MTH 243-Sections 2 & 4

Fall 2002

University of Rhode Island

Maple assignment #1

Due date 10/03/2002

This assignment is based on  Maple worksheets  "Graphs of Functions of Two Variables "(graphs.mws)  and  "Contour Diagrams" (contours.mws)

1.   Consider the function

f(x,y) = cos(x2  + y2 ) / (1+ x2  + y2 ).


(a)  Use Maple to plot the graph of the function f(x,y) for x and y in [-7, 7].

(b)  Use Maple to plot the contour diagrams of the function f(x,y) for x and y in [-7, 7].

(c)  Use Maple to plot the graph of the function f(x,y) for x and y in [-7, 7] along with the graphs of z = 0.5 and z = (x2  + y2 ) / 4. Use different colors and styles for three surfaces.

2.   Consider the functions

g(x,y) = |x  + y| 1/2  + |x - y|1/2 
and
h(x,y) = 2 - (x2  + y2 ) / 10.

(a)  Use Maple to plot the graphs of the functions g(x,y) and h(x,y)  for x and y in [-10, 10]. Use different colors and styles for two surfaces.

(b)  Use Maple to plot the contour diagrams of two functions  for x and y in [-10, 10].
 
 

3.   Consider the function

F(x,y,z) = x y5 + y z5  + z x5  - 1.


(a)  Use Maple to plot the level surfaces of the function F(x,y,z) for x and y in [-7, 7] corresponding to the level values 0 and 2. Use different colors and styles to plot  two surfaces.