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Hi all.

Assume that we have partitioned [0,a], into N equidistant subintervals and in each subinterval we have M sets of poly nomials of the following form:

where Tm(t)=tm( namely Taylor Series) and tf is a(final point)
for Example with N=4, M=3 we have:

now we want to approximate a function, asy f(t), in this interval with following form:

If we have:

(Tau is a constant number)
then: can we find L and Z matrices using maple? I have found it manualy but for large M and N this procedure is longsome.

I used Inverse command in maple but the vector's inverse is wrong(operation not defined for Vectors)

Best Wishes

Mahmood   Dadkhah

Ph.D Candidate

Applied Mathematics Department

Hi all.

Assume that we have partitioned [0,a], into N equidistant subintervals and in each subinterval we have M sets of poly nomials of the following form:

where Tm(t)=tm( namely Taylor Series) and tf is a(final point)
for Example with N=4, M=3 we have:

now we want to approximate a function, asy f(t), in this interval with following form:

How can we do this with maple????

how can we find the ci's?????

Thanks a lot

Mahmood   Dadkhah

Ph.D Candidate

Applied Mathematics Department

I have just begun thinking of trying to make some mathematically defined objects using a 3d printer. I would be happy to hear from anyone who has done this using Maple to prepare input. Pointers for a novice in 3d printing would be appreciated.  I have access to a MakerBot Replicator 2. But the people who have it have only used it to scan objects and make 3d copies of them. 

---Edwin

Hi all;

Hope all of you  be in good health

I want to construct a special function b_{nm}(t) like:

with piecewise command i did it but the result is incorrect.

any one can help me to do it?

Best wishes

 

Mahmood   Dadkhah

Ph.D Candidate

Applied Mathematics Department

Hi all 

I have the following segment of maple program which belongs to time delay systems dynamic. here C=X-X0-G.Z-X.Dtau.P+X.Dtau.Z-U.P, is a matrix(vector) which comes from reordering the system terms and my goal is to minimizing J:=X.E.Transpose(X)+U.E.Transpose(U), subject to constraint C=0, but i don't know how to do so.

I will be so grateful if anyone can guide me

best wishes

Mahmood   Dadkhah

Ph.D Candidate

Applied Mathematics Department


restart:
with(Optimization):
with(LinearAlgebra):
macro(LA= LinearAlgebra):
L:=1:  r:=2:  tau:= 1:
interface(rtablesize= 2*r+1):

Z:= Matrix(
     2*r+1, 2*r+1,
     [tau,
      seq(evalf((L/(2*(iz-1)*Pi))*sin(2*(iz-1)*Pi*tau/L)), iz= 2..r+1),
      seq(evalf((L/(2*(iz-1-r)*Pi))*(1-cos(2*(iz-1-r)*Pi*tau/L))), iz= r+2..2*r+1)
      ],
     scan= columns,
     datatype= float[8]
);
                        
Dtau00:= < 1 >:
Dtau01:= Vector[row](r):
Dtau02:= Vector[row](r):
Dtau10:= Vector(r):
Dtau20:= Vector(r):

Dtau1:= LA:-DiagonalMatrix([seq(evalf(cos(2*i*Pi*tau/L)), i= 1..r)]):
Dtau2:= LA:-DiagonalMatrix([seq(evalf(sin(2*i*Pi*tau/L)), i= 1..r)]):
Dtau3:= -Dtau2:
Dtau4:= copy(Dtau1):

Dtau:= < < Dtau00 | Dtau01 | Dtau02 >,
         < Dtau10 | Dtau1  | Dtau2  >,
         < Dtau20 | Dtau3  | Dtau4  > >;
 
P00:= < L/2 >:
P01:= Vector[row](r):
P02:= Vector[row](r, j-> evalf(-L/j/Pi), datatype= float[8]):
P10:= Vector(r):
P20:= Vector(r, i-> evalf(L/2/i/Pi)):
P1:= Matrix(r,r):
P2:= LA:-DiagonalMatrix(P20):
P3:= LA:-DiagonalMatrix(-P20):
P4:= Matrix(r,r):

