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Printing slides...

Asked by: Louis Lamarche 105
document style header
February 27 2019
1  0


Hello there,

I have created a MAPLE document in a slideshow format.

Is there a way to print a copy of my presentation with header and footer included and in a format that fits on letter format paper or pdf.

Thank you for your help.

LL

Numerical solution of PDE in three independent var...

Asked by: Melvin Brown 124
differential-equation pde numeric
February 26 2019
0  1

I understand that Maple 2018 is now able to solve 3 independent variable PDE & BC problems in bounded domains through separation of variables by product and eigenfunction expansion.

My solution domain is (x,y,t), (i.e three independent variables) but I would like to need to use numerical integration.  Are there plans to make numerical integration for PDEs with three independent availables, and if so when is that facility likely to be available?

Melvin

 

 

integration by parts...

Asked by: torabi 85
integration differential-equation pde
February 25 2019
0  3

How I can perform integration by parts, with respect to the x[0..1],y[0..1],t 

PART.mw
 

> 

restart
> 

U := (1/2)*(E*(diff(u(x, y), x)-z*(diff(w(x, y), x, x))+(1/2)*(diff(w(x, y), x))^2)/(-upsilon^2+1)+E*upsilon*(diff(v(x, y), y)-z*(diff(w(x, y), y, y))+(1/2)*(diff(w(x, y), y))^2)/(-upsilon^2+1))*(diff(u(x, y), x)-z*(diff(w(x, y), x, x))+(1/2)*(diff(w(x, y), x))^2)+(1/2)*(E*upsilon*(diff(u(x, y), x)-z*(diff(w(x, y), x, x))+(1/2)*(diff(w(x, y), x))^2)/(-upsilon^2+1)+E*(diff(v(x, y), y)-z*(diff(w(x, y), y, y))+(1/2)*(diff(w(x, y), y))^2)/(-upsilon^2+1))*(diff(v(x, y), y)-z*(diff(w(x, y), y, y))+(1/2)*(diff(w(x, y), y))^2)+E*(1-upsilon)*((1/2)*(diff(v(x, y), x))-z*(diff(w(x, y), x, y))+(1/2)*(diff(u(x, y), y))+(1/2)*(diff(w(x, y), x))*(diff(w(x, y), y)))^2/(-upsilon^2+1)+2*E*l^2*(diff(w(x, y), x, y))^2/(2+2*upsilon)+2*E*l^2*(-(1/2)*(diff(w(x, y), x, x))+(1/2)*(diff(w(x, y), y, y)))^2/(2+2*upsilon)+2*E*l^2*((1/4)*(diff(v(x, y), x, x))-(1/4)*(diff(u(x, y), x, y)))^2/(2+2*upsilon)+2*E*l^2*((1/4)*(diff(v(x, y), x, y))-(1/4)*(diff(u(x, y), y, y)))^2/(2+2*upsilon)
> 

with(IntegrationTools)
> 

``
> 

``


 

Download PART.mw

 

3 little annoying things ....

Asked by: RLessard 90
input copy
February 25 2019
1  0
 
 1)  Copy/paste problem .
 
 Looks like Maple is not able to copy/paste the output
 from a summation command . Look at my example .
 I have to use the  " lprint " command .
2)   Mysterious small box character .
 
 Suppose I want to edit a command . I want to replace a character with a left bracket
 (or right bracket or left accolade but strangely not the right accolade).
 I put the cursor on the character and type the left bracket (or right...) .
 The left bracket ( or right ...)  is inserted . Now when I try to delete the character,
 a small box appear . The  character I am trying to delete is shifting to the right .
  Like  I said , just a little annoying .
 
3)  Open file problem .
 
 The first file I open in Maple with the  ctrl-o command , the "open file window" appears in
  the center of the screen . All the others files I am opening , the "open file window"  show up
  in the bottom left corner , top center or top right corner ... randomly .
  Very annoying on a 27" screen . For this last one ,I am not shure  if it is a Maple 2018 problem
   or a Windows 10 64 bits problem . I have few programs in my computer .
  When I use Microsoft Paint or Wordpad ,I don't see this problem .
 
  I don't know if somebody else can confirm those annoying things . If I am not the only one
  then I am hoping the next updates or versions will fix that .
 
