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M.Sc. IVth Semester (CBCS) Examination, 2021
Mathematics
Optional-X (Integral Transform-II)
[Maximum Marks: 60]
Note :- All questions from each section carry equal marks. All questions are compulsory and answer limit are approximately 250 words. Start the answer of each section from new page. Maximum limit of pages of answer booklet are approximately 16 pages. Answer should be written by the student in his/her own handwriting mandatory. The first page of answersheet should be download by the student from university website is mandatory.
1.
Write relation between fourier transform and Laplace transform.
2.
Find the finite fourier sine transform of f(x)=x2, 0 < x < 4
3.
Find sine transform of
$$\frac{e^{-ax}}{x}$$
4.
Use finite fourier transform to solve
$$\frac{\partial u}{\partial t}=\frac{\partial^{2}u}{{\partial x}^{2}}$$
given that u (0,t)=0, u(π,t)=0, u(x,0)=2x where 0 < x < π, t > 0.
5.
Find the Hankel transform of $$\frac{df}{dx}$$ when
$$f=\frac{e^{-ax}}{x}$$
and n = 1.