## Hyperbolic functions of intervals...

```ii := evalr(csch(INTERVAL(-infinity .. -1, 1 .. infinity)));
INTERVAL(-csch(1) .. 0, csch(1) .. 0)

evalr(ii-ii);
-csch(1)
```

(Make sure you don't have the Typesetting level set to Extended, or ii won't be displayed correctly.)

There are no functions to test for interval membership (or to compute intersections/unions of intervals), so it's unclear how Maple treats the interval csch(1)..0, but apparently evalr is getting tripped up by it.

Also:

```evalr(sech(INTERVAL(-infinity .. -1, 1 .. infinity)));
0

evalr(arccsch(INTERVAL(-infinity .. -1, 1 .. infinity)));
Error, (in evalr/arccsch) too many levels of recursion
```

## Problem with subs function in Maple...

Hello,

For example, let's say we have the following function

Now if we want to calculate the value of a function we have to

subs([x1=10,x2=20],eval(hf));

My question is the following: How to substitute values for x1 and x2 using values from vector? something like that

x:=[10,20];

subs([x],eval(hf));

Best,

Rariusz

## Finding Skin friction using Theta method...

Hello,

I solve a partial differential equation using the THETA METHOD on Maple17, but what is also of essence is the skin friction and Nusselt Number which are {diff(u(x, t), x)} at x = 0 and {diff(T(x, t), x)} at x = 0 respectively. How can I achieve the two using the THETA METHOD? This is the PDE in it full flesh.

PDE := {diff(phi(x, t), t) = (diff(phi(x, t), x, x))/S__c, diff(u(x, t), t) = diff(u(x, t), x, x)-M^2*(u(x, t)+m*w(x, t))/(m^2+1)-u(x, t)/`&varkappa;`-2*Omega^2*w(x, t), diff(w(x, t), t) = diff(w(x, t), x, x)+M^2*(m*u(x, t)-w(x, t))/(m^2+1)-w(x, t)/`&varkappa;`+2*Omega^2*u(x, t), diff(theta(x, t), t) = lambda*(diff(theta(x, t), x, x))/P__r+D__r*(diff(phi(x, t), x, x))}

With conditions: BC := {phi(0, t) = 1, phi(12, t) = 0, phi(x, 0) = 0, u(0, t) = t, u(12, t) = 0, u(x, 0) = 0, w(0, t) = 0, w(12, t) = 0, w(x, 0) = 0, theta(0, t) = 1, theta(12, t) = 0, theta(x, 0) = 0}

Where the parameter like P_r, S_c  e.t.c are constants to assign value to.

Thanks.

## plotting comple solutions of an equation...

I want to plot the compex solutions of a single equation. I do

> plot([fsolve(x^3 = 1, complex)])

The output consists of a warning:

"Warning, unable to evaluate 2 of the 3 functions to numeric values in the region; complex values were detected"

and a horizontal line.

What am I doing wrong?

Thank you!

## Can a smooth path of fastest descent be found betw...

The linked worksheet displays the geodesic between two points on a surface z(x,y).

Surfacepath.mw

Gradient descent will find a stepped approximate path of fastest descent between the points, but is there a way to find a function defining an exact i.e. smooth path of fastest descent? If so, how can a precise time of fastest descent be determined?

## How to solve this nonstandard system?...

Namely, I mean

```solve({y >= 4*x^4+4*x^2*y+1/2, sqrt((1/2)*(x-y)^2-(x-y)^4) = -2*x^2+y^2}, [x, y]);
[]
```

The answer (no solution) is not correct in view of

```eval({y >= 4*x^4+4*x^2*y+1/2, sqrt((1/2)*(x-y)^2-(x-y)^4) = -2*x^2+y^2}, [x = 0, y = 1/2]);
{(1/8)*sqrt(4) = 1/4, 1/2 <= 1/2}
eval({y >= 4*x^4+4*x^2*y+1/2, sqrt((1/2)*(x-y)^2-(x-y)^4) = -2*x^2+y^2}, [x = -1, y = -3/2]);
{(1/8)*sqrt(4) = 1/4, -3/2 <= -3/2}
```

## For loop reverse...

Hi all, I want to ask how to use for loop reverse in Maple.

Example, i have array . In Java then

`for(int i = arr.size(); i > 0; i--) {`

`    //do something`

`}`

What is simillar for loop in Maple?

Thank you very much.

## How to solve error occur in Maple?...

Hi, when I wan to generate results, it shows this; What should I do?

Error, (in solve) a constant is invalid as a variable, I.

## How do I plot a result from fsolve as a function o...

I have a system of equations that can't be solved analytically, but can be solved using fsolve. I would like to plot the solution for one of the unknowns as a function of a parameter "DV" that is in a few of the equations. There are two issues at hand. First, even if I give DV a numerical value, the solutions are of the form { x = 0.23, y = 4.56 }, a form that plot( ) obviously can't handle directly. Generally I have dealt with this by using the op( ) command to pick out the solution I want; is there a better way?

