Indian Institute of Technology Kharagpur (IIT-K) 2008 B.Tech Mathematics and Computing Transform calculus - Question Paper
Indian Institute of Technology, Kharagpur
FN/AN Time: 2 Hrs Full Marks: 30 No. of Students: 375
Mid Autumn Semester, 2008 - 2009 Deptt.: AE+BT+CHE+EE+EX+IE+MA+MF+PH+SI Sub. No.: MA20101 2nd Yr. B.Tech. /M.Sc. Sub. Name: Transform Calculus
Date
Instructions: 1) Answer both the questions 1 & 2, each containing six parts.
2) Give the Tina! answer of all the parts in the first two pages.
I 3) Without detailed working shown, no mark will be awarded.
Q1 Answer all the six parts: (2x6=12 Marks)
<0 Evaluate the Laplace Transform of /(f) = [erf. (/)]; where [erf. (f) J is the error function.
b) Determine the Fourier Series of
/(x) = 0; for-K<jc<0,
= x ; for 0<x<7t.
and using this, evaluate + +"JT+.......
c) Solve
t
jy(T)cos(t-r)dT = y'(t); .y(0) = l.
0
Evaluate the Laplace Transform of the function /(/) = jsin -v/7 j and hence evaluate the Laplace
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Transform of Transform of |  |
c) Using Convolution Theorem, or otherwise, evaluate the Inverse Laplace Transform of
f) Solve the equation
/(/)+/(0=<5('-4); H)=4./(0)=4,
where 8 is the Dirac Delta function.
(3x6*18 Marks)
Q2 Answer all the six parts:
Name of the Paper Setter
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a) Solve the I.V.P. |
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Signature of the Paper Setter
Continued in next page
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Attachment: |
| Earning: Approval pending. |
