A Noob’s perspective — Learning Data Science, ML and AI from scratch. Pt 3

Calculus refresher

Derivatives

Definitions:

• The function f(x) maps values of x from a certain domain X to a given range Y, it can be denoted as f: x-> Y
• A function f(x) is continuous if it exist within the domain X
• The inverse of a function is such a function that can give us the input
• f(x) = y — function
• f^-1(y) = x — inverse
• if a function is continuous, then it’s differentiable or has a derivative

if you’d like to check out some common derivative check here

notes:

• The second derivative of a function is often remarked as the slope of the slope. if f(x) is position the f’(x) is velocity and f’’(x) acceleration
• The minimum or maximum of f(x) can only occur when the slope of f(x) is zero.
• e can use the second derivative to check maximums and minimums
• f’’(x) < 0 max
• f’’(x) > 0 min
• f’’(x) = 0 point of inflection

Integration

Definitions

• The function having derivative f(x) is called the antiderivative or indefinite integral. It’s denoted as

• Fundamental theorem of calculus: or a definite integral

some common integrals here

Some properties

• Integral of f(x) from a to a equals 0
• Integral of f(x) from a to b is the same as the negative of the integral of f(x) from b to a
• you can use an intermediate constant between a and b. You just have to add the integral from a to c and the integral from c to b.

more properties

Taylor series expansion

The Macluarin series is when a = 0

L’Hospital’s Rule

if the limits of f(x) and g(x) towards a go to 0 or infinity then,