Maple Questions and Posts

These are Posts and Questions associated with the product, Maple

Dear All,
I want to solve a highly nonlinear equation in one variable. The equation includes some undetermined parameters. The running time is long in serial programming. Can I help me to execute the following command in parallel? I know that the ‘solve’ command is not thread-safe.

solve(Eq1, beta);
 
 Let me know solve the problem, if the number of equations is larger than one, as below:
solve({eq1,eq2,eq3},{beta1,beta2,beta3});
Best wishes

Will Chebyshev differential equation always give  the series solution or not.?

Chebyshev differential equation have variable coefficient,Can we solve it without using any series solution method.

A question about the alias command: Can the abbreviation u[k] of the function call u[k](x, y) be implemented by the alias command, so that the type of u[k] is a function for any integer K?

example:
alias(F[k]=F[k](x));
output:F[k].
whattype(F[k]);
output:function
whattype(F[1]);
output:indexed
I want f[k] to be a function for any integer K. how to implement it? If there are experts to see this question to help answer, will be very grateful!

i want to make a costomized procedure to calculate laplace transform.please guide me why wont MAPLE calculate the limit?  I will use this procedure to make another integral transform so I can not use built-in Laplace Transform commands.

maple.mw

Hi,
Some people using the Windows platform have had problems installing MapleCloud packages, including the Maplesoft Physics Updates. This problem does not happen in Macintosh or Linux/Unix, also does not happen with all Windows computers but with some of them, and is not a problem of the MapleCloud packages themselves, but a problem of the installer of packages.

I understand that a solution to this problem will be presented within an upcoming Maple dot release.

Meantime, there is a solution by installing a helper library; after that, MapleCloud packages install without problems in all Windows machines. So whoever is having trouble installing MapleCloud packages in Windows and prefers not to wait until that dot release, instead wants to install this helper library, please email me at physics@maplesoft.com

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

How to plot graphs on the xyz axes? Can somebody tell me step by step

How to evaluate the integration when x=[-infinity , +infinity]?

integration_24sep.mw

I am trying to solve a set of ODEs with dsolve. There are 26 equations of my ODEs, but the problem is a multiple point bvp. So the range is divided into three region. In order to use dsolve, I transform the three subregion's coordinate into 0 to 1. Meanwhile, the ODEs are different in three regions, respectively. So, there are 26×3 equations in total. And according to the paper I want to replicate, it says the response is unstable,so parameter continuation is used. Similar to the paper, an additional equation is added(eq1_27 in code), also an additional condition is added(about lambda). When the lambda is less then 0.11, the dsolve works, but for other values it doesn't work. Could anyone help me?

 

Sorry for the tedious programming code, I am new to Maple.

Hi!

I would like to write an automated code, this means that I would like not to copy and paste anything.
 

 

4.22647099771398*exp(-0.0104163888375266*t) - 4.22647099771398*exp(-2.00033505979518*t)

I have this as my last result and would like to use the value of the exponential function (0.0104163888375266 and 2.00033505979518) without having to manually copy and paste it into the next function.

How can i do this?

Thank you in advice for your help! :)

Its easy to calculate a potential function for a vectorfield 
But now by hand in 2D Input mode ..a struggle 

Doing your homework in 2D Input mode is something totally different then the structurized explanations done in Maple input for lessons by an instructor. 

Partiel differentation with respect to what variable, is not notated in 2D mode, so a serie of them showing up in the document says nothing.and reexecuting them a couple of times doubles the output if you have used a inline notation. 
Basic idea here f-> f ' -> F(f ') = f  and handling variables x,y, and z for integrating/differentation 

-----------------------------------------------------------------------


 

restart

with(Student:-VectorCalculus)

BasisFormat(true)

v := VectorField(`<,>`(x, y, z))

Vector(3, {(1) = x, (2) = y, (3) = z})

(1)

Student:-VectorCalculus:-ScalarPotential(v); "_noterminate"

(1/2)*x^2+(1/2)*y^2+(1/2)*z^2

(2)

Thats easy to use the ScalarPotential for a manual exercise

Example 2: finding a Potential function

Show that F = [exp(x)*cos(y)+y*z, x*z-exp(x)*sin(y), x*y+z] is conversative and find a potential function for it.

F := VectorField(`<,>`(exp(x)*cos(y)+y*z, x*z-exp(x)*sin(y), x*y+z))

Vector(3, {(1) = exp(x)*cos(y)+y*z, (2) = x*z-exp(x)*sin(y), (3) = x*y+z})

(3)

"(->)"

y*z*x+exp(x)*cos(y)+(1/2)*z^2

(4)

NULL

NULL

NULL

ScalarPotential(F)

y*z*x+exp(x)*cos(y)+(1/2)*z^2

(5)

So "f(x,y,z):=y z x+(e)^x cos(y)+(z^2)/2 + C :"

Now manual

'F' = value(F)

F = (Vector(3, {(1) = exp(x)*cos(y)+y*z, (2) = x*z-exp(x)*sin(y), (3) = x*y+z}))

(6)

(exp(x)*cos(y)+y*z)*`#mover(mi("e"),mo("&lowbar;"))`[x]+(x*z-exp(x)*sin(y))*`#mover(mi("e"),mo("&lowbar;"))`[y]+(x*y+z)*`#mover(mi("e"),mo("&lowbar;"))`[z]

