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# Indian Institute of Technology Kharagpur (IIT-K) 2008 B.Tech Mathematics and Computing Transform calculus - Question Paper

Wednesday, 23 January 2013 12:45Web

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

 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

 a) Solve the I.V.P.

Signature of the Paper Setter

Continued in next page

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 Earning:   Approval pending.
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