Untitled2.pdf

Calculate S (100) by constructing a procedure "CalculesS" based on two iterative loops for, as

sys[1] := [-(diff(u(x, t), t, t))-(diff(u(x, t), x, x))+u(x, t) = 2*exp(-t)*(x-(1/2)*x^2+(1/2)*t-1), u(x, 0) = x^2-2*x, u(x, 1) = u(x, 1/2)+((1/2)*x^2-x)*exp(-1)-((3/4)*x^2-(3/2)*x)*exp(-1/2), u(0, t) = 0, eval(diff(u(x, t), x), x = 1) = 0]

Error, (in PDEtools:-ToJet) found functions to be rewritten in jet notation, {u(1, t)}, having different dependency than the indicated in [u(x, t)]

what is the meaning of above error and how to resolve this to get the solution from pdsolve command?

I would like to find which of my approximately 150 recorded worksheets reference the VariationalCalculus package.

Instead of tediously displaying these one at a time, is there a search mechanism that will list the names of all my worksheets containing the command with(VariationalCalculus)?

fcns:=[u(x,y,t),v(x,y,t),h(x,y,t),c(x,y,t)]:

gr:=0.5:pr:=0.71:sc:=0.7:m:=1.0:k:=0.3:
  fcns:=[u(x,y,t),v(x,y,t),h(x,y,t),c(x,y,t)]:
  IC := [u(x,y,0)=0,v(x,y,0)=0,h(x,y,0)=0,c(x,y,0)=0]:
  BC:=[u(0,y,t)=0,h(0,y,t)=0,c(0,y,t)=0,u(x,0,t)=1,v(x,0,t)=0,h(x,0,t)=1,c(x,0,t)=1,u(x,10,t)=0,h(x,10,t)=0,c(x,10,t)=0];
  eq1:={diff(u(x,y,t),t)+u(x,y,t)*diff(u(x,y,t),x)+v(x,y,t)*diff(u(x,y,t),y)=diff(u(x,y,t),y$2)+gr*h(x,y,t)+gr*c(x,y,t)-m*u(x,y,t)
,diff(h(x,y,t),t)+u(x,y,t)*diff(h(x,y,t),x)+v(x,y,t)*diff(h(x,y,t),y)=1/pr*diff(h(x,y,t),y$2),diff(c(x,y,t),t)+u(x,y,t)*diff(c(x,y,t),x)+v(x,y,t)*diff(c(x,y,t),y)=1/sc*diff(h(x,y,t),y$2)-k*c(x,y,t)}:
  pds:= pdsolve(eq1,IC,BC,fcns,numeric):
  pds:= pdsolve(eq1,IC,BC,fcns,numeric,spacestep = 1/100):

for the above problem i made this code.

How to explain the difference in the outputs of

restart; ans1 := solve(eval({-4*a^2+x^2+y^2 <= 8*y-10*x+4*a-40, -a^2+x^2+y^2 <= 6*x-4*y-13}, a = -9), {x, y});
ns1 := {x = 3-sqrt(-y^2-4*y+77), -11 <= y, y < 13/25},
 {-11 < y, x < -5+sqrt(-y^2+8*y+273), y < 13/25, 3-sqrt(-y^2-4*y+77) < x}, 
{x = -5+sqrt(-y^2+8*y+273), -11 < y, y < 13/25}, {y = 13/25, -141/25 <= x, x <= 291/25},
 {x = 3-sqrt(-y^2-4*y+77), y <= 7, 13/25 < y}, 
{13/25 < y, x < 3+sqrt(-y^2-4*y+77), y < 7, 3-sqrt(-y^2-4*y+77) < x}, 
{x = 3+sqrt(-y^2-4*y+77), 13/25 < y, y < 7}

