1  A "delta" function is a function that is zero everywhere except where the argument is zero.

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

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

(c) Using the definition of Fourier coefficients in Eq.s (3.43) and (3.46), show that