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I have theoretically 3(could eventually be more) layers with an incident wave with a wave equation for that wave.

It refracts into the 2nd layer from the first and now has a 2nd wave equation, then from the 2nd into the 3rd layer with a 3rd wave equation.

All the wave equations are of the form, Psi(z) = A_1psi_1(z) + B_1psi_2(z); this is just a general solution where psi_1&2 are linearly independant solutions that make up the general equation above and A_1 and B_1 are constant coefficients that would be A_2,B_2 and A_3,B_3 for the 2nd and 3rd layers respectively.

Transfer matrix method gives A_1,B_1 in terms of A_2,B_2(as it transfers from layer 1 to 2 they equate under boundary conditions so you can solve the simultaneous equations for results). You create a matrix of these results and multiply it with the respective matrix of the 2nd layer to 3rd layer to give you the overall transfer matrix from one side of the system to the other.

I think something to do with transfer function but not sure how to use it or set up the problem. 

Thanks in advance for any pointers.

 

I am trying to solve a system of equations with Maple 16, but it keeps returning an error message. I have the following very simple code:

_________________________________________

assume(lambda > 0);
assume(kappa > 0);
assume(omega > 0);

assume(a >= 0);
assume(alpha, 'real');
assume(b >= 0);
assume(beta, 'real');
assume(m >= 0);
assume(mu, 'real');
assume(n >= 0);
assume(nu, 'real');
assume(t >= 0);
assume(tau, 'real');
assume(p >= 0);
assume(psi, 'real');
assume(d >= 0);
assume(delta, 'real');
assume(r >= 0);
assume(rho, 'real');
assume(x >= 0);
assume(xi, 'real');

solve({d^2*lambda^2+r^2*kappa^2+(x^2-1)*omega^2 = 0, (a^2-1)*lambda^2+m^2*kappa^2+t^2*omega^2 = 0, a*exp(-I*alpha)*b*exp(I*beta)*lambda^2+m*exp(-I*mu)*n*exp(I*nu)*kappa^2+t*exp(-I*tau)*p*exp(I*psi)*omega^2 = 0, a*exp(-I*alpha)*d*exp(I*delta)*lambda^2+m*exp(-I*mu)*r*exp(I*rho)*kappa^2+t*exp(-I*tau)*x*exp(I*xi)*omega^2 = 0, b*exp(-I*beta)*d*exp(I*delta)*lambda^2+n*exp(-I*nu)*r*exp(I*rho)*kappa^2+p*exp(-I*psi)*x*exp(I*xi)*omega^2 = 0}, {a, b, d, m, mu, n, nu, p, psi, r, rho, t, tau, x, xi, alpha, beta, delta}, useassumptions, maxsols = 10)

_________________________________________

 

When this piece of code is executed, I receive the following error message:

 

Error, (in Engine:-Tarjan) invalid input: subs received {0 <= x_8, 0 <= x_10, 0 <= x_12}, which is not valid for its 1st argument

 

What does this mean? How can I find solutions to this system of equations? (I know that there exists at least one solution, and I am figuring out whether there exist more.)

Any help would be greatly appreciated.

 

Hi, i am trying to solve the equations denoted eq1 and eq2 for x and r.

f:=r*(8 - 2*x^2);
g:=subs(x=f,f):
eq1:= g-x:
eq2:= expand(diff(g,x) + 1):

I am having a bit of trouble as these simultaneous equations have many solutions and using the command solve, just basically crashes maple. I just want the commands that would give the positive set of solutions only, ie. excluding all complex and negative solutions. 

Thanks in advance.

 

hi guys i want to solve this equation with maple please help me

 

eq[1]:=0.223569c_1+2.35589c_2*c_1^2+0.002356c_1*c_2^2;

eq[2]:=1.277899c_1*c_3-2.350023c_2*c_3^2+7.5856c_3*c_2^2;

eq[3]:=3.225989c_1^2+-2.35589c_3*c_1^2-7.28356c_3*c_2^3;

 

i want solve those equations with newton method

 

 

I am using maple (version 12) for the first time.  I want equations of x and y ( in terms of a) from these two given equations. The equations I got are very complex, how to simplify these equations?

 

Equation#1 is:


Equation#2 is:

From Equation#1, i find "y"

  

Now i put y in Equation#2

and from that euation, i can get x



but these equations are very complex..

I simply want to find the equations of x and y..
How to simplify it?

 

 

 

In geom3d. I want to find the vertices A(x1,y1,z1), B(x2,y2,z2), where x1, y1, z1, x2, y2, z2 are integer numbers so that the triangle OAB  (O is origin) and perimeter and area are integer numbers. I tried

> resrart:

N:=5:

L:=[]:

for x1 from -N to N do

for y1 from x1 to N do

for z1 from y1 to N do

for x2 from -N to N do

for y2 from -N to N do

for z2 from -N to N do

a:=sqrt(x1^2+y1^2+z1^2):b:=sqrt(x2^2+y2^2+z2^2):c:=sqrt((x2-x1)^2 + (y2-y1)^2 + (z2-z1)^2):

p:=(a+b+c)/2:

S:=sqrt(p*(p-a)*(p-b)*(p-c)):

if type(2*p, integer) and type(S, posint)

then L:=[op(L), [[0, 0, 0], [x1, y1, z1], [x2, y2, z2]]]: fi:

od: od: od: od: od: od:

nops(L);

But my computer runs too long. I can not receive the result. How to get the answer?