P:= < < P00 | P01 | P02 >,
      < P10 | P1  | P2  >,
      < P20 | P3  | P4  > >;

interface(rtablesize=2*r+1):    # optionally
J:=Vector([L, L/2 $ 2*r]):      # Matrix([[...]]) would also work here

E:=DiagonalMatrix(J);

X:=  Vector[row](2*r+1,symbol=a);
U:=Vector[row](2*r+1,symbol=b);

X0:= Vector[row](2*r+1,[1]);
G:=Vector[row](2*r+1,[1]);
C:=simplify(X-X0-G.Z-X.Dtau.P+X.Dtau.Z-U.P);

Z := Matrix(5, 5, {(1, 1) = 1., (1, 2) = 0., (1, 3) = 0., (1, 4) = 0., (1, 5) = 0., (2, 1) = 0., (2, 2) = 0., (2, 3) = 0., (2, 4) = 0., (2, 5) = 0., (3, 1) = 0., (3, 2) = 0., (3, 3) = 0., (3, 4) = 0., (3, 5) = 0., (4, 1) = 0., (4, 2) = 0., (4, 3) = 0., (4, 4) = 0., (4, 5) = 0., (5, 1) = 0., (5, 2) = 0., (5, 3) = 0., (5, 4) = 0., (5, 5) = 0.})

Dtau := Matrix(5, 5, {(1, 1) = 1, (1, 2) = 0, (1, 3) = 0, (1, 4) = 0, (1, 5) = 0, (2, 1) = 0, (2, 2) = 1., (2, 3) = 0, (2, 4) = 0., (2, 5) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = 1., (3, 4) = 0, (3, 5) = 0., (4, 1) = 0, (4, 2) = -0., (4, 3) = -0., (4, 4) = 1., (4, 5) = 0, (5, 1) = 0, (5, 2) = -0., (5, 3) = -0., (5, 4) = 0, (5, 5) = 1.})

P := Matrix(5, 5, {(1, 1) = 1/2, (1, 2) = 0, (1, 3) = 0, (1, 4) = -.318309886100000, (1, 5) = -.159154943000000, (2, 1) = 0, (2, 2) = 0, (2, 3) = 0, (2, 4) = .1591549430, (2, 5) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = 0, (3, 4) = 0, (3, 5) = 0.7957747152e-1, (4, 1) = .1591549430, (4, 2) = -.159154943000000, (4, 3) = 0, (4, 4) = 0, (4, 5) = 0, (5, 1) = 0.7957747152e-1, (5, 2) = 0, (5, 3) = -0.795774715200000e-1, (5, 4) = 0, (5, 5) = 0})

E := Matrix(5, 5, {(1, 1) = 1, (1, 2) = 0, (1, 3) = 0, (1, 4) = 0, (1, 5) = 0, (2, 1) = 0, (2, 2) = 1/2, (2, 3) = 0, (2, 4) = 0, (2, 5) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = 1/2, (3, 4) = 0, (3, 5) = 0, (4, 1) = 0, (4, 2) = 0, (4, 3) = 0, (4, 4) = 1/2, (4, 5) = 0, (5, 1) = 0, (5, 2) = 0, (5, 3) = 0, (5, 4) = 0, (5, 5) = 1/2})

X := Vector[row](5, {(1) = a[1], (2) = a[2], (3) = a[3], (4) = a[4], (5) = a[5]})

U := Vector[row](5, {(1) = b[1], (2) = b[2], (3) = b[3], (4) = b[4], (5) = b[5]})

X0 := Vector[row](5, {(1) = 1, (2) = 0, (3) = 0, (4) = 0, (5) = 0})

G := Vector[row](5, {(1) = 1, (2) = 0, (3) = 0, (4) = 0, (5) = 0})

