Dear All,

I would like to perform a numerical integration of the following. Please let me know the method.

The integration consits of one variable essentially. Since the symbolic integration is not possibl and hence I have to do it numerically.

Appreciate you reply. Thanks

Here is the question:Prior to this question I was given f(z)=z^2+1, N(z)=(z^2-1)/(2z), T(z)=z-I/z+I such that T(N^k (z))=(T(z))^2^k. And L is a set of number on the real axis. Now the question is that given we have two regions of the complext plane as follow:

R₊ = {z : N^k{z) -> i as k -> ∞}; R_- = {z : N^k(z) -> -i as k -> ∞}.

Draw a diagram to illustrate these regions, the line L and the roots i and -i. We call R₊ the basin of attractionfor the root +i, and similarly R_-is the basin of attraction for the root -i.

 Show that if z is on the set L (the common boundary of the two regions R₊ and R_{_}, then N^k(z) stays on L for all values of k. (This is easy once you identify what L is.) So in this case iteration does not produce a root at all.

So basically my problem is that the fact I'm not very familar with the commands to draw such diagram, and I don't know much about Newton's method to compute complex roots. It would be appreciated if anyone can help me how to get start with the question. Thanks.

I have a diff equation in cartesian coordinates I need to transform to a certain cylindrical system. The de looks like this:

I define my new system with addcoords like this:

addcoords('AccCylinder',[r,theta,y],[r*cos(theta),y,r*sin(theta)]); # Note: y is the longitudinal axis here!

and also do

VectorCalculus:-AddCoordinates('AccCylinder'[r,theta,y],[r*cos(theta),y,r*sin(theta)],overwrite) assuming r >= 0;

and note that I had to overwrite as my system was already known, so maybe addcoords is reduncant(?)

I then do the transformation ("(7)" is the label of my above de):

changecoords((7),[x,y,z],AccCylinder,[r,theta,y]);

and get

This may be correct, but it has the expressions in the differentials, which diff does not know how to handle. I need to convert things like diff(xpr,r*cos(theta)) = diff(xpr,x)*diff(x,r) where x would be r*cos(theta). I can do this "by hand", but that seems overly tedious and error-prone. Somehow I'd expect the coordinate transforms to be able to do this but I can't figure out how.

Any idea?

Thanks,

Mac Dude,

по_альтернативной_ок.mw

Hi!

i have problems with surfdata command. I want to see beautifull surface, but see only few black lines.

and i dont know why, because i do all like in example.

Thank you vwry much for answers)

Hi everybody,

When doing calculations, I often run in the following problem.  I have the final solution wich I simplify symbolically so many terms are cancelling.  But I get this:

While I would like to regroup all the terms into the square root.  But look, even in this forum, Maple get sqrt(2) automatically out of the square root.

I know that it is the simple form.  But in some instances, I need the square root to stay together so I can show a property.  But is there a way to be able, sometimes, to tell Maple to leave all the terms under the square root?

Thank you in advance for your help.

--------------------------------------
Mario Lemelin

Maple 17.01 Ubuntu 13.10 - 64 bits
Maple 17 Win 7 -  64 bits
messagerie : mario.lemelin@cgocable.ca
téléphone :  (819) 376-0987

Hi

I have a simple Maple application with two TextArea components (TextArea0 and TextArea1) inside.

The start up code is following:

#++++++++++++++++++
Actions := module()
export DoNothing;
   
    DoNothing := proc()
    end proc;
    
end module; #Actions
#++++++++++++++++++

the action when cotents change for both TextArea components is

#++++++++++++++++++
use Actions in
DoNothing();
end use;
#++++++++++++++++++

The problem:
When I change the focus from one TextArea component to another and press Restart maple server then an error appears:

Error in Component TextArea1 with caption "TextArea": `Actions` is not a module or member.
Haw can it be fixed? Thank you.

problem_with_modul.mw

The dot product of vector v and u= ||v|| ||u||fosters also vector u*v=XvXu+Yv=A, v=<2,5>, u=<4,9>.

When I open the MapleCloud palette, I see a small list of user documents under the rubric "Popular". Is there a significantly longer list I can access to browse?

Dear users

A friend of of mine has a problem with an integral and since it's for his thesis, it's pretty important. 

That's why I ask it here cause I don't know where to ask it elsewhere, so if it's wrong posted, completely my bad.

l:=(y*o)/(v);

R:=(Phi*o)/v;

A:=5*(a*ln(R)+b);

P:=sqrt(1+4*k^2*l^2*(1-exp^(-l/a)));

M:=int((2)/(1+P),o);

With other words, I want to integrate the wole thing to the variable o, who appears in the variables l and R.

Somehow, when I put this in Maple, it won't solve it. Probably it's just a stupid fault or i just forget something, but i don't find it. Does anyone knows how to solve it?

Already a lot of thanks!

