Dear Experts,

Analytical integration is not a choice for the integrals listed here. Hence, Maple is not able to find the numerical integration for the following oscillatory functions. However mathematica can. However, before I take the mathematica results, just need to check with you.

Following link shows that for a diverging series, the (Numerical) integral is finite.

http://books.google.com.sg/books?id=vntDnyh0gacC&pg=PA664&lpg=PA664&dq=nintegrate++seqlim&source=bl&ots=iNYR1o6kVd&sig=VuiQuiUMDEEGOBnguSwfcPPSHQA&hl=en&sa=X&ei=k_J4UofXJYjNkwW79IDYBw&ved=0CE4Q6AEwBA#v=onepage&q=nintegrate%20%20seqlim&f=false

1)

 Maple: 

eval(int(r^2 BesselJ(1,r)* BesselJ(0,r), r = 0..infinity)) 

Float(undefined)

Mathematica: 

NumberForm[ NIntegrate[BesselJ[0, x]*BesselJ[1, x]*x^2, {x, 0, Infinity},   AccuracyGoal -> 20], 15]

SequenceLimit::seqlim: The general form of the sequence could not be determined, and the result may be incorrect. >>

-95982.37707206068

2)  Maple:
       eval(int(r* BesselJ(0,r), r = 10..infinity)) 

                         Float(undefined)

Mathematica: 

NumberForm[ NIntegrate[BesselJ[0, x]*x, {x, 10, Infinity},   AccuracyGoal -> 20], 15]

SequenceLimit::seqlim: The general form of the sequence could not be determined, and the result may be incorrect. >>

-0.434727

Any conclusions on the result.

a) Why maple not able to evaluate the integrals.  b) Are the result of the Mathematica can be considered as appropriate.

Attached is the maple file for your consideration.

Integrations.mw 

Lookinf forward to your reply.

Thanks.

Hello!

Im a regular student and Math is a really difficult topic for me, and every once in a while i run into a problen that i am unable to solve. This time i would like to ask this commmunity for some help. Many thanks in advance.

The function itself is: y = sqrt((x^2-5*x+6)/log[10]((x+10)^2))

I was able to determine the domain (X), but i am having very big trouble with finding the range (Y). Also i should be able to do it with pen on paper, but so far i have wasted 2 days and many papers on pointless scribblig.

Could anyone please explain how could i find the range of that function and provide a step by step solution? 

Suppose I broadcast a game show where every episode there is 5 randomly chosen topics from 8 possible topics (A,B,C….). how can I get maple to do this automatically?

 I thought I could use

  > with(combinat):

> choose([A,B,C,D,E,F,G,H], 5);

of course the output comes out ordered. is there some way to randomize it? or another way? rgds

Hi, 

I have the following six equations that I need to solve:

eq1 := A^5*f6+A^4*f5+A^3*f4+A^2*f3+A*f2+f1 = ln(V1);
print(??); # input placeholder
eq2 := B^5*f6+B^4*f5+B^3*f4+B^2*f3+B*f2+f1 = ln(V2);

eq3 := 5*A^4*f6+4*A^3*f5+3*A^2*f4+2*A*f3+f2 = F1/V1;
eq4 := 5*B^4*f6+4*B^3*f5+3*B^2*f4+2*B*f3+f2 = F2/V2;
eq5 := 20*A^3*f6+12*A^2*f5+6*A*f4+2*f3 = G1/V1-[F1/V1]^2;
eq6 := 20*B^3*f6+12*B^2*f5+6*B*f4+2*f3 = G2/V2-[F2/V2]^2;

 where V1, V2, F1 & F2 have previously been found/defined in the worksheet (document).

When I use the solve command, more often than not I get the expression for the numerical calculation for each variable f1-f6, rather than an actual value:

solutionset := solve({eq1, eq2, eq3, eq4, eq5, eq6}, {f1, f2, f3, f4, f5, f6})

{f1 = 0.4096495220755576e-2*[-1.328181534188746]^2-0.3072371415566682e-1*[-9.408269235937702]^2+12.64287210303000, f2 = .3686845698680018*[-9.408269235937702]^2-49.98313436120349-0.6690942193900774e-1*[-1.328181534188746]^2, f3 = -1.423532089212563*[-9.408269235937702]^2+150.6490386090756+.3909877105143377*[-1.328181534188746]^2, f4 = -.9490213928083751*[-1.328181534188746]^2+1.954938552571689*[-9.408269235937702]^2-190.3706247009334, f5 = .8192990441511152*[-1.328181534188746]^2-1.115157032316796*[-9.408269235937702]^2+103.8844069311055, f6 = .2275830678197542*[-9.408269235937702]^2-20.57204700597870-.2275830678197542*[-1.328181534188746]^2}

Why is Maple not giving me the actual value for the variables, and how do I get it to do so, everytime? [In fact it did output the actual values once – but I have no idea what I did differently: it seems to be very random….]

i.e. how do I output the following:

solutionset := {f1 = 9.930572749191651, f2 = -17.46685689954139, f3 = 25.33406943774393, f4 = -19.00233912206421, f5 = 6.620988906086421, f6 = -.8288827301180226}

thanks

hi

is there any way that i run my maplet output in  systems that havnt any maple install on them?

