## Minimizing the maximum...

Hello all, I have a function, a(r,zeta). For a particular range of values of zeta and r, I'd like to find out which value of zeta will give me the smallest maximum point on the function. I've used the Optimization:-Maximum function to give me the maximum point at a specific value of zeta, but after that I was changing zeta using trial an error to find the smallest maximum, and was wondering if I could get Maple to compute that for me. Thanks --Amr

## make an (animated) plot of a complex function?...

Hello everyone! My question is a stated above... I am trying to find a solution to the wave equation for a standing wave in a rope, with damping. my trial function is : exp(-I*(omega*t+k*x)) * exp(-tau*x) I am still working on my expression for tau, but besides that I have no idea how to plot this. I started to plot exp(-I*(omega*t+k*x)) with omega = 2 and k = 4. I simply can't figure it out, its probebly because it is complex.... Somebody experience with this? already thanks.

## Analytic derivatives of numerical solutions of an ...

Hello!

I have a system of ODEs which I can solve numericaly with Maple. What I try to do (still without success) is to compute the i-th derivatives of the solutions at a certain point of the interval. For example (a mini-version):

eq_0 := D(x)(t)=(-2*x(t))/(1-x(t));
eq_1 := D(x)(t)=(2*x(t))/(1-x(t));
sys := {eq_0, eq_1, x(0)=1, x(0)=0};
fcns := {x(t), x(t)};
p:=dsolve( sys, fcns, numeric, method=classical[rk2], output=listprocedure );

(OK, this is very easy, but it is only an example.)

Now I want to compute the 6-th derivative of x(t) at t=1/2. The analytic form can be obtained if D(x) is differentiated 5 times and x and x are substituted by their numerical solution. I have read about differantiating in Maple, but I still cannot get this work.

## Sign of a polynomial...

Hi -- I want to check the sign of a polynomial. Here's the polynomial expression (1/16)*(9*s^5-3*s^4*m-34*s^4*pa+12*s^3*m*pa+46*s^3*pa^2-18*s^2*m*pa^2-24*s^2*pa^3 +12*s*m*pa^3+s*pa^4-3*m*pa^4+2*pa^5-16*s^4+64*s^3*pa -96*s^2*pa^2+64*s*pa^3-16*pa^4+16*p^2*s+48*p^2*m-64*p^2*pa)/(s-pa)^4 and here's the parameterization: pa>s and pa>m. Generally checking the sign of the polynomial involves checking the signs of the factors...so, I'd like to factor the above expression. I haven't worked with "factor" much in Maple. Applying it as just factor(expr) with expr equal to the above expression does nothing. So not sure the best approach.

## obtaining distributions...

Hello again Maple experts, I have four nonstochastic variables s11, s12,s21,s22.. from there I have 2 random variables X1 and X2 (to begin, it may be a uniform distribution U[-1,1]) . I generate the random variables y1 and y2: y1 = min(s11+X1, s21+X2) y2 = min(s12+X1, s22+X2) 1. How could I obtain with MAPLE the distribution of Z= (y1)^(1/2)+log((40-y2)*(80+2*y2-3y1))? 2. And how could I obtain the expected value of Z? Thanks in advance for any help. Regards, Jean

## can't use map on nested lists...

I have a nested list, say test:=[[1,2,3,4],[5,6],[7,8,9]]: and I want to use something like map(x->1/x,test); to get [[1, 1/2, 1/3, 1/4], [1/5, 1/6], [1/7, 1/8, 1/9]] but it won't work... map doesn't go in nested lists and it rather returns [1/[1, 2, 3, 4], 1/[5, 6], 1/[7, 8, 9]] I can't find an example about this simple problem, I'm sure it must be easy though but I'm losing my mind on this one.

## Euler's Method...

Hi, I have been trying to use Euler's method to calculate approximate values on maple 11, and I cannot get it to work. Can someone show me the exact things to enter? I am given y', an initial value, and step size. I looked it up online and followed various directions, but still haven't been able to get an answer.

## Vim mode for Maple

by: Maple

The Vim editor ships with a maple.vim file, which is a "maple mode". It was first created by Charles Campbell, and I provided some updates (up to Maple 9.5). I am about to rev that up to Maple 11, so I would like to know if there are any feature requests which I should consider rolling-in at the same time? If you have little bits of vim scripts which you yourself use, by all means, send them along! [You'll get full credit for that, I am fine with being just an aggregator...

## How to count elements?...

Assuming that I have the following row1 = a, b, c row2 = a, b, c row3 = b, c , a I would like to obtain for each column the frequencies: column1 a: 2, b: 1, c:0 column2 a:0, b:2, c: 1 column3 a:1, b:0, c:2 How could I do it with maple? Do I need to use some package? Thanks in advance, Jean

## Maple does not integrate when I use "for...do" loo...

Hi, I am trying to evaluate a number of N[i,j] variables and part of the process of finding them includes "Int" and afterwards "evalf". In case I calculate them manually as in (functions, variables and constants previously defined): G11 := diff(psi2, a, a); dpsi2 := diff(psir2, a, a)+diff(psiz2, a, a); Izr := -E*(Int(u*G11, [z = -infinity .. infinity, r = 0 .. infinity]))+Int(u*((j*g0+j^2/r^2+(1/4)*g0^2*r^2-2/rho)*G11+dpsi2), [z = -infinity .. infinity, r = 0 .. infinity]): Izr2 := evalf(Izr); N[1,1] := (a*a)*Izr2; I obtain neat results for Izr2 and N[1,1] (i.e. the integration is done and results in a number).

## How to join multiple plots in 1 plot?...

Suppose I've plotted 3 functions:

plot(f(x),x=0..1);
plot(g(z),z=0..1);
plot(h(w),w=0..1);

Now I'd like to have these 3 plots following one after another (in a successive manner) in 1 plot like diagram. How can I perform such a task?

Another question:

How can I have a plot in reverse range? For example instead of plot(x^2,x=0..1), I'd like to have sth as plot(x^2,x=1..0), i.e. the horizontal range begins from 1 and ends to zero (also the vertical range is from (1)^2=1 to (0)^2=0).

## how to derivate?...

Hi everyone. Does anyone know how to derivate such function: piecewise(t and avoid in result: Float(undefined) in points where function is not continuous. You can see what I'm writing about in file trajectory I appended. The problem is that I have a big simulation of constrained robot and I need to derivate my equations which are not continuous and I cannot change it. Thanks for any help. Piotr P.S. I forgot to write I use MAPLE version 8