## error in modeling population migration...

hi. please help me about modeling population migration. i am writing a sample for drawing plot in maple, however maple has not any error, but working incorrectly. my program is:

> u := am+bm*m0*x*t+cm*n0*y*t;
> v := an+bn*m0*x*t+cn*n0*y*t;
> eq1 := diff*(x*t, t) = 2*A*(sinh(u)-x*t*cosh(u));
> eq2 := diff*(y*t, t) = 2*A*(sinh(v)-y*t*cosh(v));
> init := x*0 = X, y*0 = Y;
> sol := dsolve*({eq1, eq2, init}, {x(t), y(t)}, numeric);
> param :=A=1/(2) ,am=0 , bm=1.2*(e)^(-4) ,cm= 0.5*(e)^(-5) ,;
> m0 = 10000, an = 0, bn = -exp(-4), cn = 1.2*exp(-3), n0 = 1000;
> save u, v, param, " narm.sav";
> init := x*0 = 0, y*0 = 0.1e-1;
> eq1 := subs*(param, eq1);
> eq2 := subs*(param, eq2);
> sol := dsolve*({eq1, eq2, init}, {x(t), y(t)}, numeric);
> with*plots;
> odeplot*(sol, [x*t, y*t], 0 .. 60, numpoints = 300, view = [-1 .. 1, -1 .. 1]);
> odeplot*(sol*d, [t, x*t, y*t], 0 .. 60, numpoints = 300, orientation = [70, 55], colour = black, axes = normal);
> init := x*0 = -1, y*0 = 1;
> sold := dsolve*({eq1, eq2, init}, {x(t), y(t)}, numeric);
> odeplot*(sold, [x*t, y*t], 0 .. 60, numpoints = 300, view = [-1 .. 1, -1 .. 1], color = black);

## Double Integral of a Trig function...

Hello Everyone,

I would like  to write a code to calculate the riemann sum approximation of the curve sin(sqrt(x^2+y^2)+1

calculate the actual volume using integration

use the ranges x=[-2pi to 2pi]=y, and 20 subdivisions.

also display the curve and the parallelepiped approximations on the same plot.

my code give me  an error..please someone can advise me which part of my code is not correct..

Thanks very much in advance!

> g := proc (x, y) options operator, arrow; sin(sqrt(x^2+y^2))+1 end proc;

Z := g(x, y);

X := Array(0 .. n); Y := Array(0 .. n); Z := Array(0 .. n);

c := -2*Pi; d := 2*Pi;

a := -2*Pi; b := 2*Pi;

n := 15;

s := 0;

X[0] := a; Y[0] := c; Z := g[X[0], Y[0]]; s := 0;

dX := (b-a)/N;dY := (d-c)/N;

for i from 0 to N do      for j from o to N do     s:=s+Z[i]*dX*dY     X[i]:=X[i-1]+dX: Y[i]:=Y[i-1]+dY: Z[i]:=g([Xi],[Yi])  end do;

This the error message i am getting (Error, unterminated loop)

## question on notation.... abs(1,x) vs x/abs(x)...

When I take the derivative of abs(x), I use the chain rule and get this

When I ask Maple to differentiate abs(x), I get this:

I read the help file on "signum", and I expected this to work, but it does not.

How can I represent signum in normal calculus syntax when working the derivative of functions involving abs(x)?

## I am having some trouble with my Matlab code and I...

My assignment is to plot 3 graphs when u0=65.70 and 95 and I thought I did my code properly but now I am getting weird errors

a0:=80;
a1:=-5;
b1:=-5*(3)^0.5;
w:=Pi/12;
k:=0.2;
u0:=65;

t=0:0.001:100;
c0=u0-a0-(k^2*a1-k*w*b1)/(k^2+w^2);
c1=(k^2*a1-k*w*b1)/(k^2+w^2);
d1=(k*w*a1+k^2*b1)/(k^2+w^2);
u=a0+c0*exp(-k*t)+c1*cos(w*t)+d1*sin(w*t);
plot(t,u,'r');

I am getting an error here that says Error, (in plot) unexpected options: [65., r] and I don't know how to fix this

legend('u(0)=65');

hold on;
u0=70;
c0=u0-a0-(k^2*a1-k*w*b1)/(k^2+w^2);
c1=(k^2*a1-k*w*b1)/(k^2+w^2);
d1=(k*w*a1+k^2*b1)/(k^2+w^2);
u=a0+c0*exp(-k*t)+c1*cos(w*t)+d1*sin(w*t);
plot(t,u,'-');