Hi, I have the feeling I ran into this before, but can't find the answer, so here goes:

I want to create an animated plot of a histogram, changing the range of data to be histogrammed. So I type:

plots:-animate(Statistics:-Histogram,[dR*~WindowN(RP0,Ci,CangleWidth+Ci),ignore=true],Ci=-0.5 .. 0.2);

The error I am getting is

Error, (in MathPad:-WindowN) cannot determine if this expression is true or false: Ci < HFloat(0.39995) and HFloat(0.0) <= -HFloat(0.34995000000000004)+Ci

What happens here is that dR is a Vector of data with RP0 being another Vector equally long. I have a library function called WindowN that returns a Vector of the same length as its argument, with 1. for the elements within the window, undefined for the elements outside. The windowing algorithm is just a straightforward if, in a loop over the elements. This all works and I get a correct Histogram plot if I set the window numerically and call Histogram. CangleWidth is preset to 0.05.

Here the window to use is supposed to be set by the animate command. I expect Ci to be set to numbers in the range given (25 points default) and prepare the plots. But it looks like the WindowN routine gets an unevaluated Ci. I tried evalf(Ci) or eval(Ci) in the arglist, to no avail. Ci is not used or set before this call to animate.

I can see how I can workaround this but I think this should work as is. plots:-animate works for me in other contexts.

Any ideas?

Mac Dude

Following previous question at

http://www.mapleprimes.com/questions/149581-Improve-Algorithm-Dsolve

and also

http://www.mapleprimes.com/questions/149243-BVP-With-Constraining-Integrals

I wrote the following code

***********************

restart:

gama1:=0:


phi0:=0.00789:


rhocu:=2/(1-zet^2)*int((1-eta)*rho(eta)*c(eta)*u(eta),eta=0..1-zet):

eq1:=diff(u(eta),eta,eta)+1/(mu(eta)/mu1[w])+((1/(eta-1)+1/mu(eta)*(mu_phi*diff(phi(eta),eta)))*diff(u(eta),eta)):
eq2:=diff(T(eta),eta,eta)+1/(k(eta)/k1[w])*(2/(1-zet^2)*rho(eta)*c(eta)*u(eta)/(p2*10000)+( (a[k1]+2*b[k1]*phi(eta))/(1+a[k1]*phi1[w]+b[k1]*phi1[w]^2)*diff(phi(eta),eta)-k(eta)/k1[w]/(1-eta)*diff(T(eta),eta) )):
eq3:=diff(phi(eta),eta)-phi(eta)/(N[bt]*(1-gama1*T(eta))^2)*diff(T(eta),eta):
mu:=unapply(mu1[bf]*(1+a[mu1]*phi(eta)+b[mu1]*phi(eta)^2),eta):
k:=unapply(k1[bf]*(1+a[k1]*phi(eta)+b[k1]*phi(eta)^2),eta):
rhop:=3880:
rhobf:=998.2:
cp:=773:
cbf:=4182:
rho:=unapply(  phi(eta)*rhop+(1-phi(eta))*rhobf ,eta):
c:=unapply(  (phi(eta)*rhop*cp+(1-phi(eta))*rhobf*cbf )/rho(eta) ,eta):
mu_phi:=mu1[bf]*(a[mu1]+2*b[mu1]*phi(eta)):

a[mu1]:=39.11:
b[mu1]:=533.9:
mu1[bf]:=9.93/10000:
a[k1]:=7.47:
b[k1]:=0:
k1[bf]:=0.597:
zet:=0.5:
#phi(0):=1:
#u(0):=0:
phi1[w]:=phi0:
N[bt]:=0.2:
mu1[w]:=mu(0):
k1[w]:=k(0):

eq1:=subs(phi(0)=phi0,u(0)=0,eq1):
eq2:=subs(phi(0)=phi0,u(0)=0,eq2):
eq3:=subs(phi(0)=phi0,u(0)=0,eq3):

p:=proc(pp2) global res,F0,F1,F2:
if not type([pp2],list(numeric)) then return 'procname(_passed)' end if:
res := dsolve({eq1=0,subs(p2=pp2,eq2)=0,eq3=0,u(0)=0,u(1-zet)=0,phi(0)=phi0,T(0)=0,D(T)(0)=1}, numeric,output=listprocedure):
F0,F1,F2:=op(subs(res,[u(eta),phi(eta),T(eta)])):
evalf(2/(1-zet^2)*Int((1-eta)*(F1(eta)*rhop+(1-F1(eta))*rhobf)*( F1(eta)*rhop*cp+(1-F1(eta))*rhobf*cbf )/(F1(eta)*rhop+(1-F1(eta))*rhobf)*F0(eta),eta=0..1-zet))-pp2*10000:
end proc:


s1:=Student:-NumericalAnalysis:-Secant(p(pp2),pp2=[6,7],tolerance=1e-6);

