## Problem with numerical multiple integration...

Hello everyone !

I have a problem when I want to calculate the following multiple integration numerically:

>evalf(Int(exp(sum(x[i],i=1..6)^2),[seq(x[i]=-1..1,i=1..6)]));
value(%);

It doesn't work. But when I replace sum(x[i],i=1..6)^2 with sum(x[i],i=1..6), it works. Is there any feasible solution to my problem ?

## Error with multiple choice creation...

Hi,

I have a problem with the adaptive question designer: when I use the multiple choice question type then occasionally parts of the question environment appear multiple times in the text, duplicating each time I reopen the question to edit. This happens in particular if the answers are a bit longer (4-5 lines each). So far I couldn't figure out how to fix this, does anyone have a similar problem?

## How to combine graphs of velocity profiles for dif...

hi , kindly guide me how to draw combine graphs for velocity profile at different values of one parameter.  For example we have 3rd order ODE and A is parameter that is multiple of equation. now we want to see the effects of that parameter on this 3rd  order ODE.  Now  how can i sketch the  combine graph of Df(o) at A=1, 2, 3. (for example.)

thanks

## How to make my program runnable again...

Dear,

I have a perfectly working when all parameters are known (figure 1), however I want to perform a sensitivity analysis by derivating the code if one parameter is unknown. Because of multiple possible answers and because of the complexity of the formula, I cannot run this script and get solutions. Any ideas how I can this calculation lighter so it is able to run? Values should be real and positive (so 1 or 2 solutions are the only one I'm interested in)

Any ideas, how I can make this code runnable? (file is below)

I'm stuck on this for a while now :/ So I hope someone will be able to help me

Question.mw

Figure 1: [URL=http://s1240.photobucket.com/user/laggstar/media/Parameter%20f%20known.png.html][IMG]http://i1240.photobucket.com/albums/gg494/laggstar/Parameter%20f%20known.png[/IMG][/URL]

Figure 2: [URL=http://s1240.photobucket.com/user/laggstar/media/Parameter%20f%20unknown.png.html][IMG]http://i1240.photobucket.com/albums/gg494/laggstar/Parameter%20f%20unknown.png[/IMG][/URL]

## plotting graphs together using display...

I've got the following code:

with(plots):
a:=seq(combinat[fibonacci](k), k=2..10);
for i from 1 to 5 do
#with(plots):
multiple(plot,[sin(a[i]*x),x=-2..2,-2..2,color="Red",legend=typeset("Curve1:",sin(a[i]*x))],[sin(a[i+1]*x),x=-2..2,-2..2,color="Green",legend=typeset("Curve2:",sin(a[i+1]*x))],title=typeset("Lissajous",i));
end do;

that plots the sine functions of consecutive fibonacci numbers pairwise. Now, if I had to use the display command to plot these pairs together, how would I be able to do so?

## Plotting two equations of two variables together...

I've got the following equations :

x^3-4x=y, y^3-3y=x that I want to plot together over an appropriate range for x and y

I've tried plots[multiple]([eq1,x=-2..2,y=-2..2],[eq2,x=-2..2,y=-2..2])

but that doesn't seem to work. How can I rectify this error?

## Numerica multiple integration...

Hi, all

I use INT to calculate multiple integration as below. It runs more than 20 hours without results. I wander is there any problem in my codes.

restart;
A := sin(k*Pi*(x-h*cos(theta))/a)*sin(l*Pi*(y-h*sin(theta))/b)*sin(k[0]*h)*sin(k*Pi*x/a)*sin(l*Pi*y/b);

W := evalf[5](int(int(int(int(A, h = 0 .. (x-a)/cos(theta)), theta = Pi+arctan((b-y)/(a-x)) .. 3*Pi*(1/2)), x = 0 .. a), y = 0 .. b, numeric))

Thanks

## Multiple pointplots...

Hi there,

I am trying to display multiple pointplots in the same plot. I would like to either distinguish the plots by their color or by the symbol (square, traiangle, circle) at each data-point. May be both, although I ignore whether using symbols at data-points is possible in Maple.

The plot i would like to achieve is this:

Maple says that my points are not in the correct format: MapleSimulation_test6.mw

My data array N has two parameters, and the free variable. The two parameters are also varied over a certain range. For plotting purposes, I would like to have one of the variables fixed, select three parameters for the other variable, and plot all data-points for them.

The resulting data array N seems to be OK, but I am aware that my attempt for plotting multiple arrays may be wrong. May be pointplot is not even the best choice.

Any ideas?

Thank you,

jon

## Evaluating a function at a number of points at onc...

Is it possible to evaluate a function at multiple points described by an array or something of that sort and have Maple return the evaluations as an array. I need approximations of a function at various values of its argument so it would be nice to do it with a single command.

