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gkokovidis

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20 years, 289 days
Draeger Medical Systems, Inc.
Contact gkokovidis

 

 

Regards,
Georgios Kokovidis
Dräger Medical

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These are answers submitted by gkokovidis

Correct...

gkokovidis 2370
January 19 2012
1 3

That is correct.  It does not support the Mac platform.  Details are here.

Regards,

Georgios Kokovidis

Dräger Medical

?alias...

gkokovidis 2370
January 19 2012
1 0

One way is to use the ?alias command.

> 

restart:
> 

alias(g=1+i);

g

                                          (1)
> 

h:=(1+i)^2+(1+i)^3*A+(1+i)^4*B;

g^2+g^3*A+g^4*B

 (2)
> 

 

 

Download alias.mw

 

Regards,

Georgios Kokovidis

Dräger Medical

Vector field and animated curve...

gkokovidis 2370
January 07 2012
1 0

There are many different ways to get a vector field plot (animated or static), and the same for the curve.  The code below has a static fieldplot with an animated curve on the same plot.  Right click on the plot after executing the worksheet, and select Animation-Play.  See ?display for more help with combining multiple plots.


> 

restart:
> 

with(plots):
> 

p1:=fieldplot([x/(x^2+y^2+4)^(1/2), -y/(x^2+y^2+4)^(1/2)], x = -2 .. 2, y = -2 .. 2):
> 

p2:=animate(implicitplot,[x^2-y^2 = r, x = -2 .. 2, y = -2 .. 2],r=0.2..1):
> 

display(p1,p2);

 
> 

 

Download fieldplotanimate.mw

 

Regards,

Georgios Kokovidis

Dräger Medical

Grouping values...

gkokovidis 2370
January 07 2012
1 1

Here is one way.  For more details, see ?collect help page.

restart:

eq:=k*(2*x+y-3*z+2)+s*(5*x+5*y-4*z+3)=0;

collect(eq,[x,y,z]);

 

Regards,

Georgios Kokovidis

Dräger Medical

Digits...

gkokovidis 2370
December 31 2011
2 0

This looks like a round-off issue.  Increase Digits.  Running your example worksheet with Digits set to 52 gave consistent results every time I executed.

Regards,

Georgios Kokovidis

Dräger Medical

restart:...

gkokovidis 2370
December 30 2011
0 1

Do you have a ?restart command at the beginning of your worksheet?  If not, try adding one, and re-execute your worksheet a few times to see if the results are consistent (with what you are expecting).  Can you upload your worksheet instead of pasting the images?  It will be easier for us to try and reproduce what you are seeing, in order to come up with a possible solution.

Regards,

Georgios Kokovidis

Dräger Medical

How to open maple twice...

gkokovidis 2370
December 29 2011
0 2

Platform?  On my Win XP laptop, double clicking the Maple icon launches a new instance. In each instance, I can execute a different worksheet. You can also launch multiple instances of command line Maple on a Windows machine using a batch file. 

 

Regards,

Georgios Kokovidis

Dräger Medical

?DEtools...

gkokovidis 2370
December 16 2011
0 1

Your syntax for ode1 and ode2 does not look correct.

restart:with(DEtools):
ode1:=diff(x(t),t)=x(t); ode2:=diff(y(t),t)=-y(t);
                         d             
                        --- x(t) = x(t)
                         dt            
                         d              
                        --- y(t) = -y(t)
                         dt             
phaseportrait([ode1, ode2], [x(t), y(t)], t = 0 .. 100, [[x(0) = 2, y(0) = 1], [x(0) = 1, y(0) = 2]], stepsize = 0.02, colour = grey, linecolour = black);

Download phaseportrait.mw

 

Regards,

Georgios Kokovidis

Dräger Medical

Tan Tutor...

gkokovidis 2370
December 15 2011
0 0

See the help page for ?Student[Calculus1][TangentTutor]

Regards,

Georgios Kokovidis

Dräger Medical

?alias...

gkokovidis 2370
December 10 2011
1 1

See the help page for ?alias

> 

restart:
> 

alias(e=exp(1));

e

  
> 

evalf(exp(2));

7.389056099

  
> 

evalf(e^2);

7.389056096

  

Remove alias.

> 

alias(e=e);
> 

evalf(e^2);

e^2

  
>   

Download exp_alias.mw

Regards,

Georgios Kokovidis

Dräger Medical

What is wrong with this solve()?...

gkokovidis 2370
December 08 2011
1 0

See attached worksheet.  A restart before your Stage 2 calculations clears up the problem.

