I recently submitted my work to Maple Application Center
and I received a bug report from a staff. Then, I resubmitted
it after fixing bugs. However, I have a bug report again (^_^;
Yes, this is because my work was poor, but in other words,
all applications in Maple Application center that passed
strict check by staff are all guaranteed to have good quality.

I am sure that everyone can find good tools for education and
research. We should utilize them. If we can not find applications
that we want, let us develop works and submit them !

Yasuyuki Nakamura

Special Relativity has been around for ~100 years, General Relativity for ~90 years.  I'm hoping that with the assistance of Maple and Mapleprimes I may be able to do some tensor calculus to better understand Einstein.  Perhaps the twin paradox is within my reach.  Perhaps even the orbit of Mercury.

Of all the ways to decompose a numerical (floating point) matrix, my favorite is the singular value decomposition (SVD).  There are a lot of applications of the SVD (see my dissertation for one related to polynomial algebra) but my favorite ones are probably two applications related to image processing.

The first one I want to talk about comes from the cover of James Demmel's book "Applied Numerical Linear Algebra": image compression.  This example gives a really cool intuitive understanding of the Rank of Matrix and is also nice excuse to play with Maple's ImageTools package.

So, the first thing you need a test image. I used the classic image compression benchmark of a Mandrill.

A colleague showed this to me earlier this afternoon. I can explain, and accept, most of Maple's responses. I do have one case where I believe Maple could do better.

This arose during the creation of some Maple materials to support the derivation of the Integral Test for series convergence. Consider:

restart;
I1 := Int( 1/x^p, x=1..infinity );
                                /infinity      
                               |          1    
                               |          -- dx
                               |           p   
                              /1          x    

I would like Maple to assist me with the following definite double integral:

so far, I have failed.  Can anybody help?

Here is my worksheet:

View 4937_Page92.mw on MapleNet or Download 4937_Page92.mw
View file details

Why is the following function such a problem to differentiate?

Here is a worksheet:

View 4937_page84.mw on MapleNet or Download 4937_page84.mw
View file details

Is there an error in Wikipedia?

View 4937_page 15.mw on MapleNet or Download 4937_page 15.mw
View file details

I've made up a worksheet of the Top Ten Maple Errors, containing some of the common mistakes I often see newcomers to Maple commit (especially in the setting of my Introduction to Mathematical Computing class). I hope you will find it useful in trying to avoid those mistakes. Of course this is only a personal list, and not exhaustive. Please feel free to argue the merits of other items that should be included in the list.

Here is the link:

View 4541_topten.mw on MapleNet or

For the past decade Doug Meade, at the University of South Carolina, has created and maintained a two-page document with essential Maple commands.

The first version was created for Maple V, Release 4, in January 1998. n update has been created for each version of Maple (except Maple 10) as it was released. The document has become pretty stable - hence the omission for Maple 10.

Here are links to the complete set of documents he has created

• Maple 11 (Jan 2008)
  
• Maple 9 (Mar 2004)
  
• Maple 8 (Oct 2002)
  
• Maple 7 (Jan 2002)
  
• Maple 6 (Dec 2000)
  
• Maple V, Release 5 (Apr 1998)
  
• Maple V, Release 4 (Jan 1998)

Comments, corrections, and suggestions for improvement are welcomed. Please contact the author by e-mail.

The recipe is quite simple to understand looking at an example (and it is understood best by having paper and pencil to follow it):

f:= x -> x^2 the parabola with its inverse g:= y -> sqrt(y).

Say you want the integral of g over 0 ... 2, which (here) is the area between the graph and its horizontal axis.

That is the same as the area of the rectangle minus the area between the graph of g and the vertical axis, where the rectangle has corners 0, 2 and g(0)= f^(-1)(0) and g(2)= f^(-1)(2).

Now recall the geometric interpretation of the compositional inverse of a function: it is reflection at the diagonal.