Never before has the educational landscape been changing as fast as it is today, driven by a new generation of students who are growing up with instant access to on-demand information. This generation relies on ubiquitous network access and takes for granted technology that permeates every aspect of their lives. Phones and tablets are everyday companions and are used to connect with their peers, take classroom notes and research school projects. Beyond being mere consumers...

Never before has the educational landscape been changing as fast as it is today, driven by a new generation of students who are growing up with instant access to on-demand information. This generation relies on ubiquitous network access and takes for granted technology that permeates every aspect of their lives. Phones and tablets are everyday companions and are used to connect with their peers, take classroom notes and research school projects. Beyond being mere consumers...

restart:
> Digits:=30:
> with(linalg):
>
> h[0]:=0.156;:
> d:=0.32*h[0]:
> l:=4:
> h[1]:=h[0]-d:
> h[2]:=h[0]+d:
> g:=9.8:
> Term:=12:
> Num:=3:
> n:=4:
>
> for N from 1 to Num do
> lambda:=2*n*Pi/l:## N1 wei sha ba tiao shu
> epsilon:=evalf(0.5+2*(N-1)/(Num-1)):
> k[0]:=evalf(0.5*Pi+2*(N-1)*Pi/(Num-1)):
> tau[0]:=evalf(k[0]*h[0]):
> omega:=evalf((g*k[0]*tanh(k[0]*h[0]))^(1/2)):

An implicitplot3d of an f(x,y,z)=0 results in an ISOSURFACE structure containing the samples of a function taken over a regular grid in 3-D space and is rendered as a 3-D surface approximating the zero surface of the function.
When I select the points with values of f(x,y,z) "close" to zero, I only get a few points on the surface:

restart;
q := plots:-implicitplot3d( x^2+y^3+z^4=1 ,x=-1..1,y=-1..1,z=-1..1, 
    style=wireframe, color=black ):
pdata := plottools:-getdata(q); # doesn't work...

Hey, I have a system of ODE and I can't draw it's phase curve. I tried to use DEplot and phaseportrait, but it doesn't work. Here is my system:

 dx/dt=x

dy/dt=ky              (k is a constant)

Here is my piece of code:

DE := [diff(x(t), t) = x(t)];

DF := [diff(y(t), t) = k*y(t)];

with(DEtools);

phaseportrait([DE, DF], [y, x], t = -5 .. 5, y = -5 .. 5, x = -5 .. 5, k...

Greetings

It occured to me to try to animate this spiral.

I found some code on the interweb. but when you run the animation, only one triangle appears, to be replaced by another. how to get them to stay?

Spiral_of_Theodoru.mw

Hey, I'm trying to plot the phase curve of the simple system of ODE, BUT it shows me an error which one I don't understand at all :)

Here is my code:

DE := diff(x(t), t) = x(t);
DF := diff(y(t), t) = k*y(t);
with(DEtools);
phaseportrait([DE, D], [y, x], t = -5 .. 5, [[y(0) = 1, x(0)], [y(0) = 0, x(0) = 2], [y(0) = 0, z(0) = -2]], y = -5 .. 5, x = -5 .. 5, color = black, linecolor = red);

Error, (in DEtools/phaseportrait) invalid initial...

Hi! Any help would be greatly appreciated :)

I have two matrices S and R, where 

S := Matrix( [ [a_1, a_2, a_3, a_4], [b_1, b_2, b_3, b_4], [c_1, c_2, c_3, c_4], [d_1, d_2, d_3, d_4] ] );

such that 

a_1*d_1 = b_1*c_1
a_2*d_2 = b_2*c_2
a_3*d_3 = b_3*c_3
a_4*d_4 = b_4*c_4;

and 

R := Matrix( [ [s_1, t_1, r_1, l_1], [s_2, t_2, r_2, l_2], [s_3, t_3, r_3, l_3], [s_4, t_4, r_4, l_4] ] );

such that 

I am trying to get Maple to calculate for me.. Let X and Y have a trinomial distribution with parameters n=3, p1=1/6 and p2=1/2. I am supposed to find E(X), E(Y), Var(X), Var(Y) and Cov (X,Y). Thank you to anyone who can assist with this. And if  you can help me understand the concept behind it.. Im having some troubles with bivariate distributions in my Stats course :( Thanks!

In Maple 15.01, the commands

   f := x -> sin(2 x)
   h := n -> (1/Pi) int(f(x) sin(n x), x = -Pi .. Pi)
   g := x -> add(h(n) sin(n x), n = 1 .. 4)
   g(x)

result in

   sin(2 x)

which is what I expect.  However, the command

   evalhf(g(2))

results in the error message
   "Error, unable to evaluate function `int` in evalhf"
so evalhf is not being passed sin(4) as I want....

I am new to Maple and trying to use it for a school project. I actually have this section of code written in a textbook and I want to use Maple to solve and plot this predator prey model. Here is what I have, Im not sure why it won't work any help will be geatly apprciated.

> e1 := diff(e(t), t)-0.325e-1*e(t)+.8*e(t)*w(t);
> e2 := diff(w(t), t)+.6*w(t)-0.5e-1*e(t)*w(t);
> sys := {e1, e2};
> ic := {e(0) = 18.0, w(0) = 0.21e-1};
> ivp := `union`(sys, ic);

I'm filling an array of functions like this:

below code is calculate basis of kernel and kernel

i guess basis of image is 

remove(has, Ga, [r,u,v,w]); if this correct, i eliminate this, i can get the image

however it include variable 'a'

is it correct? if not, how to calculate? 

my final goal is to make unexact sequence into exact sequence

Hi

I am trying to do a phase plot of an autonomous system using DEplot command. However, no phase plot appears. Could you tell me what am I doing wrong? The same code worked for my professor in class, but it's not working for me. I am using Maple 16. The code is posted below.

> with DEtools

> sys := diff(x(t), t) = y(t), diff(y(t), t) = x(t)*(1-x(t)*x(t))+y(t);

> DEplot([sys], [x(t), y(t)], t = 0 .. 0.1e-8, x = -3 .. 3, y = -3 .. 3, color = black)

Dear All,

evalf(RoofOf(Z^6-3*Z^4+3*Z^2+Z-1,index=real[2]) fails to deliver a numerical value.

1. I can use fsolve to compute the real roots but I need to replace all the occurences of RootOf by its numerical value in lengthy expressions.
2. Also simplify(RoofOf(Z^6-3*Z^4+3*Z^2+Z-1,index=real[2],RootOf) does not work.
3. I read the other posts related but could not find any answer.

Thanks for any help,

S.