## How to solve Linear first-order PDE by the Lagrang...

help.mw

How to solve Linear first-order PDE by the Lagrange method?

dx/(x) =dy/0=dt/0=du/3=dv/v=dw/w, where x,y,t are independent variables and u,v,w are dependent variables.

## Phase Plane between two functions...

hello guys,

I want to plot the phase plane between F and m when:

F := 736*R^4/sqrt((-1380*Pi*R*m(r)^3 + 368*R^4 - 1587*m(r)^2*R^2 + 1280*m(r)^2*a)^2);
R := X^(1/3)/(-l^2 + 4*a) - 3*l^2*m(r)^2/X^(1/3);
X := m(r)*l^2*(sqrt((27*l^2*m(r)^4 - 16*a^2*l^2 + 64*a^3)/(-l^2 + 4*a)) + 4*a)*(-l^2 + 4*a)^2;

and

m := (l^2*r^2 + r^4 + a*l^2)/(2*l^2*r)

for positive constant a and l

thanks

## Problem with license Maple 2015...

Hello everyone. I took part in a project in which we had to solve problems with Maple 2015. The managers gave us a permanent license. However recently I had trouble on my computer and now Maple doesn't work anymore because it somehow lost the license. The project ended last year, so I can't really ask them anymore. Is there any way to get the license working again? I checked on the site but didn't found anything useful and I'd really need it for the final exam of the last year of high school...

## Simple PASS FAIL Code file...

Sorry file was not attached

ASME B31.3-2002 - Flexibility Analysis

This document considers the requirements for flexibility analysis of pipe work in accordance with standard ASME B31.3 2002 Edition.

Temperature Reduction for Swagelok fittings and tube.

Based on 316L Stainless steel fittings and tube, from Data Sheet MS-01-107 rev S and shown below a linear interpolation is used to determine the factor for operation at 100 and 130 centigrade.

Temperature values from table.

Factor values from fable.

Graph of data points.

 (1.1)

Factor for operation at 100 centigrade. =

Factor for operation at 130 centigrade.  =

Swagelok compatability

From the B31.3 standard, Table 326.1 Component Standards, Swagelok fittings are not listed directly but it is considered that they are covered under the entry for Unified inch screw threads (UN and UNR thread form) with designation ASME B1.1. Stainless steel pipe is covered directly with designation ASME B36.19M.

Therefore the use of these parts is acceptable under the standard.

 Specific Tube Sizes. The initial specification suggests a DN15 tube size. This equates to 5/8", however the range of fittings in this size is limited. A preferred size would be to either go down to 1/2" or up to 3/4" tube. These will give an actual bore of ~10mm and ~15mm respectivly. In terms of the pressure and temperature specification the following information is provided from Swagelok data sheet MS-01-181. 1/2" x 0.049" wall pressure rating at 37C.  = 3/4" x 0.065" wall pressure rating at 37C.  = Hence pressure ratings, converted to bar at 130C are:  =  = Hence the tubing used in the design is acceptable.
 Weld Fitting Specifications There are several types of welded fittings as "Tee" "Reduceing Tee" and "Reducing Unions" and they have various pressure ratings. A 3/4" tube butt weld "Tee"  = The weld fittings have pressure rating at 130C of.  = Hence the weld fittings used in the design are acceptable.

 Tube wall calculation Determine the minimum wall thickness based on the design code. Design pressure.  = Outside diameter of nominal 3/4" tube.  = Quality factor.  =  for seamless stainless steel tube. Allowable stress for 316L tube at 166C (300F). From B31.1 Table A1.  =  = Miniumum wall thickness.  = Actual wall thickness.  =  =

Conversions

From Appendix A

allowable stress for TP316L at 100C (212F). =

allowable stress for TP316L at room temperature. =

=

=

=

=

=

=

 (3.1)

 (3.2)

Helium flow rate.

Determine molar flow rate.  =

Determine mass flow rate.  =

 (3.3)

 (3.4)

 (3.5)

 (3.6)

Determine the boiling point of water at 6 bar, the maxiumum pressure delivered by the cd90e unit.

