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MA 1024 Lab 1: Surfaces



Getting Started


cp ~bfarr/Surfaces_start.mws ~

You can copy the worksheet now, but you should read through the lab before you load it into Maple. Once you have read to the exercises, start up Maple, load the worksheet Surfaces_start.mws, and go through it carefully. Then you can start working on the exercises.




Two common ways of representing the graph of a function of two variables are the surface plot and the contour plot. The first is simply a representation of the graph in three-dimensional space. The second draws the level curves $f(x,y)=C$ for several values of $C$ in the $x,y$ plane. We will explore how to produce these kinds of graphs in Maple, and how to use the graphs to study the functions.


    1. Generate a surface plot and contour plot for the following function on the given domain.

      \begin{displaymath}f(x,y) = \frac{x+y}{1+x^2+y^2} \end{displaymath}

      for $-3\leq x \leq 3$ and $-3 \leq y\leq 3$.


  1. Consider the following function

    \begin{displaymath}r(x,y) = \frac{2x+y-1}{1+x^2+2y^2} \;\;\;\;\;-3 \leq x \leq
5\,,\;\;-3 \leq y \leq 5\end{displaymath}

    which represents the deviation, in inches, of last year's rainfall from the average annual rainfall in a certain area.
    1. Graph the surface corresponding to the function $r$.
    2. What are (approximately) the maximum and minimum values of the rainfall deviation and where do they occur? (Hint - values from plots are accurate enough.)
    3. Use a contour plot to find the region in this domain in which the deviation was between $-0.4$ inches $-1.1$ inches.

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William W. Farr