HALF RANGE FOURIER SERIES |GTU Maths-3

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HALF RANGE FOURIER SERIES |GTU Maths-3

Half range fourier series :

In this method l = upper limit – lower limit .

This method is use when we have to find particular sine series or cosine series.

Half range cosine series :

half range fourier series

The above equation is used when we have to find only cosine series.

half range fourier series

At a time of cosine series bn will become 0. it means bn=0 and we only have to find a0 and an.

Half range sine series :

half range fourier series

This method is used when we have to find out half range sine series. at this time a0 and an will become 0. it means a0 = 0 and an = 0.

We have to find only bn.

half range fourier series

The above equation of fourier series is uses when we have to find half range sine series.

Example :

Find fourier sine series for

half range fourier series example

Solution :

l = upper limit – lower limit

= π -0

= π

For sine series,

half range fourier series example

Here, we write the equation of the fourier sine series and we simplify it.

In this equation put l = π and we get bn*sin(nx) in equation.

half range fourier series example

As we know in equation of sine series a0=0 and an=0. we only have to find bn.

Here, in above equation we simplify the equation by cancelling π .

half range fourier series example

We integrate the equation by u*v multiplication rule of integration.

half range fourier series example

In this step we put limit value in the equation which is π and 0.

Here, sin π =0 and sin0 = 0.

half range fourier series example

We simplify the previous step and find this step.

half range fourier series example

We get bn for the series.

half range fourier series example

After that putvalue of bn in fourier series equation.

In this equation we learn how to find half range fourier sine and cosine series.

I hope this will may help you!!


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