C := Vector[row](5, {(1) = 1.500000000*a[1]-2.-.1591549430*a[4]-0.7957747152e-1*a[5]-.5000000000*b[1]-.1591549430*b[4]-0.7957747152e-1*b[5], (2) = a[2]+.1591549430*a[4]+.1591549430*b[4], (3) = a[3]+0.7957747152e-1*a[5]+0.7957747152e-1*b[5], (4) = a[4]+.3183098861*a[1]-.1591549430*a[2]+.3183098861*b[1]-.1591549430*b[2], (5) = a[5]+.1591549430*a[1]-0.7957747152e-1*a[3]+.1591549430*b[1]-0.7957747152e-1*b[3]})

(1)

J:=X.E.Transpose(X)+U.E.Transpose(U);

J := a[1]^2+(1/2)*(a[2]^2)+(1/2)*(a[3]^2)+(1/2)*(a[4]^2)+(1/2)*(a[5]^2)+b[1]^2+(1/2)*(b[2]^2)+(1/2)*(b[3]^2)+(1/2)*(b[4]^2)+(1/2)*(b[5]^2)

(2)

Minimize(J,{C=0});






Error, (in Optimization:-NLPSolve) invalid arguments

 

#XP:=-.015+X[1]+add(X[l+1]*f1(l)+X[r+l+1]*f2(l), l= 1..r):
#plot([XP,T1], t= 0..1);#,legend= "Solution Of x(t) with r=50"):

 

 

 

 

 

 

Download work1.mwswork1.mws

I am new user of Maple. I have an expression like f(x,y)/g(x,y) and I want to have Maple name f(x,y) as something simple like "h" so that later equations write h/g(x,y) instead of the complete f(x,y)/g(x,y), and also to be able to simplify other equations in terms of h.

For example, a=(x+1)(y-5)^2/(x+y-3). Can I get Maple to let h=(x+1)(y-5)^2, so that I get h/(x+y-3) when I ask for a?

Sorry if this question is basic (and my math terminology incorrect), but I have been trying for a while.

Hi all

In matlab software we have a command namely fmincon which minimizes any linear/nonlinear algebric equations subject to linear/nonlinear constraints.

Now my question is that: what is the same command in maple?or how can we minimize linear/nonlinear function subject to linear/nonlinear constraints in maple?

thanks a lot

Mahmood   Dadkhah

Ph.D Candidate

Applied Mathematics Department

Does anyone has any maple worksheet that generate surface using the PDE method described in this article?  I am trying to learn this method but I am not familiar with the mathematics to do it although the paper gives some description of it.  I hope someone can demonstrate the procedure in Maple.  Thanks

http://www.researchgate.net/publication/259095177_Automatic_shape_optimisation_of_pharmaceutical_tablets_using_Partial_Differential_Equations/file/72e7e52a87ed129d4a.pdf

Is there any simple way to print the sum of a series with exceptions?

For example, the following works (sort of), but its not consistent with mathematical notation, where one would expect to see something like a Sigma^' printed out, and the condition, alongw ith ther limits appear under the Sigma sign:

[Sum(1/(k^2-p),k=0..infinity),And(k<>p)]

hi all.
i have a system of ODE's including 9 set of coupled OED's . 

i have  converted second deravaties to dd2 , in other words : diff(a[i](t),t,t)=dd2[i](t) . i =1..9 :

and i have set these 9 equations in form of vibrational equations such :  (M.V22)[i]+(K(t).V(t))[i]+P(t)[i] = eq[i] , where M is coefficient Matrix of second  derivatives , V22 is Vector of second derivaties , for example V22[1] = diff(a[1](t),t,t) , and  P(t) is the numeric part of equations ( they are pure number and do not contain any symbolic function ) and K(t).V(t) is the remaining part of equations such that : (K(t).V(t))[i] = eq[i] - (M.V22)[i] - P(t)[i]  , and V(t) are vector of a[i](t)'s which V(t)[1] = a[1](t) ,