I am also getting an error with the '-' portion of my plot "Error, invalid uneval"

legend('u(0)=70');

hold on;
u0=95;
c0=u0-a0-(k^2*a1-k*w*b1)/(k^2+w^2);
c1=(k^2*a1-k*w*b1)/(k^2+w^2);
d1=(k*w*a1+k^2*b1)/(k^2+w^2);
u=a0+c0*exp(-k*t)+c1*cos(w*t)+d1*sin(w*t);
plot(t,u,'g');

I am getting an error yet again with my plot and this time it is "Warning, expecting only range variable u in expression t to be plotted but found name t"

legend('u(0)=90');

## How to take a total derivative of a function in Ma...

I have the function:   f(x,y) = 1/(sqrt(2*Pi)) * e-1/2(x^2+y^2)

I need to take the total derivative of this function in maple, but I don't know the syntax.

## solve error - 'unable to compute coeff'...

Hi, I'm new to Maple and was trying to use it to solve 3 equations with 3 unknowns, in terms of another 2 parameters. This is what I put in, and the error that came up:

solve({(1-x)/(1+b) = b*y, (1-y)(1-a)/(-a*b+1) = b*z, (1-z)(1-b)/(-a*b+1) = a*x}, {x, y, z});

Error, (in SolveTools:-LinearSolvers:-Algebraic) unable to compute coeff

I want to solve the equations to get x,y,z in terms of a,b but I don't understand the error coming up - have I done something wrong or is it because not all the variables appear in all of the equations? As there are 3 equations and 3 unknowns there is a solution, but I want to check the answer I found on paper with something (the algebra got a bit messy!)

Any help greatly appreciated! :)

## Is there an error in documentation? vertical bar |...

I am trying to learn the <> notation to enter matrices and vectors. But I find this page very confusing

http://www.maplesoft.com/support/help/maple/view.aspx?path=examples%2FLA_Syntax_Shortcuts

it says:

but we see clearly the vertical bars are used to separate columns.

Isn't a column the thing that goes from the top to bottom and not from left to right in Maple LinearAlgebra?

## Unable to plot function....

For my research at my school, I need to plot the Schrodinger equation using my given wave function. I am having issues though as I am receiving an error telling me that I need to submit my argument in standard or parametric form.

restart;

schro := {[4*(x^2-1)*(diff(psi(x, y), x, x))/(x^2-y^2)+2*x*(diff(psi(x, y), x))-(y^2-1)*(diff(psi(x, y), y, y))-2*y*(diff(psi(x, y), y))+(-2/(x+y)-2/(x-y)+1)*psi(x, y)] = energy};

psi := proc (x, y) options operator, arrow; e^((-1)*.5*[2*x+2*y])+e^((-1)*.5*[2*x-2*y]);

plot3d(schro, x= 1..100, y = -1 ..1);

Unfortunately, I am unable to plot my function. I was able to substitute my psi(x,y) function into my schro equation, but I am unable to do much else. I want to plot my function such that my energy is represented in the z-axis as a relationship between x and y which are a specific coordinate system (conical coordintes).

## Why can I not define the square of a function/vari...

Greetings,

Maple 15 allows the following syntax

omega := sqrt(w0^2*(1+((z-zf)/z0)^2))

But it does not allow this one

omega^2 := sqrt(w0^2*(1+((z-zf)/z0)^2))

Why is this so for functions and variables? Is there any way around this, I am really bugged by this issue. The Maple Math told me that the syntax was invalid so I had type the commands directly.

## problem with output...

Hello, Im trying to do a jocobian

http://www.maplesoft.com/support/help/Maple/view.aspx?path=VectorCalculus/Jacobian

but when I try the example code

jacobian([rcos(t), rsin(t), r^2*t], [r, t])

i only get the output as

jacobian([rcos(t), rsin(t), RandomMatrix(4, 4*density = .75, outputoptions = [shape = tringular*lowe])^2*t], [RandomMatrix(4, 4*density = .75, outputoptions = [shape = tringular*lowe]), t])

I want the output as a matrix as in the example url.

Thanks

## Syntax error with symbolic parameters...

Hi everyone,

I have to create a double wishbone suspesione model that can be edited by different users, only introducing some reference point values (called Hard Points). So I need some tool that, in some way, passes from the entered reference point values to the actual values of the bodyframes link.

