Part (a). Buckingham's Theorem practice.

• Read Lucas's writeup on dimensional analysis
• Use Maple to solve Problem 2 on the last page. (Solve Problem 1 on your own for exam practice.)

Part (b). Fitting by visualization.

• In Question 2 on Homework 5, you had to determine if the data supported a proportionality argument by doing transformations of the z variable. You could see that as the transformations skewed z more and more, the graphs became less and less amenable to an assumption of proportionality.
• Your goal is to apply the four transformations to the y variable without changing the z variable. Then determine which, if any, of the transformations lend themselves to reasonably conclude an assumption of proportionality. For these transformations, determine the constant of proportionality like we did visually on the tutorial. [That is, find k such that z=kf(y).]

Part (c). Least-Squares fitting.

• Depending on the model you are trying to fit, it is not always possible to use the method of least squares. Maple's least squares fit will not calculate a fit when the constants you are trying to work out are related in a non-linear fashion. An example is y=ae^bx.
• What we can do is do a transformation of the data, then apply least squares to find the modified constants, and lastly reinterpret in terms of the original function.
• Important: this will NOT give a least-squares fit to the original function!
• Perform these above steps to find a least squares fit of the data in Question 2 on Homework 5 to the curve z=ae^by.