1. Physics 218: Mechanics Instructor: Dr. Tatiana Erukhimova Sections 801, 802, 803 Lecture 3

2. Overview of Today’s Class Derivatives (cont) Indefinite integrals Definite integrals

3. Quiz 6x 2 +5 If what is the derivative of x(t) with respect to t? If f(x)=2x 3 +5x what is the derivative of f(x) with respect to x?

4. Derivatives or Function x(t) is a machine: you plug in the value of argument t and it spits out the value of function x(t). Derivative d/dt is another machine: you plug in the function x(t) and it spits out another function V(t) = dx/dt

5. Derivatives A derivative of a function at a point is a slope of a tangent of this function at this point.

6. Indefinite integral (anti-derivative) A function F is an “anti-derivative” or an indefinite integral of the function f if

7. Indefinite integral (anti-derivative)

9. Definite integral F is indefinite integral

10. Definite integral

11. Integrals Indefinite integral: n – any number except -1 Definite integral:

12. Gottfried Leibniz These are Leibniz’ notations: Integral sign as an elongated S from “Summa” and d as a differential (infinitely small increment). 1646-1716

13. Leibniz-Newton calculus priority dispute

14. Have a great day! Reading: Chapter 2 Do not forget about hw quiz on Monday