mehdi jafari

559 Reputation

13 Badges

6 years, 299 days

MaplePrimes Activity


These are answers submitted by mehdi jafari


restart:

a[0]:=1:for n to 10 do a[n]:=a[0]+a[n-1];od:a[4];

5

(1)

 


Download for_loop.mw

you should change your boundary conditons. u can see here,i changed time range every thing it possibe,but it does not solve and says that your boundary conditions does not match input boundary conditions.


``

restart:

pde:=diff(u(t,x),t$2)=diff(u(t,x),x$2)-sin(u(t,x));

f:=unapply(x^2,x);

IBC := {u(0,x)=f(x),u(t,-50)=0,D[2](u)(t, 50)=0,D[1](u)(0, x)=-diff(f(x),x)};

 

pds := pdsolve(pde, IBC,time=t,range=0..1, numeric,timestep=0.01, spacestep= 0.1);

 

 

diff(diff(u(t, x), t), t) = diff(diff(u(t, x), x), x)-sin(u(t, x))

 

proc (x) options operator, arrow; x^2 end proc

 

{u(0, x) = x^2, u(t, -50) = 0, (D[1](u))(0, x) = -2*x, (D[2](u))(t, 50) = 0}

 

Error, (in pdsolve/numeric/par_hyp) values in range argument must match input boundary conditions

 

p1 := pds:-plot(t = 0);

p2 := pds:-plot(t = 1/10);

p3 := pds:-plot(t = 1/2);

p4 := pds:-plot(t = 1);

p5 := pds:-plot(t = 2);

plots[display]({p1, p2, p3, p4, p5}, title = `Sine Gordaon at t=0,0.1,0.5,1,2`);

 

 

 

``


Download error_with_boundaries.mw

 

NULL

restart

values := ([seq])(x^3+2*x+1, x = 0 .. 10, 0.1e-2):

numelems(%);

10001

(1)

V := convert(values, Vector)

V := Vector(4, {(1) = ` 1 .. 10001 `*Vector[column], (2) = `Data Type: `*anything, (3) = `Storage: `*rectangular, (4) = `Order: `*Fortran_order})

(2)

M := convert(values, Matrix)

M := Vector(4, {(1) = ` 1 x 10001 `*Matrix, (2) = `Data Type: `*anything, (3) = `Storage: `*rectangular, (4) = `Order: `*Fortran_order})

(3)

``

``

 

Download seq.mw

 


``

restart

`assuming`([solve(A*cos(x)+I*R*sin(x) = B*exp(-x)+C*exp(x), x)], [x <> 0]);

RootOf(A*cos(_Z)*exp(_Z)+I*R*sin(_Z)*exp(_Z)-B-C*(exp(_Z))^2)

(1)

`assuming`([solve(A*cos(x)+I*R*sin(x) = B*exp(-x)+C*exp(x))], [x <> 0]);

{A = A, B = A*cos(x)*exp(x)+I*R*sin(x)*exp(x)-C*(exp(x))^2, C = C, R = R, x = x}

(2)

A := 5;

5

 

6

 

7

(3)

`assuming`([solve(A*cos(x)+I*R*sin(x) = B*exp(-x)+C*exp(x), x)], [x <> 0, R::integer]);

RootOf(5*cos(_Z)*exp(_Z)+I*R*sin(_Z)*exp(_Z)-6-7*(exp(_Z))^2)

(4)

A := 5;

5

 

6

 

7

 

9

(5)

`assuming`([solve(A*cos(x)+I*R*sin(x) = B*exp(-x)+C*exp(x), x)], [x <> 0]);

RootOf(5*cos(_Z)*exp(_Z)+(9*I)*sin(_Z)*exp(_Z)-6-7*(exp(_Z))^2)

(6)

evalf(%);

.8972759170+2.061869300*I

(7)

``

``

 

Download equal.mw

your problem is that u have set m=4, but your a has three elements, and thus your vector is out of range !

set n=3

 

``

restart

solution_band_matrix := proc (n, a, b, c, d) local X, i, alpha, y, G, z, x, m; m := n; alpha[1] := a[1]; y[1] := c[1]/alpha[1]; z[1] := d[1]/alpha[1]; for i from 2 to m-1 do alpha[i] := a[i]-b[i]*y[i-1]; y[i] := c[i]/alpha[i]; z[i] := (d[i]-b[i]*z[i-1])/alpha[i] end do; alpha[m] := a[m]-b[m]*y[m-1]; z[m] := (d[m]-b[m]*z[m-1])/alpha[m]; x[m] := z[m]; for i to m-1 do x[i] := z[i]-y[i]*x[i+1] end do end proc:

a := [3, 3, 3];