 

Trade and the Environment

The Copeland and Taylor (2003) Model

Author:  Peter Kennedy, University of Victoria

Modified by:  Alan Mehlenbacher, University of Victoria

 

 

> 

restart:

Production Functions for the clean good (Y) and pollution (X)

> 

y := k^beta*l^(1-beta)

k^beta*l^(1-beta)

 (1)
> 

x := (1-theta)*k^sigma*l^(1-sigma)

(1-theta)*k^sigma*l^(1-sigma)

 (2)

Cost Minimization for an X Sector Firm

Stage 1: choose k & l to produce one unit of potential output

The Lagrangean is:

> 

LGkl := r*k+w*l+lambda*(1-k^sigma*l^(1-sigma))

r*k+w*l+lambda*(1-k^sigma*l^(1-sigma))

 (3)

First-order conditions:

> 

foc1kl := diff(LGkl, k); foc2kl := diff(LGkl, l); foc3kl := diff(LGkl, lambda)

r-lambda*k^sigma*sigma*l^(1-sigma)/k

  

w-lambda*k^sigma*l^(1-sigma)*(1-sigma)/l

  

1-k^sigma*l^(1-sigma)

 (4)
> 

solnkl := solve([foc1kl, foc2kl, foc3kl], [k, l, lambda])

[[k = -exp(ln(-(-1+sigma)*r/(sigma*w))*sigma)*sigma*w/((-1+sigma)*r), l = exp(ln(-(-1+sigma)*r/(sigma*w))*sigma), lambda = -exp(ln(-(-1+sigma)*r/(sigma*w))*sigma)*w/(-1+sigma)]]

 (5)

Thus, the solutions are

> 

kx := simplify(solnkl[1][1]); lx := simplify(solnkl[1][2])

k = -(-(-1+sigma)*r/(sigma*w))^sigma*sigma*w/((-1+sigma)*r)

  

l = (-(-1+sigma)*r/(sigma*w))^sigma

 (6)

and the unit cost function is

> 

cF := simplify(r*kx+w*lx)

r*k+w*l = -w*(-(-1+sigma)*r/(sigma*w))^sigma/(-1+sigma)

 (7)

Stage 2: choose Z (emissions subject to tax tau) and F to produce one unit of net output

> 

restart:
> 

LGzF := tau*z+cF*F+lambda*(1-z^alpha*F^(1-alpha));

tau*z+cF*F+lambda*(1-z^alpha*F^(1-alpha))

 (8)
> 

foc1zF := diff(LGzF, z);

tau-lambda*z^alpha*alpha*F^(1-alpha)/z

  

cF-lambda*z^alpha*F^(1-alpha)*(1-alpha)/F

  

1-z^alpha*F^(1-alpha)

 (9)
> 

solnzF := solve([foc1zF, foc2zF, foc3zF], [z, F, lambda]);

[[z = -cF*exp(-alpha*ln(-cF*alpha/((-1+alpha)*tau)))*alpha/((-1+alpha)*tau), F = exp(-alpha*ln(-cF*alpha/((-1+alpha)*tau))), lambda = -cF*exp(-alpha*ln(-cF*alpha/((-1+alpha)*tau)))/(-1+alpha)]]

 (10)

Thus the solutions are

> 

zx := simplify(solnzF[1][1]);

z = -cF*(-cF*alpha/((-1+alpha)*tau))^(-alpha)*alpha/((-1+alpha)*tau)

  

F = (-cF*alpha/((-1+alpha)*tau))^(-alpha)

 (11)
> 

 

 

 

Download CTmodel-1Restart.mw

 

Regards,

Georgios Kokovidis

Dräger Medical

Which edition?...

gkokovidis 2370
December 05 2011
0 0

In my edition of the book, the equation is y+dy=(x+dx)^2.  This can be expanded using FOIL.  In Maple, you will not see the steps, just the final product.

restart:

eq:=(x+dx)^2;

expand(eq);

You could do all the steps that you would do by hand in Maple and then combine them in the end.

First:=x*x;

Outter:=x*dx;

Inner:=x*dx;

Last:=dx*dx;

eq_expanded:=First+Outter+Inner+Last;

 

Regards,

Georgios Kokovidis

Dräger Medical

Plotting in Maple...

gkokovidis 2370
December 02 2011
0 0

Here is one way.  You can modify it for your own needs.

Download pointplotcircles.mw

The default option for symbolsize = 10, so your B array will need to be scaled in order for this to make sense when you display it.

Regards,

Georgios Kokovidis

Dräger Medical

How to animate a trajectory of a solutio...

gkokovidis 2370
November 27 2011
3 0

See the online help page Plotting Two-dimensional differential equations, to get you started.  The attached is a modified example from the help. 

animatede.mw 

Regards,

Georgios Kokovidis

Dräger Medical

Is there a way to have filled or coloure...

gkokovidis 2370
November 26 2011
1 1

Here is one example.  See the ?plot/options help page for more details.

restart: with(plots):

polarplot([cos(t), sin(t), t = 0 .. 4*Pi], color = "NavyBlue", thickness = 3, filled = [color = "Blue", transparency = .5]);

Download polarplotfilled.mw

 

Regards,

Georgios Kokovidis

Dräger Medical

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