restart;

Lfh := proc(numoflevel, h, fx, var)

if numoflevel = 1 then

        hello := 0;

        for i from 1 to nops(var) do

                hello := hello + diff(h[i], var[i])*fx[i];

        od;

        return hello;

else

        hello := 0;

        for i from 1 to nops(var) do

                hello := hello + diff(Lfh(numoflevel-1, h, fx, var), var[i])*fx[i];

        od;

        return hello;

end if;

end proc:

f:=[x3-x2^3,-x2,x1^2-x3];

g:=[0,-1,1];

h:=[x1,0,0];

variables := [x1,x2,x3];

Lf1h := Lfh(1,h,f,variables);

Lgf1h := Lfh(1,[seq(Lf1h,n=1..nops(variables))],g,variables);

Lf2h := Lfh(2,h,f,variables);

Lgf2h := Lfh(1,[seq(Lf2h,n=1..nops(variables))],g,variables);

Lf3h := Lfh(3,h,f,variables);

Lgf3h := Lfh(1,[seq(Lf3h,n=1..nops(variables))],g,variables);

i doubt that my book example is wrong

it said relative rank is 2, but i can not find any zero when Lgf3h

if i continue to Lgf4h, Lgf5h, Lgf6h...etc, still no zero what does it mean?

Example

Diff(x1,t) = x2^2,
Diff(x2,t) = u,
y = x1

result in

Diff(y,t$2)-4*u^2*Diff(y,t) = 0
2*u*x2 - Diff(y,t^2) = 0
x1 - y = 0

is it possible a general and generic method to apply some steps on system below

Diff(u1, t) = u1*u2-u1*u3,
Diff(u2, t) = -u1*u2+u2*u3-(1/2)*(conjugate(u2-u3)*(u1*u2-u1*u3)+conjugate(u1)*(-u1*u2+u2*u3)-conjugate(u1)*(u1*u3-u2*u3))/conjugate(u1),
Diff(u3, t) = u1*u3-u2*u3+(1/2)*(conjugate(u2-u3)*(u1*u2-u1*u3)+conjugate(u1)*(-u1*u2+u2*u3)-conjugate(u1)*(u1*u3-u2*u3))/conjugate(u1),
y = u1

I often have problem with evalf function for exaple:

Maybe you have suggest for me, how solve this problem?

Hello,

Assume a periodic signal that is the sum of four sinusoidal signals, all with different frequency and phase. The fundamental frequency has phase=0, so at t=0 its value is 0 (a zero crossing point). I need to find the influence of the other frequency components on the zero crossing point in [seconds] as an analytical expression. I made the Maple script below to find out, but get a RootOf result. How can I solve this?

Thanks for your help!

Download 20131130_Zero_crossi.mw

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?

I define a func

f(x,y):=piecewise(x=0 and y=0,139 ,x=1 and y=0,144,x=2 and y=0,149,x=3 and y=0,155,x=4 and y=0,155,x=5 and y=0,155,x=6 and y=0,155,x=7 and y=0,155,x=0 and y=1,144,x=1 and y=1,151,x=2 and y=1,153,x=3 and y=1,156,x=4 and y=1,159,x=5 and y=1,159,x=6 and y=1,159,x=7 and y=1,159,x=0 and y=2,150,x=1 and y=2,155,x=2 and y=2,160,x=3 and y=2,163,x=4 and y=2,158,x=5 and y=2,156,x=6 and y=2,156,x=7 and y=2,156,x=0 and y=3,159,x=1 and y=3,161,x=2 and y=3,162,x=3 and y=3,160,x=4 and y=3,160,x=5 and y=3,159,x=6 and y=3,159,x=7 and y=3,159,x=0 and y=4,159,x=1 and y=4,160,x=2 and y=4,161,x=3 and y=4,162,x=4 and y=4,162,x=5 and y=4,155,x=6 and y=4,155,x=7 and y=4,155,x=0 and y=5,161,x=1 and y=5,161,x=2 and y=5,161,x=3 and y=5,161,x=4 and y=5,160,x=5 and y=5,157,x=6 and y=5,157,x=7 and y=5,157,x=0 and y=6,162,x=1 and y=6,162,x=2 and y=6,161,x=3 and y=6,163,x=4 and y=6,162,x=5 and y=6,157,x=6 and y=6,157,x=7 and y=6,157,x=0 and y=7,162,x=1 and y=7,162,x=2 and y=7,161,x=3 and y=7,161,x=4 and y=7,163,x=5 and y=7,158,x=6 and y=7,158,x=7 and y=7,158)

It is really a chore . By the way , is there more concise way to definition of the same effet as this ? 

then I type:

sum(f(0, y), y = 0 .. 7) 

Maple just respond me a 0 

why ?