    Thanks !
 

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

Asked by: Pierre-alexandre 10
maplets plotting
February 24 2019
1  4

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!

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

Asked by: EB1000 35
February 23 2019
0  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

 

 

 

 

 

 

To solve a coupled first order PDE numerically usi...

Asked by: ogunmiloro 120
February 21 2019
0  0


 

> 

Local*Gamma:

v[1](x, t) = v[1]*(-x*v[1]-x*`θv`[2]-v[1]-v[2]+1)

  

v[2](x, t) = gamma*v[2]*(lambda-v[1]-v[2]-eta*(x*v[1]+x*`θv`[2]))

 (1)
> 

NULL


 

Download DTM_TO_SOlve.mw

`System error, `, "bad id" ; what does it mean?...

Asked by: dorna01 15
read save
February 21 2019
0  1

Hi everybody

I try to save an array of equations in a "mpl file", and then read file and array by command read mpl file. But system error "bad id" occurs. Previously I saved this mpl file by "save" and read array by "read" command. I ran this code several times without any problem, suddenly error "bad id" occurred. When I save mpl file by the code edit region and then read it by "read" in the same or  a new worksheet, the error doesn't happen!
 What is wrong?
"Id" refers to the array index?

Thanks.
Maple 18 and Windows 10

how I can Pdsolve this equation?...

Asked by: torabi 85
differential-equation pde pdsolve
February 20 2019
0  1

is possible to solvethis equation via maple?

hank you

EQUATION2.mw
 

> 

restartNULL
> 

alpha := 1.2*10^(-4); Betaa := 4.0*log(2); J := 13.4; delta := 15.3*10^(-9); tp := 10^(-13); tq := 8.5*10^(-12); tu := 90.0*10^(-12); kapa := 315; r0 := 2.0*10^(-7); Lx := 5.0*10^(-7); Ly := 5.0*10^(-7); Lz := 1.0*10^(-7); a := 0.7e-1*(Betaa/Pi)^.5*J/(15.3*10^(-22)); bb := exp(-((10^(-7)*x-(1/2)*Lx)^2+(10^(-7)*y-(1/2)*Ly)^2)/(2*r0^2)); print(aa = a); Q := a*exp(-z*10^(-7)/delta)*exp(-1.88*abs(t-2*tp)/tp)*bb

0.1200000000e-3

  

4.0*ln(2)

  

13.4

  

0.1530000000e-7

  

1/10000000000000

  

0.8500000000e-11

  

0.9000000000e-10

  

315

  

0.2000000000e-6

  

0.5000000000e-6

  

0.5000000000e-6

  

0.1000000000e-6

  

0.6917775548e21*ln(2)^.5

  

exp(-0.1250000000e14*((1/10000000)*x-0.2500000000e-6)^2-0.1250000000e14*((1/10000000)*y-0.2500000000e-6)^2)

  

aa = 0.6917775548e21*ln(2)^.5

  

0.6917775548e21*ln(2)^.5*exp(-6.535947712*z)*exp(-0.1880000000e14*abs(t-1/5000000000000))*exp(-0.1250000000e14*((1/10000000)*x-0.2500000000e-6)^2-0.1250000000e14*((1/10000000)*y-0.2500000000e-6)^2)

 (1)
> 

(diff(U(x, y, z, t), t)+tq*(diff(U(x, y, z, t), t, t)))/alpha = diff(U(x, y, z, t), x, x)+diff(U(x, y, z, t), y, y)+tu*(diff(U(x, y, z, t), x, x, t)+diff(U(x, y, z, t), y, y, t))+tu*(diff(U(x, y, z, t), z, z, t))+(Q+tq*(diff(Q, t)))/kapa