(i wanna run maple program without maple)

Reza²⁹⁶¹

Bonjour,

Comment se calcule avec maple le développement de laurent d'une fonction de deux variables ?

Maple n'autorise pas la commande laurent(1/x/y, [x=0,y=0]).

Merci d'avance.

Gérard.

Does N variables caylay table have N permutation group so that can generate N functions?

for exmaple 3 variables cayley table have 3 permutation group, for 1, it has a permutation group , for 2 has a permutation group etc.

then does it mean that it has 3 functions, do it need to composite 3 functions in order to get a function belong to this cayley table?

1 1 1

1 2 2

1 2 3

Compute integral In(X)/(X-A)(X-1)    0<x<∞ for positive a.

                         ∞

Compute the sum∑(k^2+k-1)/(k+2)! 

                        k=1

How to plot the function f := x->sum(sin(x/(k+1))/k, k = 1 .. infinity) on the interval 0..50? The series obviously converges.

Is there a way of extracting the terms of an expression with a certain dependence?

For example:

If I have,

expression:=f(x)+g(y)+x^2+y^3+65

I need to have,

f(x)+x^2
g(y)+y^3
65

parts separately.

(Of course, a way other than taking derivative.)

How would I find the polar representation of, say, (x^2+y^2)^2=x^2-y^2 using maple? Thanks. 

Hi! PLEASE HELP ME.. I try to give a new name in my proc where it stops at the initial condition, ic. Somehow it gave me an output like

>Orbit:=proc(Map,ic,Nit)
local orbit,z,t:
orbit:=array(0..Nit);
z:=ic:
orbit[0]:=z;
for t to Nit (while z<>ic) ot t=1 do
orbit[t]:=z;
z:=Map(z):
orbit[t]:=z:od;
return[seq(orbit[t],t=0..Nit)];
end;

>Orbit (F,[1,0],20);
##

##I want to eliminate the orbit13 and so on. I tried to give a new name where for example per:=array(0..t). I want it stops at t and do not go until Nit. Can you help me?

Hello, everyone!

Last day I’ve discovered a strange behavior of the “optimization” tool:

Mostly it copes with the task – but there are cases (the data are the same) when the tool doesn’t return the opt. value: instead it returns the parameter name.
BUT if some of the previous calculations are re-evaluated (and the same input values are received) the “optimization” tools works quite well.

The question is: how to tackle the problem?

P.S. The way to force re-evaluation of previous functions in the body of this procedure (if the optimization failed) doesn’t help: it returns the optimizing parameter name once more.

Windows 8 (64-bit)
Maple 17.00

I have  

a(t):= (0.4292960410)*(t^3+20.0*t^2+105.0*t+138.0)^5/((t+1.881246817-0.5978370144*I)*(t+2.472494183-0.1946676251*I)*(t+5.550661347)*(t+5.496908401)*(t+12.46933729)*(t+12.44618893-0.9642646277e-2*I)*(t+0.5725282710)*(t+5.589440415)*(t+12.49222265)*(t+12.44618893)*(t+12.46933729)*(t+5.496908401)*(t+5.550661347)*(t+2.472494183+0.1946676251*I)*(t+1.881246817+0.5978370144*I))

b(t)=(1.8*t^2+34.1*t+138.)/(t^3+20.*t^2+105.*t+138.)

and 

F(t):={0.5738910678*a(t)*[1-b(t)]}/t*0.5137681159

I have expanded F(t) in series form using taylor series expansion formula in terms of t.

My question is 

                           Can it be expanded in series form in terms of b(t).

Hello,

I have 2 questions about the resolution of a ODE for the simple pendulum equations.

1) I need to add 'maxfun'=10^7 in the dsolve function. With this option, dsolve works. Can you explain me in a very simple way the principle of this option ? It's just to feel better how this option runs.

2) gamma(t) is a angular parameter.

With

tgammax:=odeplot(sol,[gamma(t),x(t)],0..10,numpoints=200,color=blue,legend="z"):
display(tgammax);

I manage to plot x(gamma) but with gamma in rad.

How can i do to x(gamma) but with gamma in degree? I should do gamma_deg=360/(2*Pi)*gamma(t) but as gamma(t) is defined numerically, this lign doesn't work.

Thank you for helpe

Here some ligns of my code :

Cinit:=D(psi)(0)=0,psi(0)=-0.93,D(x)(0)=0,x(0)=1.13,D(gamma)(0)=0,gamma(0)=0.79;sol:=dsolve({sys,Cinit},numeric,'maxfun'=10^7);
tx:=odeplot(sol,[t,x(t)],0..10,numpoints=200,color=blue,legend="x"):
display(tx); 

tgamma:=odeplot(sol,[t,gamma(t)],0..10,numpoints=200,color=blue,legend="gamma"):
display(tgamma);

tgammax:=odeplot(sol,[gamma(t),x(t)],0..10,numpoints=200,color=blue,legend="z"):
display(tgammax);