1. Instructor: Dr. Tatiana Erukhimova
Physics 218: Mechanics
Instructor: Dr. Tatiana Erukhimova
Lectures 2-3

2. Overview of Today’s Class
Derivatives
Indefinite integrals
Definite integrals
Examples

3. Quiz
If f(x)=2x3-5 what is the derivative of f(x) with respect to x? 6x
8x2
I don’t know how to start
6x2

4. I don’t know how to start
1. If f(x)=2x3 evaluate
2x4
I don’t know how to start
0.5x4+Const
2x2/3

5. I don’t know how to start
1. If f(x)=2x evaluate
2x3/3
I don’t know how to start 5
x2+Const

6. Overview of Today’s Class
Derivatives
Indefinite integrals
Definite integrals
Examples

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

8. Derivatives

9. 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

10. Derivative is the rate at which something is changing
Velocity: rate at which position changes with time
Acceleration: rate at which velocity changes with time
Force: rate at which potential energy changes with position

11. -Size of pizza with respect to the price
Derivative is the rate at which something is changing
-Size of pizza with respect to the price
-Population of dolphins with respect to the sea temperature
…………………

12. GDP per capita

13. Quiz If f(x)=2x3+5x what is the derivative of f(x) with respect to x?
If what is the derivative of x(t) with respect to t?

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

15. Indefinite integral
(anti-derivative)

16. n – integer except n= -1

17. Definite integral
F is indefinite integral

18. Definite integral

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

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

21. Leibniz-Newton calculus priority dispute

22. Have a great day!
Reading: Chapter 2