1. Basic Calculus

2. Outline Differentiation as finding slope Integration as finding area Integration as inverse of differentiation

3. Limit “Limit” as finding the slope of a curve –The slope of the curve y=mx+c is m. –How about the slope of the curve y=x^2? –Approximately, the slope at x1 is (y2-y1)/(x1-x2) x1x2 y1 y2

4. Limit x1x2 y1 y2

5. Differentiation of x^2 x1x2 y1 y2 Let’s find dy/dx at x=x1

6. Differentiation of x^n

7. Differentiating a sum of two functions of x

8. Differentiation of

9. Chain Rule

10. Area under curve x Y= f(x) ba

11. Approximation by Summation xba

12. Integration: Infinitesimal Approximation by Summation xba … Divide into n stripes, and let n goes to infinity

13. The Fundamental Theorem of Calculus Integration is antiderivative:

14. Explaining Fundamental Theorem of Calculus Differentiating area gets curve Differentiating curve gets slope x Y= f(x) ba