Rolle’s Theorem – Explanation and Examples

Rolle’s theorem states that if a real-valued function is continuous in a closed interval $[a,b]$ and is differentiable on the open interval $(a,b)$ while $f(a) = f(b)$, then there must be a point “$c$” in the open interval $(a,b)$ such that $f'(c) = 0$. The graphical representation of Rolle’s theorem is given below. Rolle’s theorem […]

Parseval’s Theorem – Definition, Conditions and Applications

Parseval’s theorem is an important theorem used to relate the product or square of functions using their respective Fourier series components. Theorems like Parseval’s theorem are helpful in signal processing, studying behaviors of random processes, and relating functions from one domain to another.Parseval’s theorem states that the integral of the square of its function is […]