[3, 3, 3]

 

[0, 1, 1]

 

[1, 1, 0]

 

[0, 1, 1]

 

3

(1)

solution_band_matrix(n, a, b, c, d);

2/7

(2)

``

``

Download problem.mw

u can do sth like this :

example.mw

restart:
A:=Matrix(3,[[1,2,3],[4,8,6],[7,8,9]]);
X:=Vector(3,symbol=x);
F:=Vector(3,[8,8,9]);
Equate(X,A^(-1).F);

Each time you close maple software,it clears internal memory,just like you use restart command in maple.
as maple help page :
After restart, the variable assignment, loaded package, interface verboseproc variable, and typesetting rules are reset.  The interface elision and typesetting variables remain.for more information,see ?restart

for example :

 

restart:

f:=52;

52

(1)

f;

52

(2)

interface(typesetting = standard);

standard

(3)

restart:

f;

f

(4)

interface(typesetting);

standard

(5)

 

 

Download restart.mw

what do u want exactly? u can use select if  u want to select expressions including something.maybe u want to see these links also :

http://www.mapleprimes.com/questions/148812-How-To-Factor-X-In-This-Expression-

http://www.mapleprimes.com/questions/151261-Problem-With-Collect


restart:

eq:=(1/20)*t[1]^2*(diff(phi(x), x, x))^2*((t[1]+t[2])^5-t[1]^5)/(t[2]^2*E[T])+(1/8)*t[1]^2*(diff(phi(x), x, x))^2*(-2*t[1]-2*t[2])*((t[1]+t[2])^4-t[1]^4)/(t[2]^2*E[T])+(1/3*((1/4)*t[1]^2*(diff(phi(x), x, x))^2*(t[1]+t[2])^2/(t[2]^2*E[T])+(1/4)*t[1]^2*(diff(phi(x), x, x))^2*(-2*t[1]-2*t[2])^2/(t[2]^2*E[T])+(1/2)*t[1]*(diff(phi(x), x, x))*((-cos(a)^2*nu[A]/E[A]-sin(a)^2*nu[T]/E[T])*t[1]*phi(x)/t[2]+(-sin(a)^2*nu[A]/E[A]-cos(a)^2*nu[T]/E[T])*t[1]*eta(x)/t[2]+(1/2)*t[1]*(diff(phi(x), x, x))*(t[1]+t[2])^2/(E[T]*t[2])+2*cos(a)*sin(a)*(-nu[A]/E[A]+nu[T]/E[T])*t[1]*psi(x)/t[2])/t[2]-t[1]*(diff(psi(x), x))*(-(cos(a)^2/G[T]+sin(a)^2/G[A])*t[1]*(diff(psi(x), x))/t[2]-cos(a)*sin(a)*(1/G[A]-1/G[T])*t[1]*(diff(phi(x), x))/t[2])/t[2]+(1/2)*t[1]^2*eta(x)*(-sin(a)^2*nu[A]/E[A]-cos(a)^2*nu[T]/E[T])*(diff(phi(x), x, x))/t[2]^2+(1/2)*t[1]^2*phi(x)*(-cos(a)^2*nu[A]/E[A]-sin(a)^2*nu[T]/E[T])*(diff(phi(x), x, x))/t[2]^2-t[1]*(diff(phi(x), x))*(-cos(a)*sin(a)*(1/G[A]-1/G[T])*t[1]*(diff(psi(x), x))/t[2]-(sin(a)^2/G[T]+cos(a)^2/G[A])*t[1]*(diff(phi(x), x))/t[2])/t[2]+t[1]^2*psi(x)*cos(a)*sin(a)*(-nu[A]/E[A]+nu[T]/E[T])*(diff(phi(x), x, x))/t[2]^2))*((t[1]+t[2])^3-t[1]^3)+(1/2*(t[1]^2*psi(x)*cos(a)*sin(a)*(-nu[A]/E[A]+nu[T]/E[T])*(diff(phi(x), x, x))*(-2*t[1]-2*t[2])/t[2]^2+t[1]*(diff(phi(x), x))*(t[1]+t[2])*(-cos(a)*sin(a)*(1/G[A]-1/G[T])*t[1]*(diff(psi(x), x))/t[2]-(sin(a)^2/G[T]+cos(a)^2/G[A])*t[1]*(diff(phi(x), x))/t[2])/t[2]-t[1]*(diff(phi(x), x))*(cos(a)*sin(a)*(1/G[A]-1/G[T])*t[1]*(diff(psi(x), x))*(t[1]+t[2])/t[2]+(sin(a)^2/G[T]+cos(a)^2/G[A])*t[1]*(diff(phi(x), x))*(t[1]+t[2])/t[2])/t[2]+t[1]*(diff(psi(x), x))*(t[1]+t[2])*