1 Honors Physics 1 Class 02 Fall 2013 Some Math Functions Slope, tangents, secants, and derivatives Useful rules for derivatives Antiderivatives and Integration 1D Motion Position and velocity Velocity and acceleration

2 Functions Most of our work in introductory Physics will involve the use of continuous functions as representations of the observed world. We will take as our definition of a continuous function: Functions can usually be represented by graphs.

3 Derivatives When we write S=f(t) we are stating that position depends on time, where position is the dependent variable and time is independent. “The velocity is the rate of change of position wrt time.” can be written as: The geometric meaning can be represented as the line between two points on a graph as the time between the two points shrinks to zero. (Take a sine function as an example.)

4 Derivatives

5 Some rules for derivatives

6 Some uses of the derivative 1)Of course we can find velocity and acceleration from time derivatives of x(t). 2)Finding maxima and minima of functions. (First and second derivatives.)

7 Activity

8 Differentials

9 Antiderivatives The antiderivative of f(x) is the function that, when differentiated, yields f(x).

10 Integration: The area under a curve Graph of y=f(x)=constant. Calculate the area between y=f(x) and y=(0) over a certain range of x. If f(x) is not a constant, we can chop the area up into very small pieces and add them up to get the total area.

11 Rules for integration/antiderivatives

12 Notes 2PHYS 1100 Summer Velocity and Speed

13 Notes 2PHYS 1100 Summer Acceleration Acceleration is the rate of change of velocity.

14 Differentiating the equations of motion

15 Activity: Integrating the equations of motion

16 A differential equation you will need

17 Acceleration as a function of position