 (3.7)

 (3.8)

 (3.9)

 Input Parameters Allowable stress for calculations.  = Allowable stress at minimum temperature. Allowable stress at maximum temperature. Stress reduction factor for N=7000 to 14000 cycles. From Table C6 of standard, modulus of elasticity for stainless steel at room temperature. = Named as  =  =
 Flexibility Stress text##  =  = Allowable stress factor for analysis requirement.  = Pipe diameter for 1/2" tube.  = Pipe diameter for 3/4" tube.  = Change in temperature.  = Section A1 Combined length of section A1. = Length increase due to thermal expansion.  =  =  = Section A2 Combined length of section A2. = Length increase due to thermal expansion.  =  =  = Section A3 Combined length of section A3. = Length increase due to thermal expansion.  =  =  =   Length of section B.  =   Length of section C.  =   Length of section D.  =   Length of section E.  =   Length of section F.  =   Length of section G.  =   Length of section H.  =   Length of section I.  =   Length increase due to thermal expansion.  = Length increase due to thermal expansion.  = Length increase due to thermal expansion.  = Length increase due to thermal expansion.  = Length increase due to thermal expansion.  = Length increase due to thermal expansion.  = Length increase due to thermal expansion.  = Length increase due to thermal expansion.  =

When I have an operation to perform with Maple, my first reflex is to use the "native" Maple procedure(s) because it seems logical to think that they have been written in order to reduce the memory used and/or the execution time.
Unfortunately, this feeling is not confirmed by reading some of the answers provided on this site.

The attached file shows 4 ways (among probably several others) to center and reduce (by columns) a random matrix.
Amid them is the Statistics:-Scale procedure which appears not to be the most efficient (even a double loop outperforms in term of time).
This is just an example among many others (for instance Statistics:-Select can be easily outperformed)

So my question: why deceive the user with magic functions which sometimes have a very relative efficiency?

Scaling_efficiency.mw

## Unexpected symbols when typing simple operators...

Hello

I have used Maple almost daily for the last four years, but a few days ago two students approached me with an issue I had never encountered before. However, it had happened to both of them within a few weeks.

They described the issue as follows: When they opened a random Maple document and they tried to type in simple operators (like +, - or *), Maple would instead write an odd symbol, which none of them recognised as a mathematical symbol.

As they could not find a way to solve the problem within Maple, they tried restarting their computers. When they afterwards reopened Maple, the problem was gone and the operators worked as expected again. Neither of the students has experienced the issue since.

During the last few days, I have been trying to replicate the issue myself without success. Therefore, I also don't have any screenshots to share, so hopefully my simple explanation is enough.

My questions are: Has anyone heard about this issue before? Does anyone know what might have caused it? Is there a way to replicate it and/or prevent it from happening again in the future?

I hope someone is able to clarify it a bit for me! :)

Regards,

Frederik

## Finding the location of the poles of a normal chor...

How to find the location of the poles of a normal chord in an ellipse ?
Here is my code :

restart; with(geometry); with(plots); `local`(O);
_EnvHorizontalName := x; _EnvVerticalName := y;
corde := a*x/cos(theta)-b*y/sin(theta) = a^2-b^2;
isolate(corde, a/cos(theta));
Error, (in isolate) a*x/cos(theta)-b*y/sin(theta) = a^2-b^2 does not contain a/cos(theta)
eq1 := (a^2-b^2)*X/a^2 = a/cos(theta);
c := solve(eq1, cos(theta));
eq2 := (a^2-b^2)*Y/b^2 = -b/sin(theta);
s := solve(eq2, sin(theta));
lieu := simplify(expand((a^2-b^2)^2*X^2*Y^2*(c^2+s^2 = 1)));
allvalues(eliminate({eq1, eq2}, theta))[1][2];
ell := x^2/a^2+y^2/b^2 = 1;
P := [a*cos(theta), b*sin(theta)];
tgP := x*P[1]/a^2+y*P[2]/b^2 = 1;

sol := solve({corde, ell}, {x, y});
tgP1 := simplify(x*rhs(sol[2][1])/a^2+y*rhs(sol[2][2])/b^2 = 1);

Drawing in a case
a := 5; b := 3; theta := (1/6)*Pi;

line(l1, corde); conic(co, ell);
Pole(P1, l1, co); coordinates(P1);
a := 5; b := 3; theta := (1/6)*Pi;
Ell := implicitplot(ell, x = -a .. a, y = -b .. b, color = red);
Cor := implicitplot(corde, x = -a-1 .. a, y = -b-1 .. b, color = blue);
TgP := implicitplot(tgP, x = 0 .. 10, y = -5 .. 10, color = magenta);
TgP1 := implicitplot(tgP1, x = -5 .. 10, y = -5 .. 10, color = magenta);
lieu := subs(X = x, Y = y, lieu);
subs(x = 125*sqrt(3)*(1/24), y = -27/8, lieu);
Lieu := implicitplot(lieu, x = -a .. a, y = -b .. b, color = green);
dr := draw(P1);
display([Ell, Cor, Lieu, TgP, TgP1, dr], axes = normal, view = [-10 .. 10, -10 .. 10], scaling = constrained);

Why the drawin of the location (lieu) does not appear ? Thank you.

