http://www.mapleprimes.com:8080/maplenet/primes/worksheet/9288_probset3.mw

see worksheet

<a href='http://www.mapleprimes.com:8080/maplenet/primes/worksheet/9288_probset3.mw'>View 9288_probset3.mw on MapleNet</a> or <a href='http://www.mapleprimes.com/files/9288_probset3.mw'>Download 9288_probset3.mw</a><br/><a href='http://www.mapleprimes.com/viewfile/4149'>View file details</a>

It is the DIVERGENCE I want.  Any feedback or example how to make it work would be a help.

Your help did point me in the correct direction.  However, should MAPLE help for the GRADIENT command at least have a hyperlink to the JACOBIAN if not direct language in the HELP dialog specifying this issue?  Maybe this is intuitive for mathematicians but as a pragmatist the GRADIENT command should be capable of handling both with maybe some notational distinction so you know you are dealing with a vector instead of a scalar function.

 

just a thought

It would seem that the MAPLE help menu would have a link to the Jacobian from the gradient help page.  That would have helped me save some time.

Is the DirectionalDiff command the tool I should use to find the gradient of a vector.  MAPLE HELP has a gradient as well as NABLA command but it seems they can only be used on scalar functions to convert them into a gradient vector.  Instead of this I am seeking the gradient of a vector which then yields a 2nd order tensor.  Is there something else I should use?

I used the brackets in this web browser editor, not in my MAPLE code.  Nonetheless, I have attached my output.  I attempted to transform the integral into a simpler form using variable substitutions.  Eq. 1 shows the resulting transformation in terms of u.  To solve this a number of integration by parts is likely required.

Can MAPLE not do this operation???  Note if I attempt to integrate with respect to phi MAPLE won't do the integral either.

http://www.mapleprimes.com/files/9288_integral output.pdf

 

I was able to get MAPLE to generate an output if I had r^2-a^2*x within the sq root, but not cos(x).  Why??

To clarify I redefined a = alpha & b = beta in the specified pdf file.  I wanted to avoid variable ambiguity & ignore the substitution of v.

sorry for the inconvenience of the ambiguity

Below is the pdf file of my new output employing the "Integration Tools" module.  I would like to confirm this with anyone with more MAPLE experience.

Also, see my previous posting about selection of TOOLS modules.

<a href='http://www.mapleprimes.com/files/9288_new output.pdf'>Download 9288_new output.pdf</a><br/><a

Robert & others, Apparently the Integration Tools package is the key. I am now actually getting something other than MAPLE simply repeating what I enter. I have MAPLE 12 & I typically use the GUI interface instead of doing command line worksheets. When I go to the MENU "TOOLS" I select "Load Package" & "Integration Tools" is not an option. I have "Vector Calculus" & "Student Calculus I" as options but I am not sure if that is adequate. I entered via command as per your example & I do not get any error when entering "with(IntegrationTools)". How do I know which package I need to perform whatever type of analyses I choose to execute, especially, for tricky tasks that are not performed very often like this case? I will move forward & reply with my results & any other potential hurdles I stumble over. I was on travel yesterday so I did not get anything done until this evening.

I was not successful at uploading the images so I converted everything to pdf, so the supposed link info is below.  I do not think my solution is totally correct but it appears to be n the right track since I know from the text what the solution for the far field radiation distribution is supposed to be.  Page 1 is the derivation of the integral of concern.  Page 2 is the attempt to solve the integral.  I am pretty cdonfident in page 1.  Evaluation of the integral on p. 2 is where troubles reside & that is where I was hoping MAPLE would be of assistance.

Any feedback as to how to correctly evaluate that integral is welcome.  Maybe it can only be done numerically?

<a href='http://www.mapleprimes.com/files/9288_piston radiation model.pdf'>Download 9288_piston radiation model.pdf</a><br/><a href='http://www.mapleprimes.com/viewfile/3949'>View file details</a>

 

How do I attach a JPEG scan?  I attempted to use the Insert/Edit Image icon at the top of the editing toolbox, but it is asking for a URL address.dd

see the symbolic expression by Robert Israel.

All parameters, a, b, & c must be symbolic.  I can say in most instances b -->1.0 for my specific application.

The difficulty arises when a is something other than ZERO.

I ended up solving the integral by hand but had to employ transformations to get it in the form of:

(exp(-cx))/x

It took me about an hour.  Yesterday I spent the entire day attempting to get MAPLE to do the work.  What use is MAPLE?  Everytime I use it nothing is EVER straight forward.  Software is supposed to speed things up & provide assistance.  MAPLE never does that.

I wasted time & money on this package!!!!!

I will try to upload my solution, any comments if incorrect is welcome!!

 

YEP, I cannot seem to find an analytical antideriv either.  By appearance it appears there should be one.  In fact, if 1 exists it would describe the radiation field emanating from a point source along a radial axis which I would think someone has solved.  MAYBE NOT

Anyone has any other suggestions I welcome them!