AP Calculus Unit 1 Day 1

What is Calculus?

What is Calculus?

Calculus is the study of CHANGE

There are 2 Branches:1) Differential Calculus2) Integral Calculus

Differential Calculus

Differential Calculus deals with RATE OF CHANGE (SLOPE)

Differential Calculus

Two Types of Rates of Change

AVERAGE Rate of Change

INSTANTANEOUS Rate of Change

Tangent Line Problem

How to calculate the slope of a tangent line.

Limits!

The Limit of a function describes what the function approaches

Limits are technically NOT a calculus concept, but they are VERY important!!

This is why our WHOLE first unit is devoted to them!

Applications of Differential Calc

1) Optimization (finding local max and mins)2) Physics (position, velocity, acceleration)3) Differential Equations4) Mean Value Theorem5) Taylor Polynomials (linear approximation)6) And SO MANY MORE!

Integral Calculus

Integral Calculus is the INVERSE of Deferential Calculus

Integral Calculus allows you to find the AREA under a Curve.

Integral Calculus

How Integrals Answer This

Calculus lets us break up the curved area into shapes we CAN find the area.

Integrals to Come… Later!

Because Integrals are the INVERSE of Differentiation, we we learn about that MUCH later…

Like after Halloween later!

Calculus Controversy

https://www.youtube.com/watch?v=axZTv5YJssA