(-(cos(a)^2/G[T]+sin(a)^2/G[A])*t[1]*(diff(psi(x), x))/t[2]-cos(a)*sin(a)*(1/G[A]-1/G[T])*t[1]*(diff(phi(x), x))/t[2])/t[2]-t[1]*(diff(psi(x), x))*((cos(a)^2/G[T]+sin(a)^2/G[A])*t[1]*(diff(psi(x), x))*(t[1]+t[2])/t[2]+cos(a)*sin(a)*(1/G[A]-1/G[T])*t[1]*(diff(phi(x), x))*(t[1]+t[2])/t[2])/t[2]+(1/2)*t[1]^2*eta(x)*(-sin(a)^2*nu[A]/E[A]-cos(a)^2*nu[T]/E[T])*(diff(phi(x), x, x))*(-2*t[1]-2*t[2])/t[2]^2+(1/2)*t[1]^2*phi(x)*(-cos(a)^2*nu[A]/E[A]-sin(a)^2*nu[T]/E[T])*(diff(phi(x), x, x))*(-2*t[1]-2*t[2])/t[2]^2+(1/4)*t[1]^2*(diff(phi(x), x, x))^2*(t[1]+t[2])^2*(-2*t[1]-2*t[2])/(t[2]^2*E[T])+(1/2)*t[1]*(diff(phi(x), x, x))*(-2*t[1]-2*t[2])*((-cos(a)^2*nu[A]/E[A]-sin(a)^2*nu[T]/E[T])*t[1]*phi(x)/t[2]+(-sin(a)^2*nu[A]/E[A]-cos(a)^2*nu[T]/E[T])*t[1]*eta(x)/t[2]+(1/2)*t[1]*(diff(phi(x), x, x))*(t[1]+t[2])^2/(E[T]*t[2])+2*cos(a)*sin(a)*(-nu[A]/E[A]+nu[T]/E[T])*t[1]*psi(x)/t[2])/t[2]))*((t[1]+t[2])^2-t[1]^2)+t[1]*phi(x)*((cos(a)^4/E[A]+cos(a)^2*sin(a)^2*(-2*nu[A]/E[A]+1/G[A])+sin(a)^4/E[T])*t[1]*phi(x)/t[2]+(sin(a)^2*cos(a)^2*(1/E[A]+1/E[T]-1/G[A])-(sin(a)^4+cos(a)^4)*nu[A]/E[A])*t[1]*eta(x)/t[2]+(1/2)*(-cos(a)^2*nu[A]/E[A]-sin(a)^2*nu[T]/E[T])*t[1]*(diff(phi(x), x, x))*(t[1]+t[2])^2/t[2]+sin(a)*cos(a)*(cos(a)^2*(2/E[A]+2*nu[A]/E[A]-1/G[A])+sin(a)^2*(-2*nu[A]/E[A]-2/E[T]+1/G[A]))*t[1]*psi(x)/t[2])+t[1]*(diff(phi(x), x))*(t[1]+t[2])*(cos(a)*sin(a)*(1/G[A]-1/G[T])*t[1]*(diff(psi(x), x))*(t[1]+t[2])/t[2]+(sin(a)^2/G[T]+cos(a)^2/G[A])*t[1]*(diff(phi(x), x))*(t[1]+t[2])/t[2])+(1/2)*t[1]*(diff(phi(x), x, x))*(t[1]+t[2])^2*((-cos(a)^2*nu[A]/E[A]-sin(a)^2*nu[T]/E[T])*t[1]*phi(x)/t[2]+(-sin(a)^2*nu[A]/E[A]-cos(a)^2*nu[T]/E[T])*t[1]*eta(x)/t[2]+(1/2)*t[1]*(diff(phi(x), x, x))*(t[1]+t[2])^2/(E[T]*t[2])+2*cos(a)*sin(a)*(-nu[A]/E[A]+nu[T]/E[T])*t[1]*psi(x)/t[2])+t[1]*eta(x)*((sin(a)^2*cos(a)^2*(1/E[A]+1/E[T]-1/G[A])-(sin(a)^4+cos(a)^4)*nu[A]/E[A])*t[1]*phi(x)/t[2]+(sin(a)^4/E[A]+cos(a)^2*sin(a)^2*(-2*nu[A]/E[A]+1/G[A])+cos(a)^4/E[T])*t[1]*eta(x)/t[2]+(1/2)*(-sin(a)^2*nu[A]/E[A]-cos(a)^2*nu[T]/E[T])*t[1]*(diff(phi(x), x, x))*(t[1]+t[2])^2/t[2]+sin(a)*cos(a)*(sin(a)^2*(2/E[A]+2*nu[A]/E[A]-1/G[A])+cos(a)^2*(-2*nu[A]/E[A]-2/E[T]+1/G[A]))*t[1]*psi(x)/t[2])+t[1]*psi(x)*(sin(a)*cos(a)*(cos(a)^2*(2/E[A]+2*nu[A]/E[A]-1/G[A])+sin(a)^2*(-2*nu[A]/E[A]-2/E[T]+1/G[A]))*t[1]*phi(x)/t[2]+sin(a)*cos(a)*(sin(a)^2*(2/E[A]+2*nu[A]/E[A]-1/G[A])+cos(a)^2*(-2*nu[A]/E[A]-2/E[T]+1/G[A]))*t[1]*eta(x)/t[2]+cos(a)*sin(a)*(-nu[A]/E[A]+nu[T]/E[T])*t[1]*(diff(phi(x), x, x))*(t[1]+t[2])^2/t[2]+(4*sin(a)^2*cos(a)^2*(1/E[A]+2*nu[A]/E[A]+1/E[T])+(sin(a)^2-cos(a)^2)^2/G[A])*t[1]*psi(x)/t[2])+t[1]*(diff(psi(x), x))*(t[1]+t[2])*((cos(a)^2/G[T]+sin(a)^2/G[A])*t[1]*(diff(psi(x), x))*(t[1]+t[2])/t[2]+cos(a)*sin(a)*(1/G[A]-1/G[T])*t[1]*(diff(phi(x), x))*(t[1]+t[2])/t[2]):