Thanks

## how to plot graph and insert arrow...

i want to plot two difrent graph in one diagram.. anyone how to do it?

restart; with(plots); n := .2; B := .5; Ec := 2.0; Pr := 1.0; N := .5; l := 1; rho := .5; c := 1; T := .5; T1 := .5; c1 := .2; c2 := .2; Gr := .5; blt := 5;

Eq1 := diff(f(eta), eta, eta, eta)+f(eta)*(diff(f(eta), eta, eta))-(diff(f(eta), eta))^2+l*B*H(eta)*(F(eta)-(diff(f(eta), eta)))+Gr*theta(eta)-Mn*(diff(f(eta), eta)) = 0;

Eq2 := G(eta)*(diff(F(eta), eta))+F(eta)^2+B*(F(eta)-(diff(f(eta), eta))) = 0;

Eq3 := G(eta)*(diff(G(eta), eta))+B*(f(eta)+G(eta)) = 0;

Eq4 := G(eta)*(diff(H(eta), eta))+H(eta)*(diff(G(eta), eta))+F(eta)*H(eta) = 0;

Eq5 := diff(theta(eta), eta, eta)+Pr*((diff(theta(eta), eta))*f(eta)-2*(diff(f(eta), eta))*theta(eta))+N*Pr*(theta1(eta)-theta(eta))/(rho*c*T)+N*Pr*Ec*(F(eta)-(diff(f(eta), eta)))^2/(rho*T1) = 0;

Eq6 := 2*F(eta)*theta1(eta)+G(eta)*(diff(theta1(eta), eta))+c1*(theta1(eta)-theta(eta))/(c*c2*T) = 0;

bcs1 := f(0) = 0, (D(f))(0) = 1, (D(f))(blt) = 0, F(blt) = 0, G(blt) = -f(blt), H(blt) = n, theta(0) = 1, theta(blt) = 0, theta1(blt) = 0;

L := [0, 1, 2];

for k to 3 do R := dsolve(eval({Eq1, Eq2, Eq3, Eq4, Eq5, Eq6, bcs1}, Mn = L[k]), [f(eta), F(eta), G(eta), H(eta), theta(eta), theta1(eta)], numeric, output = listprocedure); Y || k := rhs(R[3]); YP || k := rhs(R[5]); YR || k := rhs(R[6]); YQ || k := rhs(R[7]); YA || k := rhs(R[8]); YB || k := rhs(R[10]) end do;

plot([Y || (1 .. 3)], 0 .. 10, labels = [eta, (D(f))(eta)]);

this comands will comeout to diffrent graph in two diagram.. but i want two graph in one diagram.. any one know how to do it.. beside that.. i want to know how to insert arrow in diagram..

## How to Plot Multiple Functions with Command Dualax...

Good day, Is it possible to plot multiple (more than two) functions with 'dualaxisplot'?I've found some information about it on the Internet, which helped me out a lot, but I still don't know how to put in multiple functions in one dualaxisplot.For example I would like to plot a figure which consists of four functions, all of them having their own domain(!).Three of them are related to the 'left' y-axis, and the fourth function is related to the 'right' y-axis.Comment: I wanted to insert the formula over here, which I use to plot the dualaxisplot, but the 'dualaxisplot-command' isn't working ("You have entered an invalid Maple plot command").So for example, I do know how it works with two formulas, like:dualaxisplot(plot(2x,view=[0..10,0..20],labels=[x,left=2x],legend=2x),plot(x^2,view=[0..10,0..100],labels=[x,right=x^2],legend=x^2,color=blue)); Now I can independently change the left and right y-axis like I want to. Now I would like to have the shape of the next graph:The trhee formulas which belong together, and that I want to relate to the left axis (making one line), consist of: horziontal line, linear line, horizontal lineThe other line I want to relate to the right y-axis, which is a linear line. So I can write the four functions for example like:restart;with(plots):eq1:=50,x=0..3:eq2:=(50/(5-3))*(5-x),x=3..5:eq3:=0,x=5..10:eq4:=10x,x=0..10: I thought I could 'join' the (first) three functions by using the '{' and '}' symbols, but that isn't working either. Somebody has a suggestion?Or that it just isn't possible at all.... Thanks anyway for thinking along. Greetings, Frank

## plotting a series of numbers...

hello maple support,what is the best way to solve for multiple numbers, ie the equation isx/x+1 i can plot it but i want to solve for .5.9.99.999 and 1.5,1.1,1.01 and 1.001.i have tried a number of ways and browsed tutorials on you tube and some pdfs.it is time for help on solving for multiple quantities.thanks,craig

## how to plot multiple variables for system of nonli...

hi everyone,

I need to plot a graph for system of nonlinear equations with multiple variables.

here is some example of system nonlinear

f4=c^2+d^2-1=0

with initial condition (0.7, 0.2, 0.6, 0.3)t. I solved this using Newton's method and here the iteration

## Expanding multiple integral...

Hi everyone,

I need to expand a sum inside a single multiple integral into separate integrals, as in:

/                          /                  /
|                 ...

## ODE Plot multiple plots...

Hi all,

I am trying to plot multiple ODE plots in Maple 16. I can do them all separately, but cannot figure out how to make to solutions appear in the same plot. I have numeric solutions for sol1 and sol2, and I want to plot A(t), t for each one (together).

Thanks for the help!

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