How can I expand the mutivariate taylor series of the functions below about the point (x,y)

f(h*a[2]+x, h*a[2]*k[1]+y);

 and

f(h*a[3]+x, y+h(a[3]-b[32])*k[1]+h*b[32]*k[2]);

Hello, everyone. I'm sorry for bed view. Can i solve the system of equations in maple which above this text. I had inputted the system in Maple, but there is mistake: 

Error, (in dsolve/numeric/process_input) input system must be an ODE system, got independent variables {t, tau, Q(tau)}.

Code:

eq :=

diff(x(t), t) = -y(t)-z(t)-(diff(x(Q(tau)), tau))*((diff(x(Q(tau)), tau))*(-y(t)-z(t))+(diff(y(Q(tau)), tau))*(x(t)+a*y(t))+(diff(z(Q(tau)), tau))*(b-z(t)*(x(t)-c)))/((diff(x(Q(tau)), tau))^2+(diff(y(Q(tau)), tau))^2+(diff(z(Q(tau)), tau))^2)+eps_x*q(t),

diff(y(t), t) = x(t)+a*y(t)-(diff(y(Q(tau)), tau))*((diff(x(Q(tau)), tau))*(-y(t)-z(t))+(diff(y(Q(tau)), tau))*(x(t)+a*y(t))+(diff(z(Q(tau)), tau))*(b-z(t)*(x(t)-c)))/((diff(x(Q(tau)), tau))^2+(diff(y(Q(tau)), tau))^2+(diff(z(Q(tau)), tau))^2)+eps_y*q(t),

diff(z(t), t) = b+z(t)*(x(t)-c)-(diff(z(Q(tau)), tau))*((diff(x(Q(tau)), tau))*(-y(t)-z(t))+(diff(y(Q(tau)), tau))*(x(t)+a*y(t))+(diff(z(Q(tau)), tau))*(b-z(t)*(x(t)-c)))/((diff(x(Q(tau)), tau))^2+(diff(y(Q(tau)), tau))^2+(diff(z(Q(tau)), tau))^2)+eps_z*q(t),

diff(q(t), t) = ax*(-y(t)-z(t)-(diff(x(Q(tau)), tau))*((diff(x(Q(tau)), tau))*(-y(t)-z(t))+(diff(y(Q(tau)), tau))*(x(t)+a*y(t))+(diff(z(Q(tau)), tau))*(b-z(t)*(x(t)-c)))/((diff(x(Q(tau)), tau))^2+(diff(y(Q(tau)), tau))^2+(diff(z(Q(tau)), tau))^2))+ay*(x(t)+a*y(t)-(diff(y(Q(tau)), tau))*((diff(x(Q(tau)), tau))*(-y(t)-z(t))+(diff(y(Q(tau)), tau))*(x(t)+a*y(t))+(diff(z(Q(tau)), tau))*(b-z(t)*(x(t)-c)))/((diff(x(Q(tau)), tau))^2+(diff(y(Q(tau)), tau))^2+(diff(z(Q(tau)), tau))^2))+az*(b+z(t)*(x(t)-c)-(diff(z(Q(tau)), tau))*((diff(x(Q(tau)), tau))*(-y(t)-z(t))+(diff(y(Q(tau)), tau))*(x(t)+a*y(t))+(diff(z(Q(tau)), tau))*(b-z(t)*(x(t)-c)))/((diff(x(Q(tau)), tau))^2+(diff(y(Q(tau)), tau))^2+(diff(z(Q(tau)), tau))^2))+beta*q(t):

cond := x(0) = 0, y(0) = 0, z(0) = 1, q(0) = 0:
F := dsolve({cond, eq}, [x(t), y(t), z(t), q(t)], numeric).

