## pdsolve issue with heat PDE. map expects 2 or mo...

Hello Maple experts:

Using Maple 2018.2.1 on windows, with Physics package version 301.

There is some strange issue in parsing somewhere.  This works

```r:='r'; u:='u'; t:='t';theta:='theta';k:='k';
k:=1/25;
pde := diff(u(r,theta,t),t)=k*(diff(u(r,theta,t),r\$2) + 1/r*diff(u(r,theta,t),r)+1/r^2*diff(u(r,theta,t),theta\$2));
bc1:= eval(diff(u(r,theta,t),r),r=1)=0;
bc2:= u(r,0,t)=0, u(r,Pi,t)=0;
ic := u(r,theta,0)=(r-1/3*r^3)*sin(theta);
sol:=pdsolve([pde, bc1, bc2, ic], u(r, theta, t),HINT = boundedseries(r = [0]));
```

No problem with the above, pdsolve gives solution. Now if I change k from 1/25 to 1, it gives parsing error in map

```k:=1;
pde := diff(u(r,theta,t),t)=k*(diff(u(r,theta,t),r\$2) + 1/r*diff(u(r,theta,t),r)+1/r^2*diff(u(r,theta,t),theta\$2));
bc1:= eval(diff(u(r,theta,t),r),r=1)=0;
bc2:= u(r,0,t)=0, u(r,Pi,t)=0;
ic  := u(r,theta,0)=(r-1/3*r^3)*sin(theta);
sol := pdsolve([pde, bc1, bc2, ic], u(r, theta, t),HINT = boundedseries(r = [0]));
```

Error, (in assuming) invalid input: map expects 2 or more arguments, but received 1

any K value less than one works.

Now I change K from 1 to 2, the error goes away. But no solution. Which is OK.

Why does the map error shows up when k=1 only? Same error shows up if K is missing all togother, as in

```r:='r'; u:='u'; t:='t';theta:='theta';k:='k';
pde := diff(u(r,theta,t),t)=diff(u(r,theta,t),r\$2) + 1/r*diff(u(r,theta,t),r)+1/r^2*diff(u(r,theta,t),theta\$2);
bc1:= eval(diff(u(r,theta,t),r),r=1)=0;
bc2:= u(r,0,t)=0, u(r,Pi,t)=0;
ic  := u(r,theta,0)=(r-1/3*r^3)*sin(theta);
sol := pdsolve([pde, bc1, bc2, ic], u(r, theta, t),HINT = boundedseries(r = [0]));
```

Error, (in assuming) invalid input: map expects 2 or more arguments, but received 1

## How do I create my own Heaviside function?...

Hi

I want to create a Heaviside function called MyStep() which will behave exactly like the built in Heaviside with one exception: for MyStep(0) it will return 1 instead of undefined.

MyStep(t) = 0, 0<t

MyStep(t) = 1, else

Thanks

## Nontrivial solution for large matrix...

Hi

I got an square matrix (70×70) from MATLAB (please download attached text file 1.txt). Following codes are used in MAPLE, but an unknown error is occurred. It seems that matrix is divided in two submatrices. Please hint me or run the codes to obtain fiirst three minimum real positive roots of the determinant.

Thank you for taking your time

Maple codes

Digits:=150:

LinearAlgebra:-Determinant(M):

fsolve(%,P=0..0.5)*100;

## try to set up a table in a maplet...

Good morning everyone

I'm sorry if I'm asking a simple question, but I would like to create a maplet from a maple code I written.

My first problem is I would like to now how to create a table like in excel, to be fill up by the user of the maplet.

Basically, the maplet will consist of enter two parameters who define the number of colums and row needed for the table,

Then fill up this table, which gonna be plot, and then a button to fit this curve using an equation. And the starting value in order to fit the curve will also be set up by the user.

Thanks you in advance if you can help me to set up this table in the maplet.

cheers!

## Bug in shape=triangular[upper/lower, unit]...

Hello,

in Maple 2017 (could not try 2018) the following is a bug;

with(LinearAlgebra);
U:= Matrix(4,4, shape=triangular[upper, unit], symbol =u);
-U;

It returns the wrong matrix, with +1 on the diagonal and -u_{ij} on the upper part. That is, it changes the sign only of the entries in the upper part. The bug is for any size, and also for lower triangular.

## How can I use fsolve to interatively solve a probl...

I have been trying to use fsolve to iteratively solve a free convection heat transfer problem for a heated vertical plate using units and the ThermoPhysicalData library.  I have received some help and have managed to get rid of the eror messages but I still can't seem to get it to solve.