i have used step by step time integration method (of an ebook which i have attachted that part of ebook here), when i set time step of solving process to h=0.01 , i can solve this system up to time one second or more, but when i choose h=0.001 or smaller, the answer diverges after 350 steps . i do not know whether the problem is in my ODS system, or maple can not handle this ?the answer about the time t=0.3 are the same in both steps, but after that, the one with stpe time h=0.001 diverges. my friend has solved this in mathematica without any problem, could any body help me ?! it is urgent for me to solve this problem,thnx everybody.


ebook.pdf  step_=_0.001.mw  step_=_0.01.mw 

restart;
g:=0.88641:
e:=2.53128:
eq:=tan(g)= e*sin(f)/(1+e*cos(f)):
fsolve(eq,f);

gives  1.19749

What command/option do I need to get both solutions like with Mathematica:

g = 0.886461;
e = 2.53128;
eq = Tan[g] == (e Sin[f])/(1 + e Cos[f]);
NSolve[eq, f]

  (*   {{f -> -2.56623}, {f -> 1.19756}} *)

thanks

In physics as in math, we often use delta to indicate a (small but finite) variation in a parameter (e.g. delta x). Sometimes Delta (capital delta) is used for a larger variation, and there are even constructs like delta Delta x (a small variation of a larger variation in x). (Don't laugh or frown, this is being done & makes sense in certain situations.)

How do I write this best in Maple, esp. when I use 2-d math and am working on a (live-) script that may be handed out to others incl. students,? I.e. the appearance matters. Just writing delta x is interpreted (in 2-d input) as delta*x which is not what is meant (and leads to funny effects after the first simplify). If I write deltax (one word) then delta does not typeset in its proper greek form, which becomes an issue if you have many of these. I can write delta(x) and that often works (as long as you don't try to differentiate by x), but the typeset equation does not look right either (delta is not a function of x).

Is there a god way of doing this, or am I hitting a wall here?

TIA,

Mac Dude

 

I am trying to illustrate the chain rule for multivariet functions

 

diff(f(u(x,y),v(x,y),x)

 

The Maple responce is D1(f)(u(x,y),v(x,y)*(partial of u(x,y) wrt x) +..etc

 

I would like to replace the D- notation with the standard notation for the "partial of f wrt u" for obvious reasons - this is what students are familar with. The convert cmnd Doe Not Work in this case.

 

Similarly the cmnd diff(u(x,y),v(x,y),x,x) gives rise to D1,D11, D12 symbols which I would likee to convert to standard partial notation.

 

All this is a BIG DEAL when trying to illstrate the chain rule in Cal III.

 

Joe Salacuse

Mathematics

Kettering University

Slides of the presentation at the VII Workshop Fast Computational and Applied Mathematics developed in graduate school at the National University of Trujillo. January 8, 2014.

 

Visualización_Geomét.pdf

 

L. Araujo C.

EDIT:EDIT: I found what I was looking for. Thanks!

 

eq:=(V^(1-r/(r-s))*V*k/(r-2*s)+_C1)*V^(r/(r-s))=0;

 

equation 1

 

solve(eq,C1);

 

Can anyone tell me why nothing happens when I solve the above equation for C1.

I've been coming across this problem a few times lately, but sometimes when the equations are less complicated it does work from time to time. 

Any help would be greatly appreciated.

 

EDIT:  Thanks Markiyan Hirnyk

But I'm still having some trouble.

 

f:=t->(-r*t+s*t+V)^(r/(r-s));

eq2:=diff(C*f(t),t)+C*f(t)*r/(V+s*t-r*t)=s*k*t;

solve(eq2,C);

 


When I try solving eq2 nothing happens. 


This time C is just a variable I used and not one Maple generated.

So why doesn't it work with this particular equation?

 

 

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