@Carl Love 
Thanks!

Important to know the namegiving for this all, for using all formulaes in the ricght  contect.

A surface(S) can be the top (roof) of a 3D figure and a area (A) is the bottom of that figure
A lateral surface from a solid , this all for 3D.  
A function f (x,y,z) is 4- dimensional and the surface levelcurves can be used to calculate the flux for this surface (S) (3D vectorfield)

I am just now practicing with 2D flux and 3D flux for a vectorrfield  

For 3D flux a surface integral (surface S) projected as area integral( area A) can be used and 2D flux using a circulation integral 

After this 3 integrals for vector-function/field
- Green (2D): vectorfunction : flux  
- Gauss (3D) : vectorfield : flux
- Stokes (3D) :vectorfield with rotation(curl) gives circulation

Looks not too  difficult to do this in Maple

@rlopez 
Thanks

I just did it earlier as you proposed now
I realised now that the picture in the book are hollow spheres  : two spheres are  drawed. 
Plotting a massive sphere alone does not contribute much for insight, but the idea was to use the context menu as  exerxcise.
To construct this is via "plotprogramming"  and not intuitive anymore ,
Perhaps there is option in the plotbuilder to draw the two sphere only as circles and adding dashed lines is programming
(but that i don't want to do here : take too much time ).  

I want to do some bookexercises to get used on the contectpanel
 

Drawing a sphere with  this equation x^2 + y^2 + z^2= 1 from contextmenu right away is not possible 
So you need a command to do this : apply a external command? 
i am wondering what packages are connected with the contextmenu?
with(plottools) 
with(geom3d)

To stay in normal calculus or maybe with vectorcalculus with a spacial positionvector ?
Apply a command is using help screen (examples) together with the popup command screen in the widescreen.
Plotting a smooth sphere with radius 1 and 4 
 

@janhardo 
What i did with this expression was:

answer5 := {x = 553.6, y = 455.0}, {x = 553.6, y = -455.0}

copy and paste 

x = 553.6, y = 455.0  now assigning the values to the variabeles: i typed in a semiclon : in the existing  variables x and y
then y/x for arctan , etc 
theta1:=arctan(y/x)

Not using the contectmenu.

Note: still did not find a keystroke for removing a output in a cel in documentmode as well in worksheet mode?

@tomleslie 

Thanks!

Could not find information in Maple about using external code in a procedure, but that are mainly other selfmade or premade procedures then.
What caused this error message with display3d ? ..probably:  with(plots,display3d); in the procedure

Seems to be a existing command , but there is no help for  it. 
A alias display3d, but where defined in worksheet?

  

@janhardo 

A (solution) set must be further manipulated to get a arctan values in this example

Download verzameling_oplossingen_berekening_mee_maken_vb_arctan.mw

@acer 
Thanks

Good exmples for learning the documentmode.

If the student wants to program procedures , then maple input is needed
But using the procedure ability can be handy too in the document mode i think
It seems that there are students now these days who are not using the maple input.

Using the equation labels is for commercial companies who don't have much time for doing their calculations
If this can be done for all sorts of lenghty technical calculations?   

@rlopez 

Thanks

I am glad to that there is 2D inputmode : it makes it easier to study the mathematics were i am interested in.
Did also study some basic programming constructs as maple input, so what you did now is not totally new for me

I can imagine that the student don't like to learn a extra language to learn mathematics
In 2000 there was not other choice when i studied math.
Wondering how this equation z = 4*x^2 - 6*x + 4 in 2D input can achieved ?
I did a attempt , but fill in command : eliminate , but that makes that you must know at forehand this command , lol

For me it doesn't matter if it done in Maple input or 2D input the calculation
But i am curious how it can be done in 2D input, because that is more natural to read the mathemical symbols

I understand the maple input example, so it also faster for me as for you , because 2D input takes longer as pointed out.(update :: see examples ?)
When doing this in Mapleinput you are assured that it is correct, but doing it with 2D input it is more difficult to see if it is the right answer?

In doing mathematics, i like as much as possible in 2D input.
Combining Maple input and 2D input also possible

@Carl Love 
Thanks
 

@rlopez 

Thank you very much for the thoroughly answer of my question.

I do see my book handles this task (on two ways)  also with he parameter t
A line is parametrized with t and by a given line you can then come up with more then one parametrization.
But in your example is direrctly done for the curve as function y=g(x)
Manipulation on expressions is diificult to master for me, but i can learn from this example

Complete square can also of course.be used on 4*x^2 - 6*x + 4

I looked also to eleminate in the help :

The result of this elimination is an expression sequence of lists.  Each list represents a possible elimination of the given variables. => that is not the output on screen ?
A list that has sets as elements in the examples.

The result of this elimination is an expression sequenze of sets in a list as outcome in the examples for the eliminate examples in help?
Probably i am wrong and its deeper under the hood of Maple 

@janhardo 

Seems that a equation of a intersection is needed

Download vb4-blz204-toegepate_wiskunde_deel2.mw

@tomleslie 
Thanks
I was thinking on the same for this adding a t , and add more Pi  like your example
But something went wrong en got a error in the handling of the document mode without prompt
I put a restart at the top of the page and the command was working again
A restart in the middle of the document for a new calculation seems to be not correct, because then i got a error for plotting the helix.  

 

@tomleslie 

Thanks!
Just enough to do my other exercises with different curves  : these circles definitions will be combined with other plots in plot display ( if possible ) 
The vectorcalculus SpaceCurve() circle cannot be transformed into a helix 3D ?    

@tomleslie 

Thanks

-cartesian: in x and y see my example, and in parametric form   
- polar , and in parametric form.: no in3D polar becomes cylindrical
- cilindrical (your example), and in parametric form.

But not with the vectorcalculus possible ?  
A 3D positionvector with no e3 unitvector ( notation be studied in pdf mr. Lopez )

@vv 

First as PathIntegral and x^2+y^2  is a parabolide  ..all intersection planes for z > 0 shows circles   
Plotting the Curve and the scalar function on the same way like is done in the worksheet of mr Lopez
is not that easy.
- i got plot of the parabolide : x^2+y^2
-  now a circle(Curve) in the xoy plane: can be done via with (plots) or with student Vectorcalculus as position vector. ?    
- a green surface is the lift of the circle up to the surface?
 Graphical its clear what to do.

The definiton of a circle is via plots command : spacecurve  

Student vectorcalculus for SpaceCurve command has a tutor ..   

A := PathInt(x^2 + y^2, [x, y] = Circle(<0, 0>, 1));
B := PathInt(x^2 + y^2, [x, y] = Path(<cos(t), sin(t)>, t = 0 .. 2*Pi));
                           A := 2 Pi

                           B := 2 Pi