This page is designed to provide helpful information about the laboratory questions.

The Lab Final is due on Wednesday, Dec. 13. This is mostly an individual effort, but do use the partnerships that you have developed over the semester. You will probably want to download your specific lab page (and may want to convert it to a Word document). On the cover page type your name and your group number.

Question 1: This problem is very much like the lake pollution problems that you have studied in class. For example, you may want to consult what you did on the Great Lakes problem in Lab 7. Once again, you will want to download and use the Excel spreadsheet that I have provided for numerically solving differential equations.

Question 2: This problem uses the next material that we will be studying, which is how the integral finds the area under curves. This is one of the main uses of the integral. This should be a very basic problem using definite integrals after we have introduced them in class. It becomes particularly easy if you take advantage of Maple's int command. Part b uses Excel's Trendline with a fourth order polynomial fit, while Part c uses Excel's Solver much like you did in Lab 5, Question 3 (though a simpler case here). You analyze these functions to find the maximum much as you have done before with Maple's diff and fsolve commands. The new part is finding the average using a definite integral, which is basically finding the area under the curve.

To find the area under the curve f(x) from x = a to x = b, you can type the following command in Maple.

int(f(x), x = a..b);

Its that simple! (Clearly, you have to provide an f(x) and the number values of a and b.)

Question 3: This problem is very similar to the ones we have recently done in class on Hg in fish or lead in children. This is a variation on the lead in children problem from the Worked Examples section and the homework problems. Mostly, this problem has you showing your expertise in graphing, solving differential equations, and forming tables that you have learned over the semester. There are no special instructions needed for this problem (though I might suggest using the Google search engine with key words lead and children to find more information for the last question).

Question 4: This question can be considered an extension of either your work with discrete dynamical systems or with Euler's method. You will want to set up an Excel spreadsheet. In the first column you will put the values for time in your simulation. In the second column, you begin with the initial value of infected females, while in the third column, you begin with the initial value of infected males. In the second row of the second and third columns, you enter the Euler's formula that is given on your lab, inserting the parameter values given and using the values of infected males and females from the first cells. After you have done this, you simply fill down to the desired time, and the simulation is complete. All that remains is selecting particular values and creating a graph like you have done so many times before.