## 117 Reputation

12 years, 360 days

## Undefined integral of zero....

Maple 2019

The following 2D integrals of 0 are seemingly trivial and one would expect them to evaluate to zero, but Maple evaluates them to undefined

int(0, x=0..infinity, y=0..1) # undefined
int(0, x=0..1, y=0..infinity) # undefined

When the 2D integral is split into two 1D integrals, it does evaluate to zero, as the following examples show

int(0,x=0..infinity) # 0
int(int(0,x=0..infinity), y=0..1) # 0
int(int(0,x=0..1),y=0..infinity) # 0

If infinity is replaced by a variable (say 'c'), the first two integrals are also evaluated to zero.

It may be connected by the following

int(a, x=0..infinity, y=0..1) # a*infinity
int(a, x=0..1, y=0..infinity) # a*infinity
int(a,x=0..infinity) # signum(a)*infinity

So for the 1D integrals the signum is applied to 'a' when the interval is infinite, but not for the 2D integrals. I'm not sure about this difference.

## Issues with pdsolve (2)...

Maple

Hi,

There seems to be an issue with pdsolve, which is similar to https://mapleprimes.com/questions/222498-Issues-With-Pdsolve.

pdsolve([diff(u(x, t), t) = diff(u(x, t), x, x), u(x, 0) = 1, u(0, t) = 0, u(2, t) = 0]); # works

pdsolve([diff(u(t, x), t) = diff(u(t, x), x, x), u(0, x) = 1, u(t, 0) = 0, u(t, 2) = 0]); # swapped arguments, works

pdsolve([diff(u(x, t), t) = diff(u(x, t), x, x), u(x, 0) = 1, u(-1, t) = 0, u(1, t) = 0]); # translate by -1, works

pdsolve([diff(u(t, x), t) = diff(u(t, x), x, x), u(0, x) = 1, u(t, -1) = 0, u(t, 1) = 0]); # swapped arguments and translate by -1, doesn't work

The solution for the last example doesn't incorporate the initial condition correctly, while it is the same as the third example (except for swapped arguments). Not sure if this is still a problem in Maple 2019, though.

## Problem with graphics when using eBookTo...

Maple 2018

Hi,

I'm using the eBookTools package to convert a .mw file as a chapter into a PDF file. However, a problem arises when I convert a document with a few repeated plotting commands (such as plot(x^2)). The issue is that in the final PDF the images of the various plots overlap, and that the individual plots can't be clearly seen. Is there a resolution to this?

Thanks,
Bart

## Issues with pdsolve...

Maple 2016

will give me

which is indeed a solution of the PDE1

will give me

which is not a solution of the PDE2

However, both differential equations are equal, only the arguments are swapped around. Am I doing something wrong, or is this a bug?

Thanks

## Series with equation number bug?...

Maple 2015

Hi,

When I execute the command

series(exp(x),x)

and then refer to the equation in a new execution group using a equation label (CTRL-L on Windows), the equation is shown in Maple 18, but in Maple 2015 I get an error message: 'Error, missing operator or ';'. Using the % instead does work for both versions.

Is this intended behaviour or a bug in Maple 2015?

Thanks,

Bart

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