Calculus is the mathematical study of change. It provides two major techniques: Differential calculus and integral calculus, which are, in a way, the opposite of each other.

**Differential calculus**, to find the rate of change of a given function

**Integral calculus**, to find a function to a given rate of change

Both techniques are based on the fundamental term **limit of function**.

The idea of a limit separates calculus from disciplines like algebra, geometry or trigonometry, which are useful to describe static situations.

## Mathematical Induction

- 1+2+3+…+n
- 2n³ + 3n² + n is divisible by 6
- The n-th derivative
- (n^p – n) is divisible by p
- The power set of a set with n elements contains 2^n elements
- Recursive Sequence
- Bernoulli’s inequality
- Just another inequality
- n and sqrt(n)
- n! > 2^n
- 2^n > n^3
- A sum
- A product
- Every integer n >= 2 is a product of prime numbers

## Inequations

## Limits

- Average velocity
- Instantaneous velocity
- Limit, first contact
- The area of a circle
- What is the behavior of the function f(x) = (x^2-1)/(x-1) at x = 1?
- One-sided limit