1. AP Calculus Unit 1 Day 1 What is Calculus?

2. Calculus is the study of CHANGE There are 2 Branches: 1)Differential Calculus 2)Integral Calculus

3. Differential Calculus Differential Calculus deals with RATE OF CHANGE (SLOPE)

4. Differential Calculus

5. Two Types of Rates of Change AVERAGE Rate of Change INSTANTANEOUS Rate of Change

6. Tangent Line Problem How to calculate the slope of a tangent line.

7. 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!

8. Applications of Differential Calc 1)Optimization (finding local max and mins) 2)Physics (position, velocity, acceleration) 3)Differential Equations 4)Mean Value Theorem 5)Taylor Polynomials (linear approximation) 6)And SO MANY MORE!

9. Integral Calculus Integral Calculus is the INVERSE of Deferential Calculus Integral Calculus allows you to find the AREA under a Curve.

10. Integral Calculus

11. How Integrals Answer This Calculus lets us break up the curved area into shapes we CAN find the area.

12. Integrals to Come… Later! Because Integrals are the INVERSE of Differentiation, we we learn about that MUCH later… Like after Halloween later!

13. Calculus Controversy https://www.youtube.com/watch?v=axZTv5YJss A