hitstudent

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Hi

When I try this maple retuurns FAIL and does not evaluate the expression.

is(seq(tm[i] < (1/6)*Diameter[rør][i], i = 1 .. 17));

tm is numbers in mm and diameter is also numbers in mm

Diameter[rør] := [273.05*Unit('mm'), 219.08*Unit('mm'), 168.28*Unit('mm'), 114.3*Unit('mm'), 273.05*Unit('mm'), 219.08*Unit('mm'), 1066.8*Unit('mm'), 60.33*Unit('mm'), 219.08*Unit('mm'), 168.28*Unit('mm'), 168.28*Unit('mm'), 141.3*Unit('mm'), 168.28*Unit('mm'), 114.3*Unit('mm'), 114.3*Unit('mm'), 168.28*Unit('mm'), 168.28*Unit('mm')]
tm := 8.982892831*Unit('mm'), 4.189790007*Unit('mm'), 3.913902969*Unit('mm'), 3.620745836*Unit('mm'), 4.482892831*Unit('mm'), 4.189790007*Unit('mm'), 8.793627806*Unit('mm'), 3.327643012*Unit('mm'), 4.189790007*Unit('mm'), 3.913902969*Unit('mm'), 3.913902969*Unit('mm'), 3.767378711*Unit('mm'), 3.913902969*Unit('mm'), 3.620745836*Unit('mm'), 3.620745836*Unit('mm'), 3.913902969*Unit('mm'), 3.913902969*Unit('mm')

 

please help me with this thank you

Hi.

This is probably not very much maple related question, but to some extend it is.

After failing this question on my exam I have tried to solve it, but it seems like I cant get it right.

Given a sphere z^2+r^2=4 and a cylinder r=1 I was told to set up the volume integral for the element T enclose byt the outer sphere and the inner circle.

I tried to generate a plot but my skills are rather poor in plotting, if I could get the plot right I would be able to set up the volume integral. I have also tried to figure out how to do the surface integral and chose to use a task template as it is a bit more convinient when you find the syntax hard.

I would say I am familiar with the VectorCalculus:-SurfaceInt in cartesian for when i have intersection of two surfaces given in terms of z=

 

but this kind of problem is new to me.

 


 

Surface Integration over a Surface Defined Parametrically

 

Formulate and evaluate the surface integral of f(x, y, z) over a surface defined parametrically.

NULL

 

Surface Integral on a Surface Defined Parametrically

 

 

  Integrand

"f(x,y,z)="

   

 

 

 

   " x(u,v)="

   

 

 

 

"y(u,v)="

   

 

 

 

   " z(u,v)="

   

 

 

 

 

 

`&equiv;`(F(u, v), f(x(u, v), y(u, v), z(u, v)))

`&equiv;`(LinearAlgebra[Norm](N), sqrt((`&PartialD;`(y, z)/`&PartialD;`(u, v))^2+(`&PartialD;`(z, x)/`&PartialD;`(u, v))^2+(`&PartialD;`(x, y)/`&PartialD;`(u, v))^2))

 

 

 

"&int;(&int;)[S]f &DifferentialD;sigma =(&int;)[u=a]^(u=b)(&int;)[v=g(u)]^(v=h(u))F(u,v)||N|| &DifferentialD;v &DifferentialD;u"

"="

"b="

"&int;(&int;)[S]f &DifferentialD;sigma=""(&int;)[v=a]^(v=b)(&int;)[u=G(v)]^(u=H(v))F(u,v)||N|| &DifferentialD;u &DifferentialD;v"

"="

"a="

 

 

NULLNULL

 

NULL

NULL

 

NULL

                                

 

 

NULL

with(plots):

p1 := plot3d([2*cos(u)*sin(v), 2*sin(u)*sin(v), 2*cos(v)], u = 0 .. 2*Pi, v = 0 .. Pi, color = green, transparency = .55):

p2 := plot3d([cos(u), sin(u), z], u = 0 .. 2*Pi, z = -2 .. 2, color = red, filled = true):

display(p1, p2)

 

p3 := plots:-sphereplot(2, theta = 0 .. 2*Pi, phi = 0 .. Pi, color = green, transparency = .55):

p4 := plots:-cylinderplot(1, theta = 0 .. 2*Pi, z = -2 .. 2, color = red):

plots:-display(p1, p2)

 

``

NULL


 

Download surface_int.mw

Hi.

I got 2 surfaces given by z=(r,theta)

I have plotted them by converting to cartesian, it gave me a good representation, but i dont get the surface entirely closed. I then used the task template vizual integration and got the solid i needed.

The problem with the rough representation cartesian conertation gives is that the integrals for volume, flux etc becomes so complex maple struggle to calculate it and since the surface is not completly closed it gives me the wrong value.

How can I plot cylindrical and spherical cordinates? 
 

I have checked the following helping page in maple: Set Coordinate System for 3-D Plots

plot_cylindrical.mw

Hello.

If I have several equation where some of them are given in cartesian and some in spherical I would want to work with all surfaces in cartesian coordinates. Just since that is the coordinate system i´m most familiar with.

I have cheked and tried: ChangeOfVariables, changecoords and ?coords

All of those are great recourses, but they wont let me change from [r,theta,phi],cartesian[x,y,z] How can I obtain that in maple?

Hi.

This might not be a maple question. But I know maple has very smart and many plotting tools as well as this comunity is full of very skillfull people. So I concluded that I might get an answer here.

Lets say I got some sphere that is cut off by any abirutary plane, how would I go about plotting this?

For the purpose of this example the sphere is centred at the origin with radius of 4 and are cut of by the plane z=2-y.

 

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