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TRANSFORMS AND PARTIAL DIFFERENTIAL EQUATIONS

KINGSCOLLEGE OF ENGINEERING

PunalkulamDEPARTMENT OF MATHEMATICS

ACADEMIC YEAR 2010 11(ODD SEMESTER)

QUESTION BANKSUBJECT NAME: TRANSFORMS AND PARTIAL DIFFERENTIAL EQUATIONSYEAR/SEM: II / III

UNIT IFOURIER SERIES

PART A1. Explain periodic function with two examples.2. State Dirichlets condition

3. To which value,the half range sine series corresponding tof(x)x2 expressed in theinterval (0,5)converges at x=5?

4. If f(x) = eax is expanded as a Fourier series in (0,2) what is the value ofbn . 5.Doesf(x) = tan x posses a Fourier expansion?6.Obtain the value of a0 in the Fourier expansion of f(x) = 1 cosx in (0,2) 7.In the

Fourier expansion of f(x)= 12x

-< x < 0

= 1

2x

, 0 < x < in (-, ).

Find the value of bn the coefficient of sin nx.

,-

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TRANSFORMS ANDPARTIAL DIFFERENTIALEQUATIONS

15. Wri

tetheComple

xformoftheFourierseriesoff(x).

16. De

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fineroot

meansquare

valueofafun

ctionf(x)i

na