Engineering Mathematics-II Unit 2 Notes AKTU (BAS203)

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

AKTU Engineering Mathematics-II (BAS203) Unit 2 notes for B.Tech Semester 2 – Laplace Transform. Topics: Laplace Transform Fundamentals, Special Functions…

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Unit 2: Laplace Transform – AKTU syllabus topics

  • Laplace Transform Fundamentals: Existence Theorem, Properties of Laplace Transform, LT of Derivatives and Integrals
  • Special Functions Laplace Transform: Unit Step Function, LT of Periodic Functions
  • Inverse Laplace Transform: Convolution Theorem
  • Applications of Laplace Transform: Solving ODE Using Laplace, Simultaneous ODE Using Laplace

Most asked AKTU PYQ questions from Unit 2

  1. Q4b. Use convolution theorem to evaluate L⁻¹[ p² / (p²+4)(p²+9) ] (7 marks, 2024-25)
  2. Q2b. Solve the following differential equations using Laplace Transform: d³y/dt³ + 2d²y/dt² − dy/dt − 2y = 0; y(0) = 1, y'(0) = y''(0) = 2 (7 marks, 2024-25)
  3. Q4b. Using Laplace Transform, solve: y'' + 3y' + 2y = e^(−t), y(0) = 0, y'(0) = 1 (7 marks, 2023-24)
  4. Q2b. Using convolution theorem, find the Inverse Laplace Transform of 1 / [(s²+a²)(s²+b²)] (7 marks, 2023-24)
  5. Q4a. State convolution theorem of the Laplace transforms. Hence, find inverse Laplace transform of 1 / [s²(s + 1)²]. (7 marks, 2022-23)
  6. Q4b. Using Laplace transform, solve the following differential equation: d²y/dx² + y = 6 cos 2x, y(0) = 3 & y'(0) = 1. (7 marks, 2022-23)
  7. Q1d. Find inverse Laplace Transform of F(s) = (s−1)/(s²+3s+2). (2 marks, 2024-25)
  8. Q1b. Explain the first shifting property of the Laplace transform with example. (2 marks, 2022-23)
  9. Q1f. Find the inverse Laplace transform of F(s) = 1 / (s² + 2s + 2). (2 marks, 2022-23)
  10. Q4a. Find L{ (1 − cos t) / t² } using properties of Laplace Transform. (7 marks, 2023-24)

AKTU paper codes: BAS203, KAS203

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