## Use the Maple debugger in a package...

Hello,

For a quite long program, i have to use the Maple debugger. But, i have never used it before.

For a package containing subpackages like this :

Package

Subpackage1

proc 1

proc 2

Subpackage 2

It seems that i have a mistake for one of procedure.

Consequently, for using the Maple debugger, i have tried this :
with(package);
with(subpackage1);
stopat(proc 1)

But, it does nothing.

May you explain me how i can use the Maple debugger in a package ?

I find in the web this vidéo : https://www.youtube.com/watch?v=cUVbMOTQzRA

It describes how to use the Maple debugger but only on a very short procedure and not in a package.

## Bug in EllipticCPi...

Hi there.

It seems like EllipticCPi(n,k) has a bug when n close to 1:

Both answers should be equal by definition and first is true.

ell_error.mw

## Marking an intersection of point plots in Maple...

I have the following program in Maple:

``````with(plots);
my_array := [[.1, .1], [.3, .45], [.55, .78], [.8, .9]]; #define an array of points
my_graph := pointplot(my_array, connect = true); #plot the array on a graph, connecting points
line := plot(.7, x = 0 .. 1); #plotting a horizontal line
display(my_graph, line); #displaying on the same graph``````

The output looks as follows:

I want to add a vertical line corresponding to the intersection of these two lines. Is there a way to do it?

## plotting fsolve for given values...

Hi,

I have two coupled algebraic equations (not differential equations; but only simple algebraic equations; call them "equ1" and "equ2") in which there are three parameters: "x", "y", and "z".

I want to use "fsolve" (Numerical solve) for solving them and then plotting. But since there are three parameters and two equations hence one of the parameters must be given. I want to give a range for "z", for example [2..9], and step size, for example "0.5", such that maple first puts "2" in both equations and solve them numerically and get the values of "x" and "y" and then record them, and then set the value "2.5" for "z" and again repeat the above cycle until the value "z=9". Finally plot both "x" and "y" in terms of "z".

How do I write this?

## How do i find a relations between two expressions?...

hello dear fellows maple users,

I need help to find a relation between multiples expressions (A,B..etc) and one term (R). (otherwise, I want to write those expressions in terms of R).

```#A is given by

A:=nu^(2/3)*B/(g^(1/3)*(sin(beta))^(1/3)*h):

#and R is defined as:

R:=h^3*g*sin(beta)/(3*nu^2):```

I hope I expressed myself clearly.

## How do I solve a IF..THEN..problem with DIFF...

Is there any way to use DIFF for the function formula in IF..THEN..?

g := proc(x) if x <= 0 then x^2 + x; else if x < 3*Pi then sin(x); else x^2 - 6*x*Pi + 9*Pi^2 - x + 3*Pi; end if; end if; end proc;

diff(g, x);

Like the above example, but the diff result is 0.....

## Gradient of a vector field and the Physics package...

Vector calculus is very nicely handled in Maple's Physics package:

 > with(Physics[Vectors]):

The gradient of a scalar field in Cartesian coordinates

The gradient of a scalar field in cylindrical coordinates

But the gradient of a vector field is not available:

 > Gradient(_rho*f(rho,phi,z) + _phi*g(rho,phi,z) + _k*h(rho,phi,z));

Error, (in Physics:-Vectors:-Nabla) Physics:-Vectors:-Gradient expected a scalar function, but received the vector function: _rho*f(rho, phi, z)+_phi*g(rho, phi, z)+_k*h(rho, phi, z)

I suppose this is because the gradient of a vector field needs to be
expressed in terms a basis consisting of the dyadic products  of the basis vectors

as in   , , etc., which does not seem to be implemented.

That said, it is quite possible that this is already done and I have missed it in
the documentation since the Physics package is so huge.  But if it's truly not there,
it would be a very useful feature to add.  Calculating gradients of vector fields

is central to continuum mechanics (including elasticity and fluid mechanics).

They are easy to represent in Cartesian coordinates but their calculation in the

frequently needed cylindrical and spherical coordinates are nontrivial and can use

Maple's help.

## How to increase the number of arrows in a vector f...

Hi,

I want my vector field plot to have more arrows, and am wondering how to do this.  Here is the file: