@rlopez 
Thanks!

Very helpful to see a graph to understand the concept of a lineintegral of a scalar
It was in the book of Calculus early trancedentials (Stewart) that i understood the concept 
(my old Dutch study book shows nothing)  
Using a Riemann sum with the rectangles and plot this as replacement for the lineintergral is a idea. 

@Kitonum 
Thanks

You can give the aera of this curvilinear integral as mass
Not work, because there is no vector involved

@Kitonum 

Thanks

It is indeed not related with vectorcalculus this example, because there is no vectorfield involved

I studied some more and i think i understand now the concept 
A visualization says more then a formula, especially in Calculus 
Maybe i can make a plot of the example 
The 2D input is not suited for a detailled plot ( a sort of fench ) for this task 
Mapleinput is needed for plotting.   

is there default command what shows vertical lines in a 2D or 3D  from domain to  functiion values ? ( must be a plot option ? )  

Thanks

The book is not helping  by explaining the method used
In Dutch language it is lijnintegraal
There are lineintegrals in Maple too( looked there), but they are all related with vectorfields, although there is a definition of curvilinear integral  under 2.a in maple help to find
But there was no example to find here.   
 

Its only by graphing this path integral for some t -values i was hoping that it becomes more clear for me

@janhardo 

I made a little start inthe vectorcalculus by drawing a 3D vectorfield. 
-don't know the type of vectorfield  and the meaning of a flowline at a given point.
I used the VectorfierldTutor() and a command generated by the tutor of the same field, but the plots differ.

Using a example in a Dutch studybook and at time there was no visulisiation of a vectorfield possible (1996/97), because no example in the book   
A 2D velocity vector field transformed as a system of a ODE and  the flowlines are integralcurves to start with. 

Download Toegepaste_wiskunde_-vectoranalyse-lijn-en_oppervlakte_integralen.mw

@rlopez 
Thanks!
Yes, Maple apps .? ..portal 
DifferentialGeometry package.has certainly my interest, but it seems not easy accesible for a starter
It's not a topic in engineering mathematics ?
Luckily these days a lot of information can be found on internet. 
Tensor  algebra/calculus as the next step after vector calculus..interesting 

@rlopez 

Thanks!

Useful to use a paper oversight what is to see in the webinar.
I looked also to : Classroom tips and techniques: vectors in the LinearAlgebra, etc 
Can't download as a Maple file on website
 

Its from 2007: does it have still importance this worksheet?  

@rlopez 
Thanks!

I studied already parts of the webinair.
It stays always difficult (impossible too) to study a particular math concept not in a classroom teached
So i must use different sources of studymaterial for vectorcalculus

Doing this with Maple is another challence.  

@tomleslie 

Thanks
Its only not the whole folium ?

@acer 

Thanks!

Yes, the textbook from mr.  Lopez is interesting, but a little bit too expensive for me now ( no-second hand to find yet)
But the links are helpful too , because its only related the information with mr. Lopez.

Note: to be a engineer always desired and got a  education in mechanical engineering prior to a technical college what i did not finished , because a lot of reasons.  
 

@tomleslie 
Thanks
Yes, examples i can study the examples  them and then a textbook. 

Try to get the folium of descartes as positionvector defined , but did not get the graph yet.

Folium_of_Descartes_via_vector_functie.mw

I try to define this position vector for the folium in the Position Vector Constructor too, but no idea how this constructor exactly works ( video ?--or examples ).  
In student vectorcalculus there are the basic coordinate sytems and the Posion vector Constructor is from the main vector calculus package : i need a definition for the polar positionvector as example made by the constructor

 

@janhardo 

Ok, it doesn't matter if  i use a Maple prompt or not in documentmode for the 2D input , because it generated the same 2D output.
I practiced  further with matrix and vector notation and now is all working as intented.

@janhardo 

What is the best way to do vectorcalcus :  documentmode with a maple prompt? 

Some calculations with the new basigrid plot showing coordinate transformation, but its going not well unfortunaly.
I studied the  vidoexample for vectorcalculus , but nothing about how to do in what calculation mode to perform the vectorcalculus? 
I think a do vector calculus in the document mode - with or without maple prompt what makes the difference ?


Maple Worksheet - Error ..This error why ?

Failed to load the worksheet /maplenet/convert/vb_coordinaten_transformatie_-zie_boek-blz115.mw .
 

Download vb_coordinaten_transformatie_-zie_boek-blz115.mw

@janhardo 

No, it is not shocking after studying the code again, because the old procedure is more userfriendly for the procedure input parameters.
Makes corrections if you input the wrong datatype too.
It has 3 errortypes:
-3rd argument in the form [a,b] required
-Argument could not be converted to type Vector
-Vectors must have two components

The modern parameter specification comes also with error message whatever the input parameters are :
-Error, (in Basisgrid) 3rd argument in the form [a,b] required
-Error, (in Basisgrid) Vectors must have two components

The error :Arguments could not be converted to type Vectors this type error this will the modern procedure not show i think 

  

@Carl Love 
Thanks

Your procedure did the job and shows the grids, well done!
Comparing the two procedure code is  litttle bit shocking

Indeed its confusing/complicated to introduce 3 args and check these args if they are the right datatype on this way
This modern parameter specification is be used/developed in the latest versions of Maple ? 
If there is a wrong parameter specification then Maple take care for this and no need to program this error messages  as it seems.