select(has,eq,sin(a));

(1/3)*((1/4)*t[1]^2*(diff(diff(phi(x), x), x))^2*(t[1]+t[2])^2/(t[2]^2*E[T])+(1/4)*t[1]^2*(diff(diff(phi(x), x), x))^2*(-2*t[1]-2*t[2])^2/(t[2]^2*E[T])+(1/2)*t[1]*(diff(diff(phi(x), x), x))*((-cos(a)^2*nu[A]/E[A]-sin(a)^2*nu[T]/E[T])*t[1]*phi(x)/t[2]+(-sin(a)^2*nu[A]/E[A]-cos(a)^2*nu[T]/E[T])*t[1]*eta(x)/t[2]+(1/2)*t[1]*(diff(diff(phi(x), x), x))*(t[1]+t[2])^2/(E[T]*t[2])+2*cos(a)*sin(a)*(-nu[A]/E[A]+nu[T]/E[T])*t[1]*psi(x)/t[2])/t[2]-t[1]*(diff(psi(x), x))*(-(cos(a)^2/G[T]+sin(a)^2/G[A])*t[1]*(diff(psi(x), x))/t[2]-cos(a)*sin(a)*(1/G[A]-1/G[T])*t[1]*(diff(phi(x), x))/t[2])/t[2]+(1/2)*t[1]^2*eta(x)*(-sin(a)^2*nu[A]/E[A]-cos(a)^2*nu[T]/E[T])*(diff(diff(phi(x), x), x))/t[2]^2+(1/2)*t[1]^2*phi(x)*(-cos(a)^2*nu[A]/E[A]-sin(a)^2*nu[T]/E[T])*(diff(diff(phi(x), x), x))/t[2]^2-t[1]*(diff(phi(x), x))*(-cos(a)*sin(a)*(1/G[A]-1/G[T])*t[1]*(diff(psi(x), x))/t[2]-(sin(a)^2/G[T]+cos(a)^2/G[A])*t[1]*(diff(phi(x), x))/t[2])/t[2]+t[1]^2*psi(x)*cos(a)*sin(a)*(-nu[A]/E[A]+nu[T]/E[T])*(diff(diff(phi(x), x), x))/t[2]^2)*((t[1]+t[2])^3-t[1]^3)+(1/2)*(t[1]^2*psi(x)*cos(a)*sin(a)*(-nu[A]/E[A]+nu[T]/E[T])*(diff(diff(phi(x), x), x))*(-2*t[1]-2*t[2])/t[2]^2+t[1]*(diff(phi(x), x))*(t[1]+t[2])*(-cos(a)*sin(a)*(1/G[A]-1/G[T])*t[1]*(diff(psi(x), x))/t[2]-(sin(a)^2/G[T]+cos(a)^2/G[A])*t[1]*(diff(phi(x), x))/t[2])/t[2]-t[1]*(diff(phi(x), x))*(cos(a)*sin(a)*(1/G[A]-1/G[T])*t[1]*(diff(psi(x), x))*(t[1]+t[2])/t[2]+(sin(a)^2/G[T]+cos(a)^2/G[A])*t[1]*(diff(phi(x), x))*(t[1]+t[2])/t[2])/t[2]+t[1]*(diff(psi(x), x))*(t[1]+t[2])*(-(cos(a)^2/G[T]+sin(a)^2/G[A])*t[1]*(diff(psi(x), x))/t[2]-cos(a)*sin(a)*(1/G[A]-1/G[T])*t[1]*(diff(phi(x), x))/t[2])/t[2]-t[1]*(diff(psi(x), x))*((cos(a)^2/G[T]+sin(a)^2/G[A])*t[1]*(diff(psi(x), x))*(t[1]+t[2])/t[2]+cos(a)*sin(a)*(1/G[A]-1/G[T])*t[1]*(diff(phi(x), x))*(t[1]+t[2])/t[2])/t[2]+(1/2)*t[1]^2*eta(x)*(-sin(a)^2*nu[A]/E[A]-cos(a)^2*nu[T]/E[T])*(diff(diff(phi(x), x), x))*(-2*t[1]-2*t[2])/t[2]^2+(1/2)*t[1]^2*phi(x)*(-cos(a)^2*nu[A]/E[A]-sin(a)^2*nu[T]/E[T])*(diff(diff(phi(x), x), x))*(-2*t[1]-2*t[2])/t[2]^2+(1/4)*t[1]^2*(diff(diff(phi(x), x), x))^2*(t[1]+t[2])^2*(-2*t[1]-2*t[2])/(t[2]^2*E[T])+(1/2)*t[1]*(diff(diff(phi(x), x), x))*(-2*t[1]-2*t[2])*((-cos(a)^2*nu[A]/E[A]-sin(a)^2*nu[T]/E[T])*t[1]*phi(x)/t[2]+(-sin(a)^2*nu[A]/E[A]-cos(a)^2*nu[T]/E[T])*t[1]*eta(x)/t[2]+(1/2)*t[1]*(diff(diff(phi(x), x), x))*(t[1]+t[2])^2/(E[T]*t[2])+2*cos(a)*sin(a)*(-nu[A]/E[A]+nu[T]/E[T])*t[1]*psi(x)/t[2])/t[2])*((t[1]+t[2])^2-t[1]^2)+t[1]*phi(x)*((cos(a)^4/E[A]+cos(a)^2*sin(a)^2*(-2*nu[A]/E[A]+1/G[A])+sin(a)^4/E[T])*t[1]*phi(x)/t[2]+(sin(a)^2*cos(a)^2*(1/E[A]+1/E[T]-1/G[A])-(sin(a)^4+cos(a)^4)*nu[A]/E[A])*t[1]*eta(x)/t[2]+(1/2)*(-cos(a)^2*nu[A]/E[A]-sin(a)^2*nu[T]/E[T])*t[1]*(diff(diff(phi(x), x), x))*(t[1]+t[2])^2/t[2]+sin(a)*cos(a)*(cos(a)^2*(2/E[A]+2*nu[A]/E[A]-1/G[A])+sin(a)^2*(-2*nu[A]/E[A]-2/E[T]+1/G[A]))*t[1]*psi(x)/t[2])+t[1]*(diff(phi(x), x))*(t[1]+t[2])*(cos(a)*sin(a)*(1/G[A]-1/G[T])*t[1]*(diff(psi(x), x))*(t[1]+t[2])/t[2]+(sin(a)^2/G[T]+cos(a)^2/G[A])*t[1]*(diff(phi(x), x))*(t[1]+t[2])/t[2])+(1/2)*t[1]*(diff(diff(phi(x), x), x))*(t[1]+t[2])^2*((-cos(a)^2*nu[A]/E[A]-sin(a)^2*nu[T]/E[T])*t[1]*phi(x)/t[2]+(-sin(a)^2*nu[A]/E[A]-cos(a)^2*nu[T]/E[T])*t[1]*eta(x)/t[2]+(1/2)*t[1]*(diff(diff(phi(x), x), x))*(t[1]+t[2])^2/(E[T]*t[2])+2*cos(a)*sin(a)*(-nu[A]/E[A]+nu[T]/E[T])*t[1]*psi(x)/t[2])+t[1]*eta(x)*((sin(a)^2*cos(a)^2*(1/E[A]+1/E[T]-1/G[A])-(sin(a)^4+cos(a)^4)*nu[A]/E[A])*t[1]*phi(x)/t[2]+(sin(a)^4/E[A]+cos(a)^2*sin(a)^2*(-2*nu[A]/E[A]+1/G[A])+cos(a)^4/E[T])*t[1]*eta(x)/t[2]+(1/2)*(-sin(a)^2*nu[A]/E[A]-cos(a)^2*nu[T]/E[T])*t[1]*(diff(diff(phi(x), x), x))*(t[1]+t[2])^2/t[2]+sin(a)*cos(a)*(sin(a)^2*(2/E[A]+2*nu[A]/E[A]-1/G[A])+cos(a)^2*(-2*nu[A]/E[A]-2/E[T]+1/G[A]))*t[1]*psi(x)/t[2])+t[1]*psi(x)*(sin(a)*cos(a)*(cos(a)^2*(2/E[A]+2*nu[A]/E[A]-1/G[A])+sin(a)^2*(-2*nu[A]/E[A]-2/E[T]+1/G[A]))*t[1]*phi(x)/t[2]+sin(a)*cos(a)*(sin(a)^2*(2/E[A]+2*nu[A]/E[A]-1/G[A])+cos(a)^2*(-2*nu[A]/E[A]-2/E[T]+1/G[A]))*t[1]*eta(x)/t[2]+cos(a)*sin(a)*(-nu[A]/E[A]+nu[T]/E[T])*t[1]*(diff(diff(phi(x), x), x))*(t[1]+t[2])^2/t[2]+(4*sin(a)^2*cos(a)^2*(1/E[A]+2*nu[A]/E[A]+1/E[T])+(sin(a)^2-cos(a)^2)^2/G[A])*t[1]*psi(x)/t[2])+t[1]*(diff(psi(x), x))*(t[1]+t[2])*((cos(a)^2/G[T]+sin(a)^2/G[A])*t[1]*(diff(psi(x), x))*(t[1]+t[2])/t[2]+cos(a)*sin(a)*(1/G[A]-1/G[T])*t[1]*(diff(phi(x), x))*(t[1]+t[2])/t[2])