                   HFloat(6.600456858832996)

p2:=%:



ruu:=evalf(2/(1-zet^2)*(Int((1-eta)*F0(eta),eta=0..1-zet))):
phb:=evalf(2/(1-zet^2)*(Int((1-eta)*F0(eta)*F1(eta),eta=0..1-zet))) / evalf(2/(1-zet^2)*(Int((1-eta)*F0(eta),eta=0..1-zet))) :
TTb:=evalf(2/(1-zet^2)*(Int((1-eta)*F2(eta),eta=0..1-zet))):
rhouu:=evalf(2/(1-zet^2)*(Int((1-eta)*(F1(eta)*rhop+(1-F1(eta))*rhobf)*F0(eta),eta=0..1-zet))):
with(plots):
res(parameters=[R0,R1]):
odeplot(res,[[eta,u(eta)/ruu],[eta,phi(eta)/phb],[eta,T(eta)/TTb]],0..zet);

*************************************

as you can see at the second line of the code, the value of phi0:=0.00789. however, I want to modify the code in a way that phi0 is calculated with the following addition constraint

evalf(2/(1-zet^2)*(Int((1-eta)*F0(eta)*F1(eta),eta=0..1-zet))) / evalf(2/(1-zet^2)*(Int((1-eta)*F0(eta),eta=0..1-zet)))-0.02=0

I would be most grateful if you could help me in this problem.

Thanks for your attention in advance

Amir

I need to create a function from one list to another, but I don't want to define an operation.  I only want to assign a 1-1 mapping from a list of 64 elements to another list of 64 elements, i.e. the 1st element in list a is assigned to the 1st element in list b, etc.  I see plenty of examples of how to do this with an operation, but I don't want the mapping to perform any operation, just the mapping.  How is this done?

[> restart;
[> OPTIMAL:=proc(f,Condition::set)
local vars,L,S,SS,k,m,K,Fmax,Fmin,sol_min,sol_MIN,sol_max,sol_MAX;
vars:=indets(f,name) union indets(Condition,name);
L:=map(convert,Condition,equality);
K:=combinat[choose](L);
S:=NULL:
for k to nops(k) do if solve(K[k])<>NULL then
extrema(f,K[k],vars,'s||k'):S:=S,a||values(s||k):fi od:
SS:={}
for k to nops([s]) do
if type(s[k],set) then SS:=SS union evalc(s[k]) fi od;
SS:=remove(has,SS,l);
S:=NULL:
for k to nops(ss) do if type(SS[k],set(equation)) and
map(evalb,evalf(simplify(subs(SS[k],Condition))))={true}
then S:=S,vatue(ss[k]) fi od;
SS =[s];
Fmax:=-infinity:
for k to nops(SS) do
if evalf(simplify(subs(ss[k],f)))>evalf(Fmax)
then Fmax:=simplify(value(subs(SS[k],f)));sol_max:=SS[k]; fi;od;
sol_MAX:=sol_max:
for k to nops(SS) do
if Fmax=simplify(value(subs(SS[k],f)))
and (SS[k] minus sol_max)<>{} then
sol_MAX:=sol_MAX,Ss[k] fi od;
‘Fmax'=simplify(expand(Fmax)),sol_MAX:
Fmin:=infinity:
for k to nops(SS) do
if evalf(simplify((subs(SS[k],f))))<evalf(Fmin)
then Fmin:=simplify((subs(SS[k],f)));sol_min:=SS[k]; fi;od;
sol_MIN:=sol_min:
for k to nops(SS) do
if Fmin=simplify(value(subs(SS[k],f)))
and (SS[k] minus sol_min)<>{} then
sol_MIN:=sol_MlN,SS[k] fi od;
RETURN('F[min]'=simplify(expand(Fmin)),sol_MlN,
'F[max]'=simplify(expand(Fmax)),sol_max);
end: ↵

" Error, unable to match delimiters"
  Please, help me.
I don't understand. Thank you, thank you.

C(n,k)=((2*(k-2-n))/(k*(k-1)))*C(n,k-2)
if n in {even} then C(n,0)=((-1)^(n/2))*(factorial(n)/factorial(n/2)) and C(n,1)=0
if n in {odd} then C(n,0)=0 and C(n,1)=(2*(-1)^((n-1)/2))*(factorial(n)/factorial((n-1)/2))

i've been trying for hours to get a procedure involving this to work :(

Thanks

I want to make a plot of this function sine and imaginary cosine below,

psi(x):=sin(k*x)+I*k*l[2]*cos(k*x);

where

k:=n*pi/L;
 
L=1,n=1,l[2]=1;

plot(psi(x),x=0..5);

Plotting error, empty plot.

i always recieve this Error. Can someone help me with this. You can take any range of x including Pi if you wish , and as well provide me with refrences Text book on ploting functions if He/She knows. Looking forward for feedbacks. Thank you very much .