8333.333333*(diff(U(x, y, z, t), t))+0.7083333333e-7*(diff(diff(U(x, y, z, t), t), t)) = diff(diff(U(x, y, z, t), x), x)+diff(diff(U(x, y, z, t), y), y)+0.9000000000e-10*(diff(diff(diff(U(x, y, z, t), t), x), x))+0.9000000000e-10*(diff(diff(diff(U(x, y, z, t), t), y), y))+0.9000000000e-10*(diff(diff(diff(U(x, y, z, t), t), z), z))+0.2196119222e19*ln(2)^.5*exp(-6.535947712*z)*exp(-0.1880000000e14*abs(t-1/5000000000000))*exp(-0.1250000000e14*((1/10000000)*x-0.2500000000e-6)^2-0.1250000000e14*((1/10000000)*y-0.2500000000e-6)^2)-0.3509398517e21*ln(2)^.5*exp(-6.535947712*z)*abs(1, t-1/5000000000000)*exp(-0.1880000000e14*abs(t-1/5000000000000))*exp(-0.1250000000e14*((1/10000000)*x-0.2500000000e-6)^2-0.1250000000e14*((1/10000000)*y-0.2500000000e-6)^2)

 (2)
> 

``

 

Boundary condition:

> 

U(0, y, z, t) = 300; U(Lx, y, z, t) = 300; U(x, 0, z, t) = 300; U(x, Ly, z, t) = 300; U(x, y, 0, t) = 300; U(x, y, Lz, t) = 300

#####################################

INITIAL CONDITIONS:

 

> 

U(x, y, z, 0) = 300; (D[1](U))(x, y, z, 0) = 0

(D[1](U))(x, y, z, 0) = 0

 (3)

NULL

 

``


 

Download EQUATION2.mw

 

 

convert Surface data to region...

Asked by: kinoshocknet 5
plotting surfdata
February 18 2019
1  1

help pls how to convert a data surface into a region:

surfdata([[1, 1, .69], [1, 2, .48], [2, 1, .37], [2, 2, .44]], axes = frame, labels = [x, y, z], filled = true)

I've tried to fill the volume below using the option "filled " without any results. I will appreciate any suggestion

how to find back the system which solution is maxw...

Asked by: ComputerUser 535
February 16 2019
0  0

how to find back the system which solution is maxwell equations?

as maxwell equations is an invariant, 

if solution is maxwell which is invariant, how to find back the system which solve it, the solution is maxwell?

will there a multiple systems which solution is maxwell equations?

if can not find, how to enumerate all combinations of systems to search maxwell equations?

A remark about Statistics:-Sampling(..., method=[e...

Asked by: mmcdara 6149
sample statistics
February 15 2019
0  8

Hi, 

Recently a few questions concerning the sampling of the Cauchy distribution and the sampling of a truncated Normal distribution have been posted (mainly by  @jalale).
This post is concerned by the sampling of a truncated (standard) Cauchy distribution.

In a first part the efficiency fo two methods is adressed in the case of a non-truncated Cauchy distribution:

  • The "standard" Maple's command Statistics:-Sample(Cauchy(0, 1), N)
  • And a general method a priori very efficient if one knows the ICDF (Inverse Cumulative Function Distribution). It happens that this ICDF is just cot(U*Pi)  where U is a Uniform RV over [0, 1].
     

The second part adresses the sampling of a truncatedCauchy distribution with two methods:

  • The "standard" Maple's command Statistics:-Sample(Cauchy(0, 1), N, method=[envelope, range=...])
  • The method based on the use of the ICDF

 

Results:

Test1 (non-truncated Cauchy distribution) 

  • "Standard" Maples sampling outperforms the ICDF based method in terms of :
    • memory occupation: ICDF is twice more demanding
    • cpu time: ICDF is ten times slower
       

Test2 (truncated Cauchy distribution) 

  • ICDF based method i outperforms "Standard" Maples sampling oin terms of :
    • memory occupation: Maples "envelope sampling" method is twice more demanding
    • cpu time: Maples "envelope sampling" method is two times slower


But, beyond these simple observations, a disturbing problem is: the "envelope sampling" method seems to not return the correct distribution (at least when used this waymethod=[envelope, range=a..b]  with a < b)
This is confirmed by the two last plot where histogram and PDF are uperimposed.

Do you think this problem can be avoided by another parameterization of the "envelope sampling" method or that it reveals some underlying problem with it?

PS: I did not investigate further for other distributions .

