1 A "delta" function is a function that is zero everywhere except where the argument is zero.
![1005_1.png](https://secure.tutorsglobe.com/CMSImages/1005_1.png)
At this point the function is infinite so that the area under the curve is unity. The delta function obeys the relation
(a) Show that the following function
![1128_2.png](https://secure.tutorsglobe.com/CMSImages/1128_2.png)
i.e. show that it is zero everywhere except the origin and that it integrates to unity.
(b) A step function, 0 (t) , a.k.a. the "Theta" function or the Heaviside function, is zero for negative arguments and is unity for positive arguments. Show that
![1538_3.png](https://secure.tutorsglobe.com/CMSImages/1538_3.png)
(c) Using the definition of Fourier coefficients in Eq.s (3.43) and (3.46), show that
![305_4.png](https://secure.tutorsglobe.com/CMSImages/305_4.png)