## poly generator

by: Maple
Hi I wonder if anyone knows of any maple code to generate polynomials with algebraic constants. eg an order 1 poly would be: a+b*x, order 2: a+b*x+c*x^2, order 3: a+b*x+c*x^2+d*x^3, ...... etc what i'm looking for is a procedure where i input the order, eg 3, and it spits out a+b*x+c*x^2+d*x^3 thanks in advance

## How do I numerically solve differential equations?...

None of the built-in features of Maple will help me numerically solve the kinds of complicated differential equations I want. I was hoping that Maple's option in dsolve of solving by Taylor series would at least grind out the first nine terms of the Taylor series expansion of the solution y(x) of e.g. x^3 + (y'(x) - 9*x)^(5/(y(x)+2)) + 4*(x-y(x))^(y'(6*x+4)) = 0 subject to y(1)=0. I dumped in functional equations, too, to see if Maple could handle it. Ok. So, for something like this, R(x,y(x),y'(x),y'(6x+4))=0 Maple should be at least able to do the first 9 differentiations to express

## how do i get both real part and imaginary part fro...

My expression is exp(mu*t), and 'mu' is a complex number.

## Maximization of a function over a given range...

I am having difficulty getting Maple to find the optimal solution over a specified range. That is, I want to limit the possible range of my maximizers. For my problem I am maximizing the expression "payoff" with respect to p and s and want to tell Maple to search for all solutions where s<pa.

I have the following expression for variable x

x:=-1/4*(s^2-pa^2+4*pa-4*s-4*p)/(s-pa);

where x is an input to the function payoff that I wish to maximize:

payoff:=p*x + s*subs(Q=x,y) + m*(1-subs(Q=x,y)));

and

y:=int((d-s/2),d=s/2..Q+s/2)+int(Q,d=Q+s/2..1));

Now, defining the FOC of payoff as

## solve for infinity...

A colleague just asked me what Maple would do if asked to solve an equation in which the right hand side is infinity. I didn't really know what it would do, so we did some tests:
```f := (x-1)/expand((x-1)*(x+1)*(x-2)):
solve( f=infinity, x );
1, -1
solve( 1/f=0, x );
2, -1
solve( denom(f)=0, x );
1, 2, -1
```
I could not explain the response to the first solve command. Can you? Thanks in advance, Doug

## Customized Units...

Hello, I am very new to using Maple, so I must apologize for my ignorance in advance. I basically have 2 questions, 1) How do I force the use of a preferred unit that may not be the default for a particular unit system. For example, I prefer cm for length and keV for energy. I would like these to always be assumed by Maple. also 2) How can I use a unit that does not appear to be part of any unit system, such as "neutrons". I would like to enter values such as 1E8 [neutrons/cm^2] . . . etc. How does one do this in Maple. I appreciate your input. Best regards, GL Columbi

## How to make the "plot" command work?...

In maple 11 I have defined: f := x -> e^(-x)*sin(x); then I have tried to get maple to draw the above mentioned: plot(f(x),x=0..2*Pi); What happens is that I see a the coordinat-system but with no drawings in it. Can anybody help me? Regards Simon

## Plotting multiple systems ?superimposed? onto...

Maple
I need help. A homework problem superimposes a graph atop a DE. What am I doing wrong: _____________ plot1 := phaseportrait(eqn,y(x), x=-0.25..0.25, [[y(-1/2)=2],[y(3/2)=0]],titlefont=[TIMES,ROMAN,18],title=`Sec 2.1 #17`, color=grey, linecolor=[red,blue]): plot2 := (1/2)*x^2: display([plot1,plot2]); Error, (in DEtools/phaseportrait) the 'number' option must be specified before initial conditions Error, (in plots:-display) expecting plot structures but received: [plot1, (1/2)*x^2] _____________

## Fourier transform of a non-integrable function ......

Fourier transform of a non-integrable function ... Dear all, I am working on Fourier Transform of a non-integrable function. And I am working on the numerical implementation of the FT, using FFT. Let's call this function F(v). One example is F(v)=-1/(5*i*v)*(1-exp(5*i*v)) The function has a 1/v term in its asymptotic expansion, which corresponds to a jump or Heaviside function in its transform. Using FFT, I can see the jump, with some overshooting after the jump and undershooting before the jump, along with some ripples. I want to reduce these artifacts as much as possible, because I am going to integrate this transform against other functions later. Hence obtaining a smooth function without much numerical artifacts is vital. How do I do that?

## How to plot vector valued function...

How do I plot a vector-valued function with maple11? Example: r(t)=(t)i+(t^2)j+((1/2)t^3)k I am a new user, so if you could explain to me step by step that would be helpful. Thank you, Jerry8273

## Coords Help...

I am wanting to have maple11 convert a point, example(x,y,z), from one system to another among the rectangular, cylindrical, spherical coordinate systems. does anyone know how to do this. I am a new user of maple, so please explain step by step or show an example. Thanks

## Optimization and NAG

by: Maple
I had the pleasure of visiting Oxford while on vacation in England. I regret that I did not get a chance to visit the NAG headquarters there, but that thought gave me the idea for this next blog entry. The Optimization package for local optimization uses as its underlying engine the NAG E04 optimization suite. It is possible to use the Optimization package without knowing the internal workings of the commands. However, for those of you who are interested in such details, it is possible to get more information. If you set infolevel[Optimization] to 2 or higher, the names of the NAG routines (e.g. E04UCA) are displayed. It is useful to set the infolevel value in any case, as the messages provide valuable information about how the computation is proceeding.

## How do I find a fraction that is close to - but si...

I saw a function in Maple that would take a fraction like 77/45 and come up with a simpler version that was close to that value. In this case 9/5. Now I can't remember what that function was called and where to find it. Anybody seen this? Thanks!!

by: Maple