Calculus

1. Calculus

CALCULUS IS BROADLY DIVIDED INTO DIFFERENTIAL AND
INTEGRAL CALCULUS. IT DEALS
WITH LIMITS AND INFINITESIMALS TO
DESCRIBE CONTINUOUS CHANGE

2. Limits & Continuity (The Foundation)

Limits & Continuity (The Foundation)
•Before any differentiation, we establish the limit. A function must be
continuous and differentiable on an interval. If the left-hand and righthand limits differ, the limit does not exist

3. Differential Calculus

•The derivative represents differentiation with respect to an independent
variable. We find stationary points where the gradient is zero, then use
the second derivative test to classify concavity

4. Integral Calculus

•Integration is the inverse operation of differentiation. The definite integral
computes the accumulated quantity — physically, displacement from
velocity; geometrically, area

5. The Fundamental Theorem of Calculus

•The Fundamental Theorem of Calculus is the bridge. FTC1 shows that
every continuous function has an antiderivative. FTC2 allows us to
evaluate definite integrals exactly without limits of Riemann sums. This is
the pinnacle of elementary calculus