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Course: MPZ 3132 - Engineering Mathematics IB

Model Answer No.01

Academic Year 2012/2013

These are the common solutions for the

assignment No. 1. You can find your solutions

after substituting your values of and .

1.

Drichelet’s condition for a Fourier series

If the function for the interval

a. is single valued

b. is bounded

c. has at most finite number of maxima and minima

d. has only a finite number of discontinues

e. is for values of outside , then

converges to as at the values of for which is continuous and

Department of Mathematics & Philosophy of

Engineering

Faculty of Engineering Technology

The Open University of Sri Lanka –Nawala,

Nuggegoda

Nawala - Nugegoda

2

1.

3

Therefore by

2.

2.1 The graph of is

The extended odd function is

2.2 The graph of in is

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2.3 Since is odd function

Suppose is odd then

Suppose is even then

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3.

3.1 3.1.1

The graph of a odd function is skew symmetric about y – axis

Other values of

3.1.2 The graph of a odd function is symmetric about y – axis

Other values of

3.1.3

Other values of

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3.2

3.2.1

3.2.2

3.2.3

3.3 3.3.1

Since is odd function

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3.3.2 Since is even function

3.3.3

Other values of

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4. If exists for all

4.1

Similarly in the above manner

4.2

4.3 is substituted instead of

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4.4 By integrating both sides

When

4.5

Differentiating both sides

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5. If exists for all

5.1

5.2

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