and

restart; ans2 := solve(eval({-4*a^2+x^2+y^2 <= 8*y-10*x+4*a-40, -a^2+x^2+y^2 <= 6*x-4*y-13}, a = -9), [x, y]);
ans2 := [[x < 3, -6 <= x, y = -2-sqrt(-x^2+6*x+72)], 
[x < 3, -6 < x, y < -2+sqrt(-x^2+6*x+72), -2-sqrt(-x^2+6*x+72) < y], 
[x < 3, -6 < x, y = -2+sqrt(-x^2+6*x+72)], [x = 3, y <= 7, -11 <= y],
 [x <= 291/25, 3 < x, y = 4-sqrt(-x^2-10*x+264)],
 [x < 291/25, 3 < x, y < -2+sqrt(-x^2+6*x+72), 4-sqrt(-x^2-10*x+264) < y],
 [x < 291/25, 3 < x, y = -2+sqrt(-x^2+6*x+72)]]

?

In the former x is expressed through y and in the latter y is expressed through x. I find explanation  in neither ?solve nor ?solve,details.

can anyone one tell me the meaning of builtin with examples?

A:={4,5,6,-9};
                          A := {4, 5, 6, -9}

E:={a,a,-2,4,-6};
                         E := {-2, 4, -6, a}

how does maple treat sets , and  what is the diffrence between sets and lists ?

restart;
with(DEtools);
assume(r::real, a::real, b::real, upsilon::real, sigma::real, x::real, y::real, t > 0);
assume(sigma > 0); assume(-b^2-r+2 > 0);
V := -2*exp(I*(sqrt(-b^2-r+2)*x+b*y+r*t))*sqrt(1/sigma)*sech(-t*(-2*sqrt(-b^2-r+2)-2*b)-x-y):
pde[1] := I*(diff(V, t))+diff(V, x, x)+diff(V, y, y)+sigma*abs(V^2)*V = 0: evalc(pde[1]);

solution.mw

I do not know what I am doing wrong. I am trying to plot each of the solutions to an ODE. One of the solutions Maple gives is  LegendreQ((1/2)*sqrt(5)-1/2, x) and the other is LegendreP((1/2)*sqrt(5)-1/2, x)

Maple can plot the  LegendreP, but gives an error plotting LegendreQ((1/2)*sqrt(5)-1/2, x)

ode:=(1-x^2)*diff(y(x),x$2)-2*x*diff(y(x),x)+y(x)=0:
sol:=dsolve(ode,y(x));

sol := y(x) = _C1*LegendreP((1/2)*sqrt(5)-1/2, x)+_C2*LegendreQ((1/2)*sqrt(5)-1/2, x)

Now when I do 

plot(LegendreQ((1/2)*sqrt(5)-1/2, x),x=-1..1);

Maple says

Warning, unable to evaluate the function to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct
 

Why is that? I tried x=-0.5..1 and x=0.5..1 and keep getting same error message. It works ok for 

plot(LegendreP((1/2)*sqrt(5)-1/2, x),x=-1..1);

Mathematica can plot both with no problem.

Dear all

Represent

x+(( y^(2+x) )-4)/3

as a binary tree and rewrite this expression in postfix notation

Can this quesiton be solved using maple

Many thanks

Hi Users!

Hope everyone in fine and enjoying good health. I am facing problem to differential the following expression with respect to first variable (mentioned as red). Please help me to fix this query

f(z*sqrt(a/nu[f]), U*t/(2*x))

Thanks in advance

create the sequence of exp (((aπ) / b)) for a varying from 1 to 15 and b varying from 1 to 10.

Hey.
I have been trying to convert my maple .mw file to a PDF under 'Print...' but it does not work. The problem is when I click on the "Save as PDF" and I name my pdf and click on 'Save' it does not save my file anywhere. It simply will not save it. 
Does somebody know why it will not save as a PDF? It saves all other files properly (also converts word files to PDF fine). 

Can I somehow define a function based on a result from a PolynomialFit.
It doesn't seem to read it as a function the way I try to define it now (see attached maple file).

I could copy the result into a function, but then I lose some information since the values are approximated.

Define.mw