What program (Maple,Matlab,mathcad...) can solve, if Maple can't.

Thank's.

Hello everyone

Here is my problem: I have a procedure depending on a variable and a parameter, let's say F(x,a). I have another procedure that gives me a specific value for x depending on the parameter a, let's say X1(a). I would like to make a list of values of F(X1(a),a) for different values of a. So the list would go F(X1(a1),a1), F(X1(a2),a2), and so on. Here is what I tried

xlist:=[seq(X1(i),i=1..10)]:

flist:=[seq(F(xlist,i),i=1..10)]:

but it doesn't work.

Another thing I tried was

Matrix([seq(eval(map(evalf@F(xlist,i),xlist),i=1..10)]):

Also doesn't work. Not with evalhf either. I can do it for specific values of xlist by choosing xlist[i] inside F, but that's it. If I leave i unspecified it can't do it.

Thanks for the help

Dear All,

I would like to perform a numerical integration of the following. Please let me know the method.

The integration consits of one variable essentially. Since the symbolic integration is not possibl and hence I have to do it numerically.

Appreciate you reply. Thanks

Here is the question:Prior to this question I was given f(z)=z^2+1, N(z)=(z^2-1)/(2z), T(z)=z-I/z+I such that T(N^k (z))=(T(z))^2^k. And L is a set of number on the real axis. Now the question is that given we have two regions of the complext plane as follow:

R₊ = {z : N^k{z) -> i as k -> ∞}; R_- = {z : N^k(z) -> -i as k -> ∞}.

Draw a diagram to illustrate these regions, the line L and the roots i and -i. We call R₊ the basin of attractionfor the root +i, and similarly R_-is the basin of attraction for the root -i.

 Show that if z is on the set L (the common boundary of the two regions R₊ and R_{_}, then N^k(z) stays on L for all values of k. (This is easy once you identify what L is.) So in this case iteration does not produce a root at all.

So basically my problem is that the fact I'm not very familar with the commands to draw such diagram, and I don't know much about Newton's method to compute complex roots. It would be appreciated if anyone can help me how to get start with the question. Thanks.

I have a diff equation in cartesian coordinates I need to transform to a certain cylindrical system. The de looks like this:

I define my new system with addcoords like this:

addcoords('AccCylinder',[r,theta,y],[r*cos(theta),y,r*sin(theta)]); # Note: y is the longitudinal axis here!

and also do

VectorCalculus:-AddCoordinates('AccCylinder'[r,theta,y],[r*cos(theta),y,r*sin(theta)],overwrite) assuming r >= 0;

and note that I had to overwrite as my system was already known, so maybe addcoords is reduncant(?)

I then do the transformation ("(7)" is the label of my above de):

changecoords((7),[x,y,z],AccCylinder,[r,theta,y]);

and get

This may be correct, but it has the expressions in the differentials, which diff does not know how to handle. I need to convert things like diff(xpr,r*cos(theta)) = diff(xpr,x)*diff(x,r) where x would be r*cos(theta). I can do this "by hand", but that seems overly tedious and error-prone. Somehow I'd expect the coordinate transforms to be able to do this but I can't figure out how.

Any idea?

Thanks,

Mac Dude,

Given the following system of first order ODE,

dx/dt=0.2x(1-0.5 x)-(1.5 xy)/(1+0.116 x),

dy/dt=(1.3 xy)/(1+0.1x)-0.8y.

Draw a DEplot (for t from 0 to 50) and indicate the particular

trajectory with the initial conditions x(0)=1,y(0)=2. If I

switched to forward Euler method,what would the DE plot look

like then? Is it possible to make the plot made by the

forward Euler method look close to the one which used the

default method?

Hello !

I installed Maple 14 on my windows8 computer (with compatibility windows7). My program worked the 2 first times, and suddently it bugged on the third, though I changed NOTHING.

It puts me an "Error: recursive assignment". The concerned line is: 

if a < 2 then broSet := broSet union {[param[1, j], param[2, i]]} fi:

There should be no problem.

Does anyone have any idea ?

по_альтернативной_ок.mw

Hi!

i have problems with surfdata command. I want to see beautifull surface, but see only few black lines.

and i dont know why, because i do all like in example.

Thank you vwry much for answers)