Mathematical Notations and Terminologies

A lot of the notations and terminologies are explained using programming analogies wherever possible.

Summation

Represented using \(\Sigma\), it is used to denote an iterative addition operation.

For example, \(\sum_{i=0}^{n} x_i\) is equivalent to

sum = 0
for i in range(n):
    sum += x[i]

Derivative

Derivative or differentiation of a function \(f(x)\) w.r.t \(x\) is represented as \(\frac{d}{dx}f(x)\) or \(f'(x)\). For more info on derivates, check here.

Maximas and Minimas

In calculus, minima and maxima (collectively called extrema) are the “peaks” and “valleys” of a function.

• Local Extrema: These are the peaks or valleys within a specific neighborhood. A function can have many of these.
• Global (Absolute) Extrema: These are the single highest or lowest points over the entire domain of the function.