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MSc 1st Semester Classical Mechanics Question Paper 2025 : Click Here
Paper Code: 41171
B-1521
M.A./M.Sc. Mathematics (Semester Third) Examination, 2023-24
Partial Differential Equation with Applications
Time: Two Hours ] [Maximum Marks: 70
Note: Attempt all the Sections as per instructions.
Section-A
(Short Answer Type Questions)
Note: Attempt any three questions out of the following.
Each question carries 10 marks. Answers are required not exceeding 300 words.
1. Define one dimensional wave equation.
2. Define the characteristic for PDE.
3. What is Hopf-Lax formula prove it.
4. Find the solution of the Hamlton-Jacobi equation U,+H (Du)0 in Rx (0,0∞)
5. Define properties of Harmonic function.
6. Write a short note on Bender-Schmidt method.
MSc Maths 3rd Semester Question Paper 2025 PDF
Section-B
(Long Answer Type Questions)
Note: Attempt any two questions out of the following.
Each question carries 20 marks. Answer are required not exceeding 600-800 words.
7. Write short note on Hodograph.
8. Derive Hamilton-Jacobi equation.
9. Find the extremals of the functional I[y(x)] = (1+2dx
10. Solve the heat equation by Crank Nicolson method subject to boundary and intial condition: u(x,0)=0, u (0, t) = 0, u (1,t) = t.
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