Your illness has to be regretted. The way to handle its consequences
for your studies is to resolve issues through the administration of
your faculty or your teachers, may be the students council may assist
you. Quite certainly this board is not the very place for that.

Whatever your personal reasons are, there is no excuse for your manners.

You bump in grawling in capital letters, do not even give your name in
the profile, sling some exercises onto the desk and order a solution
ASAP in your prefered format, without caring for any of the rules for
the Student's section - especially without doing a single jota of own
work.

Reading your reply I can not find "sorry for ..." and the spirit does
merely indicate anything towards that. At least a consistent attitude.

Get well soon, in any sense.

The poem is about some clock around midnight, the witching hour, and the spirit at that time. Partially it is onomatopoeic (playing with the sound of spoken words), it uses coinage (new, artificial words) and some non-sense ... almost impossible to translate between languages. This kind of humor thus is somewhat hidden for non-natives. And for natives it is definitely matter of taste :-)

NB Concerning product names: for M$ Vista a German spoofing is "Was da?" ~ "What is there?"
 

In Maple one gets f_xy = f_yx, except in (x,y) = (0,0) and the double-limits are not interchangeable in zero being +1 and -1.

Also tried the DifferentialGeometry package, but I am not used to it, needed some time to write it down (+ manual work).

NB: what is interesting in that example that it shows, that a continous extension is not analytic for dimension beyond 1

I am not aware of a similar political / social interpretation ...

only just being remembered to the " Zwölfelf ", a poem by Morgenstern, a poet from Munich
en.wikipedia.org/wiki/Christian_Morgenstern, impossible to translate to English I guess

My personal view on the bad 13 is: the old system counting in 12 (possibly based on the
moon through the year) switches to something new, causing phobia .. will see next Tuesday

18 = A H is used for Adolf Hitler by right wing extremists and Nazis

They use it as the inital letters A.H., A ist the 1st and H is the 8th letter in alphabet, while the 19 19 stands for the usual doubled S  in 'SchutzStaffel'

ok, off topic and certainly not what you wanted to initiate ... more towards political education

I do not mind the product name ... in different cultures there are other 'bad' numbers ... beyond Wiki (which might give several examples) for example the Neonazis use '18' for AH or '19 19' etc, since in Germany such propaganda is forbidden by law.

@Alex: Agreed ... however my pain barrier moves if working with computers (the first test was to write down x = x+1 without epilepsy)

@Alejandro: good to see such stuff - Maple 12? Of course the marketing #$%&! (censored by me) are too lame to point to such things ...

Certainly some global option "give me the assumptions for which the result is true" would be fine ( like for int(x^n, x) giving x^(n+1)/(n+1) ), since otherwise one always has to read it as "as far as it is defined" or similar - which is, how I read it.

However that may become complicated (ok, truth has no reason to be simple ...), the standard example is solving a linear or quadratic equation (depending on the leading coefficient).

For the commuting derivatives and their use in differential equations: I never feel sure about any of the packages when I know that a common assumption may be 'analytic' - and I have not ensured that it is the case when using it. I think it is reasonable to leave that to the user.

And may be Maple is not the only CAS doing so in general. For example what would you expect to write even down an expression like diff( f(x), x ) or dito for int? Generically a function is not differentiable: en.wikipedia.org/wiki/Pathological_%28mathematics%29#Pathological_functions

Alec - I am the most alert listener of your courses you have never seen :-) Fine to read you again ...

Ok, "New Tools for Engineers" Plotting enhancements (2 y-axes - nice!),  "Wavelet transforms" (will see) and
"The World’s Richest Computational Environment" seems to be the stuff I was looking for

"For a moment, nothing happened. Then, after a second or so, nothing continued to happen."

What I was wondering is: there one passes to Reals/group, the circle,
while in the cases above one does not consider the quotient.

But that would drift of the topic I guess

After a day of work I am brainwashed and can look at that differently.

I did not understand Alejandro's suggestion, because in alg Geometry
I would divide out the invariance ... however what he says in his
first contribution should be understood by me in the way his task
was set up and solved, as it is what is shown at the Wiki as well:

For certain invariance one simply knows by experience, that one may
use a different coordinate system (polar, cylinder, sphere) hoping
to achieve a (simplier) problem. Astonishing the Wiki examples do
even turn out to be products (as an experiment one could start with
a more complicated situation from there to get ugly ones in IR^n).

Those transformations are known well enough to determine how the
domains transform.

hmm: would one resort 1-dim Fourier problems or periodics to this
as well?

For the invariance may be one can use Lie stuff from Maple (for DE)
to find that out (never worked with it).

May be also some stuff like Arnold's "Geomterische Methoden" for
DE helps for more ideas (that's what Alejandro may have had in
mind with his response).



The other thing are the domains and the boundarys, seems to be one
of Jacques' central points.

Here I see, that the Wiki suggests to find a parametrization of the
boundary curve (that's what is done at 'normal domains', not sure
whether one could also try to use Stoke's Theorem).

But beyond that I think one would try to use transforms for which
one *knows* which geometry is left invarint (or how it transforms),
like Moebius transforms or whatever.

This also applies to the question 'what happens under linear trans-
forms?' - if non-degenerated (which always is needed) it just maps
quadrilaterals to quadrilaterals, since it respects affine lines
(yes Alejandro already answered that more concretly). And circles
transform to ellipsoids etc.

The second question I think is too general - just think of the
homotopy invariance in complex analysis :-( ...  

x = (-a(y)+b(y))*xi+a(y) for Int(Int(f(x,y), x=a(y)..b(y)),y=0..1)

gives me  Int( (-a(y)+b(y)) * J(y), y = 0 .. 1), 
          J(y) = Int( f((-a(y)+b(y))*xi+a(y)), xi = 0 .. 1)

So it becomes an integral over the unit square, but I think it is
an approach inverse to parametrizing the boundaries.

Alejando, Thx for encouraging :-) It's simply that my geometric
thinking ignores group operations ...

Anyway: yes, the general approach may be difficult. But practical
most stuff is done along recipies or proved concepts, even in one-
dimensional cases.

The Wiki examples just show that (ok, they are educational): these
are transforms, where phi^(-1)(V) can be described and turns out to
be useful.

Kawski's article/code on visualization might be of help for more.

However my starting point was: "What is the general formula?"

The point is: in dim=1 (if the transform is bijective [which may
be the first error to do]) the pre-image automatically is an inter-
val (if such is given).

Already for curve integrals and complex variables it is not so clear
what to do to achieve at a simplier task - so why should it be the
case in a general setting?

PS: I like Joe Riel's solution, even it is not quite handy ...
was not aware of this :-(