Maple #9 is due Thursday 6 Apr 2000 For FULL credit STAPLE your sheets together. ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ Each plot must be rotated to a "nice" position and "look good (smooth)". Each plot must have include axes and the title must include your name and what was plotted. Note that the expressions below are not necessarily in a form that Maple likes. Be sure to answer the questions in 4. 1. Plot the following surfaces from u=0..2, v=0..4 (from test 3 fall 98) a. b. <(2+u)cos 2v, (2+u)sin 2v, v> c. d. 2 & 3. Line integrals. Use maple to draw `plots like in maple lecture12' Eventually each line integral over a curve C reduces to integrating a function like int(g(t),t=a..b). What we want is a `curtain' of height g(t) over the curve C. If C is given by , t=a..b then we want to plot the surface t=a..b, s=0..1. We can do this with plot3d as follows plot3d([x(t),y(t),s*g(t)],t=a..b,s=0..1,title=`line curtain`,axes=BOXED); #2. Draw the curtain for #2 in 18.2 of the text #3. Draw the curtain for #3 in 18.2 of the text. #4. Use Maple to do the surface integral for #3 in 19.2 5. Plot a Klein bottle. The following should help c:=.6;a:=.2; plot1 the handle: Range u=Pi/2..5*Pi/2,v=Pi/4..5*Pi/4 A:=c*(cos(v)*sin(v) -0.5 + a*sin(u)*sin(v)/sqrt(sin(v)^2+cos(2*v)^2)); B:=a*c*cos(u); C:=cos(v)+a*c*sin(u)*cos(2*v)/sqrt(sin(v)^2+cos(2*v)^2); parametric equations of this part of the surface [A, B, C] plot2 the bulb: v=5*Pi/4..9*Pi/4 Range u=Pi/2..5*Pi/2,v=5*Pi/4..9*Pi/4 r:=sin(v)*cos(v) - (a+1/2); A:=c* sin(u) * r; B:= -c * cos(u) * r; C:=cos(v); parametric equations of this part of the surface [A, B, C]