 


 

> 

 

Sampling the Cauchy distribution

Maple's default sampling method outperformes the adhoc method

> 

restart
> 

with(Statistics):
> 

C := RandomVariable(Cauchy(0, 1))

_R

 (1)
> 

f := unapply(CDF(C, t), t);

proc (t) options operator, arrow; 1/2+arctan(t)/Pi end proc

 (2)
> 

finv := unapply(-solve(f(t)=u, t), u)

proc (u) options operator, arrow; cot(u*Pi) end proc

 (3)
> 

# "natural" way to proceed

N  := 10^6:

S1 := CodeTools:-Usage(Sample(C, N)):

memory used=7.71MiB, alloc change=39.63MiB, cpu time=69.00ms, real time=69.00ms, gc time=8.72ms

  
> 

# Let's try the sampling strategy based on the inverse of the CDF
# Usually it starts from sampling a Uniform RV on [0, 1] and
# next applies finv to the result.
#
# Smart but inefficient

U  := RandomVariable(Uniform(0., 1)):
S2 := CodeTools:-Usage(finv~(Sample(U, N))):

memory used=145.02MiB, alloc change=7.63MiB, cpu time=4.94s, real time=3.04s, gc time=2.61s

  
> 

# Much more efficient
#
# Given the special form of finv it's simpler to sample a Unirorm RV
# on [0, Pi] and apply "cot" to the result

pi := evalf(Pi):
U  := RandomVariable(Uniform(0., pi)):
S2 := CodeTools:-Usage(cot~(Sample(U, N))):

memory used=15.28MiB, alloc change=0 bytes, cpu time=652.00ms, real time=237.00ms, gc time=577.78ms

  

Sampling a truncated Cauchy distribution

Example 1:
with(Statistics) + method=[envelope, range=-10..10]

The adhoc method outperforms Maple's default sampling method

> 

S1 := CodeTools:-Usage(Sample(C, N, method=[envelope, range=-10..10])):

Histogram(S1);

memory used=8.88MiB, alloc change=-7.63MiB, cpu time=322.00ms, real time=260.00ms, gc time=93.77ms

  

 
> 

p  := Probability(C < -10, numeric);
q  := 1-Probability(C > +10, numeric);
U  := RandomVariable(Uniform(p*pi, q*pi)):
S2 := CodeTools:-Usage(cot~(Sample(U, N))):

Histogram(S2);

HFloat(0.03172551743055352)

  

HFloat(0.9682744825694465)

  

memory used=15.28MiB, alloc change=7.63MiB, cpu time=170.00ms, real time=113.00ms, gc time=92.11ms

  

 

Sampling a truncated Cauchy distribution

Example 2:
with(Statistics) + method=[envelope, range=-1..1]

The adhoc method outperformes Maple's default sampling method

> 

S1 := CodeTools:-Usage(Sample(C, N, method=[envelope, range=-1..1])):


scaling := Probability(C < +1, numeric) - Probability(C < -1, numeric);
plots:-display( Histogram(S1), plot(PDF(C, t)/scaling, t=-1..1, thickness=3, color=red) );

memory used=8.08MiB, alloc change=0 bytes, cpu time=246.00ms, real time=215.00ms, gc time=46.62ms

  

HFloat(0.5)

  

 
> 

p  := Probability(C < -1, numeric);
q  := 1-Probability(C > +1, numeric);
U  := RandomVariable(Uniform(p*pi, q*pi)):
S2 := CodeTools:-Usage(cot~(Sample(U, N))):

plots:-display( Histogram(S2), plot(PDF(C, t)/scaling, t=-1..1, thickness=3, color=red) );

HFloat(0.25)

  

HFloat(0.75)

  

memory used=15.28MiB, alloc change=7.63MiB, cpu time=163.00ms, real time=106.00ms, gc time=85.93ms

  

 
> 

 


 

Download CAUCHY_adhoc-sampling.mw

Laplacian and Euler Lagrange equation...

Asked by: maple2015 140
vectorcalculus laplacian euler-lagrange
February 15 2019
1  0

Hi

Please download the attachment.

 

I try to find a relation between EL and Lap(EL) in polar coordinate for one variable function w(r), where Lap is laplacian and EL is Euler Lagrange equation. Please check the Maple code and help me to do some manipulations to find a general relation (if any relation exists!).

