MTH 243-Sections 2 & 4

Fall 2002

University of Rhode Island

Instructor: Dr. M. Kulenovic
Maple assignment #3

Due date 12/05/2002

This assignment is based on  Maple worksheets  "Parametric Surfaces" (parsur.mws) ,  "Graphics Showcase" (show.mws) and  "Taylor Polynomials in Two Variables" (taylorpoly2var.mws)

1.   Consider the function

f(x,y) = ln(x+2y+4) + tan(x2  + y2 ) .



(a)  Use Maple to find Taylor polynomial of degree 5 of this function at the point (0, 0).

(b)  Use Maple to the graph of f(x,y) together with first five Taylor polynomials for x and y in [-2, 2] and in [-0.4, 0.4]. Use different colors and styles for the  surfaces.

(c)  Use Maple to plot the error function in  for x and y in [-1, 1].

(d)  Use Maple to plot the error function  in the region where the error is less  than or equal to the tolerance (acceptable error)  0.1.
 
 

2.   Plot the parametric surface given by

x =1 + cos(v)/4, y = 6u, z = u + sin(v)/4,
for u,v in [0, 2p].
 

3.   Plot the parametric surface given by

 r = 1+cos(q)+z2
for z in [0, 7] and q in [0,2p] . Use cylinderplot option.

4.   Plot the parametric surface given by

 r = 1+cos(q)sin(2f) + fq,
for f in [0, p] and q in [0,2p] . Use sphereplot option.