Mathematics-IV Unit 2 – Applications of PDE and Fourier Transform: important questions for AKTU
Unit 2 (Applications of PDE and Fourier Transform) questions that AKTU repeats most often. This unit carries about 29 marks per paper. Start with the repeated questions, then the most asked topics.
Most repeated Unit 2 questions
- A string is stretched and fastened to two points l apart, motion is started by displacing the string into the form y = k(lx – x²) from which it is released at time t=0. Find the displacement of any point on the string at a distance of x from one end at time t. (7 marks, 2025, Heat and Wave Equations) – also asked in 2021, 2022, 2023, 2024, 2026
- Solve the one-dimensional heat equation ∂u/∂t = c² (∂²u/∂x²), 0 < x < L, t > 0 subject to the boundary conditions u(0,t) = 0, u(L,t) = 0 and the initial condition u(x, 0) = x(L - x) using the method of separation of variables. (7 marks, 2026, Heat and Wave Equations) – also asked in 2021, 2022, 2023, 2024
- Solve the wave equation ∂²u/∂t² = c² ∂²u/∂x², 0 < x < L subject to u(0,t) = 0, u(L,t) = 0, u(x, 0) = sin(πx/L), ∂u/∂t(x, 0) = 0. (7 marks, 2026, Heat and Wave Equations) – also asked in 2021, 2022, 2023, 2024
Most important Unit 2 topic
- Heat and Wave Equations (Unit 2: Applications of PDE and Fourier Transform) – asked 37 times in 2021, 2022, 2023, 2024, 2025, 2026
Most asked Unit 2 topics
- Heat and Wave Equations – asked 37 times
- Method of Separation of Variables – asked 5 times
- Fourier Transform and Inverse – asked 4 times
More Unit 2 previous year questions
- Write the one-dimensional heat equation and mention the physical meaning of each term. (2 marks, 2026, Heat and Wave Equations)
- Using the Fourier transform method, solve the partial differential equation ∂u/∂t = k ∂²u/∂x², -∞ < x < ∞, t > 0 subject to the initial condition u(x, 0) = e^(-a|x|). (7 marks, 2026, Fourier Transform and Inverse)
- How many arbitrary constants in the solution of 1-dimensional wave equation? (2 marks, 2025, Heat and Wave Equations)
- Classify the following operator: t(∂²u/∂t²) + 2(∂²u/∂x∂t) + x(∂²u/∂x²) - (∂u/∂x). (2 marks, 2025, Heat and Wave Equations)
- A tightly stretched flexible string has its ends fixed at x = 0 and x = l. At time t = 0, the string is given a shape defined by F(x) = μx(l − x), μ is a constant and then released. Find the displacement y(x,t) of any point x of the string at any time t > 0. (7 marks, 2025, Heat and Wave Equations)
Unit 2 syllabus topics
- Method of Separation of Variables
- Heat and Wave Equations
- Fourier Transform and Inverse