How to draw graphs in the Fourier series? Hello friends, today I’ll show how to draw graphs in the Fourier series. Have a look!!

### How to draw graphs in the Fourier series

Draw graph of a function_compressed

In one of my earlier posts on Fourier series, I have shown how to describe the graphs in Fourier series. And now I’ll show how to draw these graphs.

So here you go!

#### Solved examples of how to draw graphs in the Fourier series

Disclaimer: None of these examples is mine. I have chosen these from some books. I have also given the due reference at the end of the post.

So here is the first example of how to draw graphs in the Fourier series.

##### Example 1

According to Stroud and Booth (2011)*, “Draw the graph of

”

##### Solution

Now here the given function is

As I can see, the function has two different values. One is and the other one is .

When the value of is between and , the value of is .

So, first of all, I’ll draw the graph of when is in between and .

###### Step 1

Thus the graph of , when is in between and , looks like the following:

Now I can see, when is between and , the value of is .

So, I’ll draw the graph of when is in between and .

Now I’ll combine these two graphs. So this gives

Also I can see that . So this means the function has a period of .

Now I’ll draw the graph of when is in between and .

###### Step 2

Since the function has a period , the function will repeat itself in the interval .

So the function will be

Next, I’ll draw the graph of in this interval.

Therefore I can say that the graph of , when is in between and , looks like

Next, I’ll draw the graph of when is in between and .

At first, I’ll draw the graph of when is in between and . Then I’ll draw the graph of when is in between and .

###### Step 3

Since the function has a period , will repeat itself in the interval .

So the function will be

Next, I’ll draw the graph of in this interval.

So it will look like

Now I’ll draw the graph of when is in between and .

###### Step 4

As I have mentioned before, the function has a period . So the function will repeat itself in the interval .

Thus the function will be

Next, I’ll draw the graph of in this interval.

So it will look like

Therefore I can say that the graph of , when is in between and , looks like

###### Step 5

At the end, I’ll bring together all these graphs. So the graph of in the interval of to looks like as follows:

And this is the answer to this example.

Now I’ll give another example.

##### Example 2

According to Stroud and Booth (2011)*, “Draw the graph of

”

##### Solution

Now here the given function is

As I can see, the function has three different values. One is and the other two are .

When the value of is between and , the value of is .

So, first of all, I’ll draw the graph of when is in between and .

###### Step 1

Thus the graph of , when is in between and , looks like the following:

Now I can see, when is between and , the value of is .

So, I’ll draw the graph of when is in between and .

And this looks like

Also the value of is , when is in between and .

So the graph of , when is in between and , looks like

Now I’ll combine these three graphs. So this gives

Also I can see that . So this means the function has a period of .

Now I’ll draw the graph of when is in between and .

###### Step 2

Since the function has a period , the function will repeat itself in the interval .

So the function will be

Next, I’ll draw the graph of in this interval.

Therefore I can say that the graph of , when is in between and , looks like

Next, I’ll draw the graph of when is in between and .

At first, I’ll draw the graph of when is in between and . Then I’ll draw the graph of when is in between and .

###### Step 3

Since the function has a period , will repeat itself in the interval .

So the function will be

Next, I’ll draw the graph of in this interval.

So it will look like

Now I’ll draw the graph of when is in between and .

###### Step 4

As I have mentioned before, the function has a period . So the function will repeat itself in the interval .

Thus the function will be

Next, I’ll draw the graph of in this interval.

So it will look like

Therefore I can say that the graph of , when is in between and , looks like

And this is the answer to this example.

Now I’ll give another example.

##### Example 3

According to Stroud and Booth (2011)*, “Draw the graph of

”

##### Solution

Now here the given function is

As I can see, the function has two different values. One is and the other one is .

When the value of is between and , the value of is .

So, first of all, I’ll draw the graph of when is in between and .

###### Step 1

Thus the graph of , when is in between and , looks like the following:

Now I can see, when is between and , the value of is .

So, I’ll draw the graph of when is in between and .

Now I’ll combine these two graphs. So this gives

Also I can see that . So this means the function has a period of .

Now I’ll draw the graph of when is in between and .

###### Step 2

Since the function has a period , the function will repeat itself in the interval .

So the function will be

Next, I’ll draw the graph of in this interval.

Therefore I can say that the graph of , when is in between and , looks like

Next, I’ll draw the graph of when is in between and .

###### Step 3

As I have already mentioned before the function has a period . So the function will repeat itself in the interval .

Thus the function will be

Next, I’ll draw the graph of in this interval.

Therefore I can say that the graph of , when is in between and , looks like

Now I’ll draw the graph of when is in between and .

###### Step 4

As I have mentioned before, the function has a period . So the function will repeat itself in the interval .

Thus the function will be

Next, I’ll draw the graph of in this interval.

So it will look like

Therefore I can say that the graph of , when is in between and , looks like

And this is the answer to this example.

Dear friends, this is the end of today’s post on how to draw graphs in the Fourier series. Thank you very much for reading this. Please let me know how you feel about it. Soon I will be back again with a new post. Till then, bye, bye!!

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