But even after I have the solution I want, fsolve( ) won't work until I give it a value for DV. Thus a plot( ) command like

plot(op(2, op(2, fsolve({e1, e2}, {x, y})), DV = -1 .. 1)

fails with an "Error, (in fsolve) DV is in the equation, and is not solved for" error.

There's got to be an esy way to do this!

## Product of intervals...

Here Maple treats the intervals as independent, as I think it should:

```INTERVAL(1 .. 2)+INTERVAL(1 .. 2);
INTERVAL(1 .. 2) + INTERVAL(1 .. 2)

INTERVAL(1 .. 2)-INTERVAL(1 .. 2);
INTERVAL(1 .. 2) - INTERVAL(1 .. 2)
```

(even though for the first one an autosimplification to 2*INTERVAL(1..2) wouldn't matter). But as soon as there are non-linear terms, Maple ignores that rule:

```INTERVAL(1 .. 2)^2-INTERVAL(1 .. 2)^2;
0

INTERVAL(1 .. 2)/INTERVAL(1 .. 2);
1

INTERVAL(-1 .. 1)*INTERVAL(-1 .. 1);
2
INTERVAL(-1 .. 1)
```

That means I cannot substitute intervals for variables in a formula. In fact, I don't know how INTERVAL(-1 .. 1)*INTERVAL(-1 .. 1) can be computed as a product of two independent intervals at all, there doesn't seem to be any way to pass it to evalr.

## Truncating Small Errors ...

Hello,

This is a problem encountered in most engineering equations. An equation is given with some variables very small that they can be ignored. Basically the mathematical equivalent of an engineering approximation.

Below is a very simple example:

Both R and r are between 10E3 and 50E3.
gm is between 1 and 10.

So regardless of actual values the answer to 4significant figures can always be approximated by:

eqn1~ R*gm*r

Is there any way to tell MAPLE to approximate an equation such that it is only accurate to certain decimal places? I have tried using "fnormal()" with "assuming"  statements but it always requires some of the variables be assigned actual numeric values.

I was wondering if there was a way to get this approximation without having to assign values to any of the variables but only by specifying the range of values for each variable.

Thanks.

## 3d^2+f^2-4e^2+2td^2-4te^2+2tf^2+3f^2+4td^2+..........

How can ı write 3d^2+f^2-4e^2+2td^2-4te^2+2tf^2+3f^2+4td^2+....... as  (.......)d^2 +(......)e^2+ (.......)f^2

`so`

3d^2+f^2-4e^2+2td^2-4te^2+2tf^2+3f^2+4td^2+....... = (.......)d^2 +(......)e^2+ (.......)f^2  ??????

```
```

## how i can use parts if V function contain non diff...

hi

i have an Integral equation like below

now i want to use Parts That u=op(1,A), but when I use Parts it dont work properly, actually i want to get

but when i use

A := Expand(Parts(Int(A, x), op(1, A)))

maple solve it like bellow

i know that i can separate these terms One by one, but there are many functions like this in my code , so i want to know if there is any way to solve this function.

thank you.

## procedure; recursive formula...

Hi!
I am quite new to maple.
I have uploaded two printscreens of two similar procedures. The only difference is that in prosedure nr. 2 the number "a"(rate of change given in the exercise), is supposed to variate in term of k.

I assume that i have to define an if-sentence that will tell the procedure to use a=0.15 when, n=0, and a1:=a(1-(k/Km)) when n>0.  Can someone please help me with solving this?

Regards Paul

## How to deal with a differential of a solution obta...

I am now working on differential equations like the following, and wonder how I can deal with diff(C(x,t),x).  In particular, I would like to know the values of diff(C(x,t),x) at specific sets of (x, t).  I also would like to know how to integrate diff(C(x,t),x) for a time period (at x = 0.5L or x = L).

restart;

C0 := 10;

K  := 3.0e6;

d  := 5.0E-14;

hm := 5.0E-4;

L  := 0.001;

DE1 := diff(C(x, t), t) = d*diff(C(x,t), x, x);

IC := C(x, 0) = piecewise(x < 0, 0, 0 <=x <= L, C0, L < x, 0);

BC1 := D[1](C)(0, t) = 0;

BC2 := -d*D[1](C)(L, t) = hm * C(L, t) / K;

pds:=pdsolve(DE1, {IC, BC1, BC2}, type=numeric, spacestep=L/10000, timestep=10000);

T := 60*60*24*100;

pds:-plot(t=T, x=0..L);

#I tried the following, but these seem to always return zero (while the plot suggests some negative value of diff(C(x, t), x));

v1 := pds:-value(diff(C(x, t), x));

v1(L, T);

v2 := pds:-value(int(diff(C(x, t), x), t = 0 .. T));

v2(L, 0);

 5 6 7 8 9 10 11 Last Page 7 of 1512
﻿