## MaplePrimes Questions

Hello, I am just learning how to use Maple and only have Maple 9.5. I am attempting to read in a single column of data from a pre-made txt file into Maple but I am having difficulty. For some reason Maple states that it cannot find the file that I am pointing it to. This was what I wrote... >restart; >RD:=readdata("c:\temp\test.txt"); I tried using " instead of ' and it gave me an error message as well. Any ideas what the problem might be? Thanks.

## Hermitian / Unitary Matrices...

Two matrices U and H are related by U = exp(i*a*H), where I assume a is a real constant, and i denotes the square root of -1. (a): If H is Hermitian, show that U is unitary. (b): If U is unitary, show that H is Hermitian. (H is independent of a.) Any advice or hints greatly appreciated, v/r, This is from the title "Mathematical Methods for Physicists" by Arfken and Weber. 6th ed. (section 3.4)

## Seeking Optimization...

I've got two procedures set up that work, but I know there have to be better ways to accomplish the same goals. First, I've got a procedure that finds to how many digits two floats (a and b) agree. I had tried a few methods of examining the SFloatMantissa and SFloatExponent of the difference, but those methods would fail in unpredictable ways. My current method explodes the floats into lists and compares every entry in a for loop. The example below is basically the heart of my procedure (I do take into consideration things like the location of the decimal and trailing zeros):

## obtaining distrutions/densities...

I already was explained that with maple is difficult to obtain the CDF of CharacteristicFunction of Z= (y1)^(1/2)+log((40-y2)*(80+2*y2-3y1))? where y1 = min(s1+X1, s2+X2) y2 = min(s3+X1, s4+X2) and Xi is IID uniforme[-1,1]. But .. could someone help me with some bibliographical references to deal with my problem?. It would help me to understand better and if possible to modify my formulation. Thanks in advance! Jean (I am using maple 10 under windows).

## 2-D plot with context menu...

I am trying to produce a 2-D plot of the function (sin(x))^2 using the context menu in document mode but Maple returns this error: sin(x)^2 -> Error, invalid input: smartplot uses a 1st argument, f (of type {algebraic, algebraic = algebraic, {set({algebraic, algebraic = algebraic}), list({algebraic, algebraic = algebraic})}}), which is missing It does the same when I change the function. What's wrong? Thanks Stéphane

## CriticalPoint Question...

All: I am trying to find the critical points for f(x):=((x-1)^2)^(1/3)-.5*x^2 over [-2, 2] It has two stationary points solve(diff(((x-1)^2)^(1/3)-.5*x^2,x)=0,x); -.5732093133, 1.180229770 and one singular point. 1 But CriticalPoints(((x-1)^2)^(1/3)-.5*x^2, x); only finds -.5732093133, 1 Can anyone explain why? Thanks

## 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[0])(t)=(-2*x[0](t))/(1-x[1](t));
eq_1 := D(x[1])(t)=(2*x[0](t))/(1-x[1](t));
sys := {eq_0, eq_1, x[0](0)=1, x[1](0)=0};
fcns := {x[0](t), x[1](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[0](t) at t=1/2. The analytic form can be obtained if D(x[0]) is differentiated 5 times and x[0] and x[1] are substituted by their numerical solution. I have read about differantiating in Maple, but I still cannot get this work.