Class Notes (3-24-08)
To start class, we passed in the 50 Multiple Choice problems that were due today.
Slope Field Review
Purpose: The purpose is to find the tendencies of an antiderivative by graphing short segments of the derivative at each point on an coordinate system.
For example, if you are given the equation dy/dx=x+y and you have to plot the slope at point (1,1), you will draw a short line with a slope of 2 at (1,1).
Once you have draw all of the short derivatives, and your task is to draw a possible shape of the antiderivative. To do this, you will be given a starting point. From that point, you will move along the x-axis, but you have to make sure the line you are drawing follows the slopes of the lines you drew earlier.
If you need more help or want extra practice, see the handouts “Hands-On Activity 10.2: Slope Fields” or “Slope Fields.”
Differential Equations
Differential equations are derivative equations. This means that you can take the indefinite intergral to get the antiderivative.
In order to do this, you must separate the variables so the y’s are on one side and the x’s are on the other:
From here, you would take the definite integral of both sides, giving you the following equation:
From here you can use algebra to find the final antiderivative. You end up with this (the equation of a circle):
After this, we went over the AP Problems that we had for a quiz that turned into a take home assignment. Some important notes are that you always go out to three decimal places and that when doing definite integrals, you don’t always have to show the antiderivative. Since it is a calculator problem, you can just jump to showing the value of the definite integral.
HOMEWORK: Do the Chapter Review at the end of chapter 1 on page 33.