If I the length of the side are 6, 25, 29. I tried 

DirectSearch:-SolveEquations([(x2-x1)^2+(y2-y1)^2+(z2-z1)^2 = 6^2, (x3-x2)^2+(y3-y2)^2+(z3-z2)^2 = 25^2,  (x3-x1)^2+(y3-y1)^2+(z3-z1)^2 = 29^2], {abs(x1) <= 30, abs(x2) <= 20, abs(x3) <= 20, abs(y1) <= 20, abs(y2) <= 20, abs(y3) <= 20, abs(z1) <= 20,abs(z2) <= 20, abs(z3) <= 20}, assume = integer, AllSolutions, solutions = 1);

 

 

I used implitplot to plot solutions to some (tricky) equations in 2 variables, of the form implicitplot([f(x,y)=0]).  Now I have a (tricky) change of parameterization G:R^2->R^2 of the form G(x,y)=(g(x,y),h(x,y)). I'd like to plot the image of the solution set of f(x,y)=0 under the map G. Of course, if I could invert G I'd implicitplot           G^(-1)(f(x,y))=0, but the functions I have dont lend themselves to this.

 

Presumably MAPLE stores the points it plots somewhere, and I should be able to apply G to this set of points. But I don't know how to approach this. Anybody know? 

eq1:=
(1/4)*D^2*Pi-(1/4)*D^2*arccos((-D+2*h)/D)-(1/2)*sqrt(h)*sqrt(D-h)*D+h^(3/2)*sqrt
(D-h);
                          
eq2 :=
-(1/2)*sqrt(h)*sqrt(D-h)*D+h^(3/2)*sqrt(D-h)+(1/4)*D^2*arcsin((-D+2*h)/D)+(1/8)*
D^2*Pi;

These equations are the same. yet simplify(eq1-eq2,trig);
<>0
The Mathematica COMMAND FullSimplify[..] gets zero.

Hi everyone,

I am a new user of maple and i want to know the procedures to follow when solving 4 differential equations simultaneously.

e.g

ds/dt=Λ0-βcSI/N-μS

dL/dt=Λ1+βcSI/N-μ1L+ΑcIT/N

dI/dt=kL-μ2I

dT/dt=r1L+r2I-ΑcIT/N-μT

Any help will be highly appreciated. Regards

Suppose I have a set of P polynomial equations in terms of N variables which are the coefficients of the equations. The equations are generated by the main program and are not known beforehand.

Example (P = 2):

e1 := c1 + 2*c2 + (c3+3*c4)*x*y + (c5+c6)*y^2 +(c8-2)*y^3*x^2 = 0;
e2 := (c4 + 2*c5 + c7)*x + (c9+ 2*c3+5*c4)*x^2 + (2*c7+5*c5+c6)*y^2*x^3 =0;

Because e1 and e2 must be zero for all x and y this implies that all the coefficients must be zero:

c1 + 2*c2 = 0
c3+3*c4 = 0 etc

This gives M linear equations in terms of N unknowns with N > M.

Given the P equations is there a way to automatically set up the M equations and solve for the N unknowns? In some cases it is possible that there are specific values of some of the c's eg c8 = 2 otherwise some of the c's will be expressed in terms of the other c's eg c1 = - 2*c2.

Thanks.

Suppose one sets a system of differental equations in vector form, say 2 ODE's, like this:

restart;
with(LinearAlgebra):
ode:=Vector([diff(x(t),t),diff(y(t),t)])=Vector([2*x(t)+y(t),3*y(t)-x(t)]);

Then to solve these, what would be an easy way to do it, without having to rewrite them again manually as a set, as what one would normally do. Clearly one needs to map dsolve, and also convert the vectors to a set somewhere? I am not able to get the syntax right.

Is there an easy way to automatically convert/rewrite the above to

ode2:= diff(x(t),t)=2*x(t)+y(t)  ,   diff(y(t),t)=3*y(t)-x(t);

so that I can just do

dsolve({ode2},{x(t),y(t)});

Or, a way to map dsolve directly into the first from as shown?( the Vector = Vector form).

Himmelblau.mw

On the basis of Dragнilev method…Is there anyone interested in the algorithm to reduce the distance between the points of the given constraints? The algorithm is adapted for use in R ^ n. This is an example of its work on the surface:  f = - (x1 ^ 2 x2-.3) ^ 2 - (x1 x2 ^ 2-.7) ^ 2 - 5;  
Almost all the information is on the Russian-language  forum:
 http://forum.exponenta.ru/viewtopic.php?t=12848&start=0  
I will answer all possible questions, I'll try in English. Ivanov Alexey B.  

Aslam-u-Alikum...How are you? Hope you will be fine. I want nontriavial solution of the System of equations urgently please help me .Help.mw

Aslam-u-Alikum... How are you. Hope you will be fine. I want to solve nonlinear Equation for the root 0, 4.4934, 7.7253,10.9041,14.0662,17.2208, but my code give the solutions in Rootof form. Please help me as early as possible...Help.mw

Aslam-ul-Alikum I need some help urgently. I want to compare the coefficients of like powers of Y_1*Y_2, please help how i compare it in mapleHelp.mw

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