Here is the code

restart;
with(Units:-Standard); with(ThermophysicalData);

conv_VerticalPlate_proc := proc (T__side, T__amb, Area, L, varepsilon, q__i)

local sigma, g, T__s, `T__&infin;`, T__f, k, rho, Cp, Pr, mu, nu, alpha, beta, Ra__L, Nus__L, h, q__h, q__r, q__total;
g := 9.81*Unit('m'/'s'^2); sigma := 5.6703*Unit('W'/('m'^2*'K'^4))/10^8;

if type(T__side, with_unit) then
T__s := convert(T__side, temperature, kelvin)
elif T__side = 0 then
T__s := 273.15*Unit('K')
else
T__s := T__side*Unit('K')
end if;

if type(T__amb, with_unit) then
'T__&infin;` := convert(T__amb, temperature, kelvin)
elif T__amb = 0 then
'T__&infin;` := 273.15*Unit('K')
else
`T__&infin;` := T__amb*Unit('K')
end if;

T__f := (1/2)*T__s+(1/2)*`T__&infin;`;

k := Property(thermal_conductivity, temperature = T__f, pressure = Unit('atm'), air);
rho := Property(density, temperature = T__f, pressure = Unit('atm'), air);
Cp := Property(Cpmass, temperature = T__f, pressure = Unit('atm'), air);
Pr := Property(prandtl, temperature = T__f, pressure = Unit('atm'), air);
mu := Property(viscosity, temperature = T__f, pressure = Unit('atm'), air);

if type(k, with_unit) and type(rho, with_unit) and type(Cp, with_unit) and type(mu, has_unit) then
nu := mu/rho;
alpha := k/(rho*Cp);
beta := 1.0/T__f;
Ra__L := g*beta*abs(T__s-`T__&infin;`)*L^3/(alpha*nu);
Nus__L := (.825+.387*(Ra__L^(1/6))/(((1+(.492/Pr)^(9/16))^(8/27))))^2;
h := Nus__L*k/L; q__h := h*(T__s-`T__&infin;`)*Area;
q__r := varepsilon*sigma*(T__s^4-`T__&infin;`^4)*Area;
q__total := q__h+q__r
else
0.1e-6*Unit('W')
end if

end proc;

conv_VerticalPlate_proc(31.5*Unit('degC'), 20*Unit('degC'), Unit('m'^2), Unit('m'), .9);

100.8567010 Unit(W)

conv_VerticalPlate_proc(x*Unit('degC'), 20*Unit('degC'), Unit('m'^2), Unit('m'), .9);

0.001 Unit(W)

fsolve(100*Unit('W')-conv_VerticalPlate_proc(x, 20*Unit('degC'), Unit('m'^2), Unit('m'), .9), x = Unit('degC') .. 100*Unit('degC'));

I would appreciate help wih this.

Thanks

## Ways (simplest) to remove a single data point...

For example if a:=[3,3,1,5,7,8,5,4,4,4,4,3,9]

What is the simplest way, or alternate ways, to remove only one 4 for example from the dataset.

## What command shuld we use to solve system automati...

model.mw

after loop how to pick equations automatically solve system of equations???

## Typesetting:-mparsed(...) error on latest 2018.2.1...

Hi

I've just upgraded from v2017.3 to 2018. It worked OK until I installed latest service pack 2018.2.1 (server license provided by my University). Ever since I cannot use Maple. Anything I type I get Typesetting:-mparsed(...) error and the text/command I typed.

I’ve contacted our software tech support and they told me to change the typesetting level from advanced to standard and it did fix the problem.

But why does it happen in the first place? I’m running Windows 8.1 64bit. Out tech support told me to has something to do with 3D display issue on my machine and told me to bring my laptop on Monday to see if they can resolve the issue.

Anyone else have this problem? Why didn’t it happen with older Maple versions? What am I missing by using standard typesetting instead of the default advanced?

Thanks

## get positive output...

how can I get a positive output in the following example

solve((hv*hw+lv*lw)/(lv+hv)*(lv+hv) = dw*(lv+hv), hv)

instead of -lv*(dw-lw)/(dw-hw) I would like lv*(dw-lw)/(hw-dw)

## Linear composition of vectors...

Hi. how can maple determine whether a vector is linear compostion of two or more vectors?
for example w=a*v+b*u so that w is linear compostion of vectors u and v ( a and b are scalar numbers). tnx for the help.

## How to determine the number of circles of graph ...

Given  any graph , I want to  determine the number of cycles of  graph .  What should I do?

## Help solve equation...

I have this equation but maple solve root is 2

Root_eq.mw

Root is 4 x1 =1, x2= 8.95006470,

x3 =0 .6939575785

x4 = -0.6440222825

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