cauchy Integral formula evaluate ∫_c sin z / (z² + 25) dz where c is circle |z| = 8 (10 marks, 2018-19)
  3. Q2e. Expand f(z) = 1 / ((z − 1)(z − 2)) in regions (i) 1 < |z| < 2 (ii) 2 < |z| (10 marks, 2018-19)
  4. Q7b. Use contour integral to evaluate: ∫₀^(2π) cos 2θ / (5 + 4cosθ) dθ (7 marks, 2024-25)
  5. Q7a. Expand f(z) = (z² − 1) / [(z + 2)(z + 3)] in Laurent's series valid for |z| > 3. (7 marks, 2023-24)
  6. Q1g. Find the residue at the simple pole of the following function: f(z) = 8z³ / [(z−1)(z+1)³] (2 marks, 2024-25)
  7. Q1e. Find the residue of f(z) = cos z / [z(z+5)] at z = 0 (2 marks, 2023-24)
  8. Q1j. Find residue of f(z) = cos z / z(z + 5) at z = 0 (2 marks, 2018-19)
  9. Q7a. Evaluate ∮_c eᶻ / [z(1 − z)³] dz, where c is (i) |z| = 1/2 (ii) |z − 1| = 1/2 (iii) |z| = 2. (10 marks, 2021-22)
  10. Q7b. Find the Taylor's and Laurent's series which represent the function (z² − 1) / [(z + 2)(z + 3)] when (i) |z| < 2 (ii) 2 < |z| < 3 (iii) |z| > 3. (10 marks, 2021-22)

AKTU paper codes: BAS203, KAS203

Other Engineering Mathematics-II units

Engineering Mathematics-II previous year papers

More Engineering Mathematics-II resources

Browse all notes · Semester 2 notes