Exercises

1. 3d Plots.

   Textbook Ch. 10.2/Problems 14,16,18,20,22. Use Maple plot3d or implicitplot3d commands to display the surfaces and match them with the pictures in the book (Plot H in the text should contain the lower half as well). Your answer should include one nice informative plot of every function. You should also state clearly which function it is and which picture in the book corresponds to it.

2. Mexican hat

   The following commands plot a cowboy hat. Your assignment is to construct the most attractive Mexican hat you can. Mexican hats are circular symmetric.

     > CowboyHat:=(x,y)->sin(sqrt((3*x/4)^2+y^2)):
   
     > plot3d(CowboyHat(x,y),x=-6.4..6.4,y=-sqrt(41-x^2)..sqrt(41-x^2), 
       orientation=[30,45]);
   

   You may find it helpful to write out on paper the function and the display limits for the cowboy hat. One way to get a Mexican hat is to modify the cowboy hat to make it circular and increase its rim.

3. Contour plots.

   Match each of the following functions with one of the contourplots given below. Optionally you may give fun, creative, fitting names to the functions.

   

   

   

   

   

   

    
   Figure 1:  Plot A
   

    
   Figure 2:  Plot B
   

    
   Figure 3:  Plot C
   

    
   Figure 4:  Plot D
   

    
   Figure 5:  Plot E
   

    
   Figure 6:  Plot F