Heaviside unit step function. Hi friends, today it’s all about the Heaviside unit step function. So here it goes!!

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**Heaviside unit step function**

**Solved examples of Heaviside unit step function**

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

So here is the first example.

**Example 1**

According to Stroud and Booth (2011)*, “Express in terms of the Heaviside unit step function

”

**Solution**

Now here the given function is:

As I can see, here the function has a break at .

So I’ll write this function in such a way so that the first part of the function is switched off at . Also, the second part of the function is switched on at .

Therefore, in the unit step form, the function will be

Now here the second term switches off the first function at . And the third term switches on the second function .

Next, I’ll simplify the function in unit step form to get

Hence I can conclude that this is the answer to the given example.

Now I’ll give you another example.

**Example 2**

According to Stroud and Booth (2011)*, “Express in terms of the Heaviside unit step function

”

**Solution **

Now here the given function is:

As I can see, here the function has two breaks – one is at and the other one is at .

So I’ll write this function in such a way so that the first part of the function is switched off at . Also, the second part of the function is switched on at . Next, the function is switched off at . Finally, the function is switched on at .

Therefore, in the unit step form, the function will be

Now I’ll simplify it to get

Hence I can conclude that this is the answer to the given example.

Now I’ll give you another example.

##### Example 3

According to Stroud and Booth (2011)*, “A function is defined by

Determine the function in terms of the unit step function.”

**Solution**

Now here the given function is:

As I can see, here the function has two breaks – one is at and the other one is at .

So I’ll write this function in such a way so that the first part of the function is switched off at . Also, the second part of the function is switched on at . Next, the function is switched off at . Finally, the function is switched on at .

Therefore, in the unit step form, the function will be

Now I’ll simplify it to get

Hence I can conclude that this is the answer to the given example.

Dear friends, this is the end of today’s post. 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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