## 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 :

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

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.

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

### Example :

Find fourier sine series for

### Solution :

l = upper limit – lower limit

= π -0

= π

**For sine series,**

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.

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 .

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

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

Here, sin π =0 and sin0 = 0.

We simplify the previous step and find this step.

We get bn for the series.

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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