(exp(x)*cos(y)+y*z)*`#mover(mi("e"),mo("&lowbar;"))`[x]+(x*z-exp(x)*sin(y))*`#mover(mi("e"),mo("&lowbar;"))`[y]+(x*y+z)*`#mover(mi("e"),mo("&lowbar;"))`[z]

(7)

"(->)"

F

(8)

F

Vector(3, {(1) = exp(x)*cos(y)+y*z, (2) = x*z-exp(x)*sin(y), (3) = x*y+z})

(9)

NULL

NULL

M := exp(x)*cos(y)+y*z; N := x*z-exp(x)*sin(y); P := x*y+z

x*y+z

(10)

"(->)"

x

(11)

M1 := exp(x)*cos(y)+y*z

exp(x)*cos(y)+y*z

(12)

 =

exp(x)*cos(y)+y*z

(13)

"(->)"y   ( to z )

NULLNULL 

M2 := exp(x)*cos(y)+y*z

exp(x)*cos(y)+y*z

(14)

 =

exp(x)*cos(y)+y*z

(15)

"(->)"-exp(x)*sin(y)+z (to y) NULL

N1 := x*z-exp(x)*sin(y)

x*z-exp(x)*sin(y)

(16)

 =

x*z-exp(x)*sin(y)

(17)

"(->)"x  (to z)

N2 := x*z-exp(x)*sin(y)

x*z-exp(x)*sin(y)

(18)

 =

x*z-exp(x)*sin(y)

(19)

"(->)"-exp(x)*sin(y)+z (to x)

P1 := x*y+z

x*y+z

(20)

 =

x*y+z

(21)

"(->)"x  (to y )

P2 := x*y+z

x*y+z

(22)

 =

x*y+z

(23)

"(->)"y  ( to x )

 

 

Test for to be a conservative field

P1=N1 ,  M1=P2, N2=M2

 

int(F, x).... integrating F  with respect to x ,holding  y and z fixed
Its a vector form F , probably F must be converted to scalar form? (command?)

exp(x)*cos(y)+y*z+x*z-exp(x)*sin(y)+x*y+z

exp(x)*cos(y)+y*z+x*z-exp(x)*sin(y)+x*y+z

(24)

"(->)"

x*z+(1/2)*x^2*y+(1/2)*x^2*z+y*z*x+exp(x)*cos(y)-exp(x)*sin(y)

(25)

Ok, can integrate to 3 variables now

Now the partial diretives from f

M1 = exp(x)*cos(y)+y*z"(->)"y*z*x+exp(x)*cos(y) + g(y,z) constant of integration of f (the potential function)NULL

So : "f(x,y,z)= "y*z*x+exp(x)*cos(y)NULL + g(y,z) (1) # a total mess as notation here done by me

 

The logic from this all not yet completely understood and lost oversight , but this equation (1) must be further  integrated/differentiated  to get

y*z*x+exp(x)*cos(y)+(1/2)*z^2+C

Step by step following the text example in Thomas Calculus (page 1075, example 2) in 2 D mode is not going well.

 

``


 

Download thomas_calculus-vb2-blz_1075_-vraag_forum.mw

 

Is there a way to find what changed in each Physics update? Even if it is just one or two lines short summary? I am not able to find how to do this.

For example, after doing Physics:-Version(latest); and getting a new version, how to find what was fixed/added to new version?

There is a page in help titled "Overview of the Physics Updates" but I am asking about what specific change made in each update and not as general overall description as the above page talks about.

Again, even if the changes are short, it will be nice to know what changed each time.  

 

Hi,

I can’t block the display of my p and A variables even if I finish my commands with both points.

Ideas? ThanksTrianglesQuelconques.mw

After running the program without any error, no plot obtained.

What is the reason?

Thanks3.mw

 

Hello,

I'm writing a script that solves a system of equations. I have 2 unknows that I seem to get when using "explicit" et "allvalues". The result I get from "allvalues" is in this form. My question is : how can I get just the result, without the "lambda22=" (other than copy/paste of course ;))?

lambda22 = sqrt(10)*sqrt(lambda11*(pi*lambda11 + 90))/(30*lambda11)

My code is

kappa:=30:
tensF:=Matrix([[lambda11,0,0],[0,lambda22,0],[0,0,lambda22]]):
tensFbar:=Matrix([[lambda11bar,0,0],[0,1/sqrt(lambda11bar),0],[0,0,1/sqrt(lambda11bar)]]):
tensBbar:=Multiply(tensFbar,Transpose(tensFbar)):

tensPK:=Matrix([[pi,0,0],[0,0,0],[0,0,0]]):
tensPK1:=Multiply(Transpose(MatrixInverse(tensF)),(2/Determinant(tensF))*a*(tensBbar-(1/3)*Trace(tensBbar)*Matrix(3,shape=identity))+kappa*(Determinant(tensF)-1)*Matrix(3,shape=identity)):
eq1:=tensPK[1,1]=tensPK1[1,1]:
eq2:=tensPK[2,2]=tensPK1[2,2]:
sys:={eq1,eq2}:
sol1:=solve( sys, {lambda11bar,lambda22},explicit):


allvalues(sol1[1][1]);
allvalues(sol1[1][2]);

This should be something easy to get but I don't find the method anywhere.

Many thanks in advance if you know how to do this,

Manon

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