In fact I need the inverse of Euler Lagrange equation to obtain f(r) for an arbitrary function g(r) in equation below

EL(f) = Lap(EL(g))

Or f=inverseEL(Lap(EL(g)))

Thank you for taking your time

 

 

 

restart; s := proc (f) subs(d[0] = w(r), seq(d[n] = diff(w(r), `$`(r, n)), n = 1 .. 10), f) end proc; ss := proc (f) subs(seq(diff(w(r), `$`(r, 11-n)) = d[11-n], n = 1 .. 10), w(r) = d[0], f) end proc; EL := proc (eq) s(diff(ss(eq), d[0]))+add((diff(s(diff(ss(eq), d[n])), `$`(r, n)))*(-1)^n, n = 1 .. 10) end proc

f := (diff(w(r), r, r))^2*r^4+4*r^6*(diff(w(r), r, r, r))^2:

a1 := EL(F):

a2 := VectorCalculus:-Laplacian(EL(f), 'polar[r, t]'):

simplify(a1-a2)

8*r^6*(diff(diff(diff(diff(diff(diff(diff(diff(w(r), r), r), r), r), r), r), r), r))+248*r^5*(diff(diff(diff(diff(diff(diff(diff(w(r), r), r), r), r), r), r), r))+2582*r^4*(diff(diff(diff(diff(diff(diff(w(r), r), r), r), r), r), r))+10910*r^3*(diff(diff(diff(diff(diff(w(r), r), r), r), r), r))+17786*r^2*(diff(diff(diff(diff(w(r), r), r), r), r))+8192*r*(diff(diff(diff(w(r), r), r), r))-92*(diff(diff(w(r), r), r))

 (1)

``


 

Download EL.mw

Sets????...

Asked by: tomleslie 13771
February 13 2019
0  2

You use curly braces, ie '{}' as a container. Within Maple such curly braces designate a set, and Maple will always display sets in "lexicographic" order.

Since order has no meaning for entries in a set, trying to "sort" a set is meaningless. You can only sort lists, Arrays etc where the concept of order meaningful

See the attached for examples of sorting sets, lists, Arrays, and note that sorting of sets doesn't do anything useful

For future reference

  1. This should be a "Question", not a "Post" (and if I knew how to move it I would!)
  2. When posting on this site, try to avoid using third party sites like dropbox. Upload code (not pictures of code) using the big green up-arrow in the Mapleprimes toolbar
> 

  restart;
  alpha:=[2,3,4,5];
#
# Try sorting sets - won't work because
# order is meaningless in a set
#
  sort( {abs(alpha[1]-30),abs(alpha[2]-30),abs(alpha[3]-30),abs(alpha[4]-30)}, `<`);
  whattype(%);
  sort( {abs(alpha[1]-30),abs(alpha[2]-30),abs(alpha[3]-30),abs(alpha[4]-30)}, `>`);
  whattype(%);
#
# Do the same thing with lists, where order is significant
#
  sort( [abs(alpha[1]-30),abs(alpha[2]-30),abs(alpha[3]-30),abs(alpha[4]-30)], `<`);
  whattype(%);
  sort( [abs(alpha[1]-30),abs(alpha[2]-30),abs(alpha[3]-30),abs(alpha[4]-30)], `>`);
  whattype(%);
#
# You can also sort entries in an Array()
#
  sort(Array([abs(alpha[1]-30),abs(alpha[2]-30),abs(alpha[3]-30),abs(alpha[4]-30)]), `<`);
  whattype(%);
  sort(Array([abs(alpha[1]-30),abs(alpha[2]-30),abs(alpha[3]-30),abs(alpha[4]-30)]), `>`);
  whattype(%);

alpha := [2, 3, 4, 5]

  

{25, 26, 27, 28}

  

set

  

{25, 26, 27, 28}

  

set

  

[25, 26, 27, 28]

  

list

  

[28, 27, 26, 25]

  

list

  

Vector[row](4, {(1) = 25, (2) = 25, (3) = 25, (4) = 25})

  

Array

  

Array(%id = 18446744074423548974)

  

Array

 (1)
> 

 

Vector[row](4, {(1) = 25, (2) = 25, (3) = 25, (4) = 25})

  

Array

  

Array(%id = 18446744074423548974)

  

Array

 (2)
> 

 

Download sortSet.mw

solving couple pde in maple?...

Asked by: torabi 85
differential-equation pde
February 09 2019
0  7

Is possible to solve this differential equation by maple?

thaks...

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