Presentation exercises are marked with a *.
Section 10.1 : Exercises 1, 2, 3, 5*, 8, 13. 14, 15.
Section 10.2: Exercises 1, 3, 13, 15
Section 10.3: Exercises 1, 2*, 4, 14, 16* (do it with the computer, see below).
Section 10.4: Exercises 6, 9, 11, 14*, 15.
Technical problem: It seems that my Java applet will not open with older operating systems or web browsers. It works just fine on my (newer) computers, but it doesn't work in the Math Lab, or on some of the computers which students in this class have tried. One thing which will probably work is to download a recent version of Netscape or Explorer; one student reported success with a new version of Netscape after his old version of Explorer refused to open the applet.
Another problem is that even if the Java applet works, it is not possible to print out the results directly from the browser. A work-around for this is to capture and print a portion of the screen.
It's better if you can get this to work and play around with the applet with different slope fields. However, if you find this impossible, you can use these canned pictures.
Logistics slope field with r = 2 and A = 2.
Computer Work: Open the Java Applet from inside a web browser.
Do, or repeat, exercise 10.3.2, using the Java applet. Note the "x" variable is called "t" in the applet. Type in the formula for the slope field: t+y. Press the button for setting the new functions. Type in the appropriate t and y limits and hit the button for setting the limits. Click with the mouse in order to start solution curves at the required points. Print out the results.
Do exercise 10.3.16 using the Java applet. Set the slope fields and t and y limits as described above. For the Gompertz equation, set the slope field to be -y*ln(y/2) (use this notation). Set the t limits to be 0 to 5 and the y limits to be 0.15 to 4. (For smaller y, one gets a numerical error because of trying to evaluate ln(y/2) for small y.) For the logistic type equation, use the same t and y limits, but set the slope field to be y*(2-y). Start a few representative solution curves. Print out your results.
