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Fourier Series Expansions

Authored by rpoornima MATHEMATICS-HICET

Mathematics

University

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Fourier Series Expansions
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10 questions

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1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Which of the following is not Dirichlet’s condition for the Fourier series expansion?

(x) is periodic, single valued, finite

f(x) has finite number of discontinuities in only one period

f(x) has finite number of maxima and minima

f(x) is a periodic, single valued, finite

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

At the point of discontinuity, sum of the series is equal to ___________

a) 1/2([f(x+0)–f(x−0)])

1/2([f(x+0)+f(x−0)])

1/4([f(x+0)–f(x−0)])

1/4([f(x+0)+f(x−0)])

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the Fourier series expansion of the function f(x) in the interval (c, c+2π)?

a0/2+∑∞n=1ancos(nx)+∑∞n=1bnsin(nx)

a0+∑∞n=0ancos(nx)+∑∞n=0bnsin(nx)

Eulers formula

None of the above

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Find an if the function f(x) = x – x^3.

finite value

infinite value

zero

can’t be found

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Find bn if the function f(x) = x^2.

finite value

infinite value

zero

can’t be found

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

If the function f(x) is even, then which of the following is zero?

an

bn

a0

nothing is zero

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

If the function f(x) is odd, then which of the only coefficient is present?

an

bn

a0

everything is present

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