I found an already done model (from this link) that seems to be perfect to me because contains an attached Maple document that does exactly what I need working on the base of symbolic parameters applied to the MapleSim model. Now my problem is that I need to deeply change the model and so having the possibility to change the parameter set and insert for example nex parameters. But when I try to do that some problems come out with the Maple document: the syntax of the nex parameter set is different from the default (in the sense of already built in the model I downloaded) one and there are some syntax errors. Below I'll put a screenshot of the error.

under the XData code line, you can also see the syntax of one of the parameters that is very long and complicated: below I'll insert another image from which it can be seen the syntax with the original parameter set.

Now if you another idea for solving the initial problem, that would be great! Instead do you have an idea on how to fix the problem with the downloaded model? In my opinion there is a different MapleSim version problem, in the sense that could be thatn the model I downloaded has been done in another MapleSim version in which the parameter set syntax was different.

## problem in using fsolve when determine a range for...

i want to solve an equation by fsolve but i cant assign a value as an input for next step!

s := fsolve(G), x = -1 .. 1

s := .1449607418, x = -1 .. 1

a:=s+1

Error, invalid input: subs received .1449607418, which is not valid for its 1st argument

## how to write a^tilde on maple...

Hello,

how to write a^tilde , a^check on maple

thank,

Gerard.

## Conversion of chemical formulas to string...

Hi everyone

Right now I am working on a command that calculates the molar mass of molecules. Mostly it is working like a charm but in some cases the interpretation of the input goes wrong.
The command converts the input to a string, e.g.:

f:=convert(Ca3(PO4)2, string) = "Ca[3](PO[4])[2]"

f := StringTools:-Remove("[]_*^+-", f) = "Ca3(PO4)2"

However, sometimes information such as parentheses is lost (which is understandable considering the fact that maple does not know chemical syntax):

f := convert(NH[3][3]*PO[4], string) = "NH[3][3]*PO[4]"

f := StringTools:-Remove("[]_*^+-", f) = "NH33PO4"

In special cases it goes completely nuts (I am aware this is not a real molecule):

f := convert(Al(OH)2(NH3)2, string) = "Al(`#msub(mfenced(mi("OH")),mn("2"))`)(NH[3])[2]"

The problem could of course simply be solved by typing the input as a string with no subscripts but is looks much nicer with the correct chemical syntax as input.

Do any of you know a way to translate the input charactor by charactor into a (understandable) string?

Thanks in anvance,

## How to Correctly Define Elements of a Matrix Using...

I'm used to Mathcad, and I am very new to Maple. Something I cannot figure out right now is how to define multiple elments of a matrix using a function.

Input Data

Define system dimensions as n:=2;

i:=1..n;

j:=1..n;

lambda:=Matrix(n);

Lambda:=Matrix(n);

upsilon:=vector(n);

Minor side note: I originaly had upsilon defined using the syntax "Vector[row](ncomp)", but this was giving me an 'exponentiation' operation error, so I changed it to what it is now (basically a list/array, which I guess has different type definitions that no longer cause the error?).

lambda[1,2]:=471.0433;

lambda[2,1]:=883.7530;

upsilon[1]:=58.69;

upsilon[2]:=18.07;

The Problem I'm Having

Now I just want to define Lambda using a function to define all elements (like I would in Mathcad).

Lambda[i,j]:= (upsilon[j]/upsilon[i]) * exp (-lambda[i,j]/2853);

which gives me an extremely long error message:

Error, invalid input: exp expects its 1st argument, x, to be of type algebraic, but received Matrix(2, 2, {(1, 1) = -0.3504976272e-3, (1, 2) = -.16509955895845776, (2, 1) = -.30975332953088164, (2, 2) = -0.3504976272e-3}, datatype = float[8]

As far as I can tell (keep in mind that this is my very first Maple project) that it doesn't like lambda as a matrix? But shouldn't it just evaluate to the element? and why is (2,2) and (1,1) giving values, because it should intialize to zero, so exp(0) = 1 in these cases??

I tried to simplify further by just trying

Lambda[i,j]:=(upsilon[j]/upsilon[i]);

but then it just gives me 1, and when I look into Lambda all the elements are now 1 when only the diagnol elements should be 1 (the rest some fractional amount)??

I am at a complete loss. I thought about doing something like For i = 1 to n etc. but then it just looks like coding, which defeats the purpose of trying to make a calculation sheet documenting the procedure...

Any help and/or insights into what I am doing wrong here would be most welcomed :)

P.S. I've just noticed that there is an upload option :/ Wilson_Equation.mw.

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