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

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

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?

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

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

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

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 …………………

GDP per capita

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

Indefinite integral (anti-derivative)

Definite integral F is indefinite integral

Definite integral

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

Have a great day! Please return the folders Reading: Chapter 2 Do not forget about hw quiz on Monday