(1)

 

 

Download select.mw

import your data to a .txt file or save them in a .txt file,and read them like this :

restart:
A:=Vector(15):
FileTools[Text][Open]( "testfile.txt" );
0
for i to 15 do
A[i]:=FileTools[Text][ReadFloat]( "testfile.txt" );
od:

if testfile.txt contains 15 number of data .

good luck



restart:with(Optimization):

Minimize(x^2 + y^2 + 25*(sin(x)^2+sin(y)^2), x=-2*Pi .. 2*Pi , y= -2*Pi .. 2*Pi,initialpoint = {x =Pi}, assume = nonnegative);

f:= (x,y)->cos(x)*sin(y) -(x/(y^2+1));

Maximize((f(x,y), x = -1 .. 2, y = -1 .. 1));

Minimize((f(x,y), x = -1 .. 2, y = -1 .. 1));

as maple help page :

The Minimize and Maximize commands use various methods implemented in a built-in library provided by the Numerical Algorithms Group (NAG). The solvers are iterative in nature and require an initial point. The quality of the solution can depend greatly on the point chosen, especially for nonlinear problems. It is recommended that you provide a point using the initialpoint option. Otherwise, a point is automatically generated.

good luck!

1.an unbalanced parantheses in first limit !

2. make some paramteres local

3. your guess1 depends on itself ! thus it is in infinite loop and it can not be calculated ! change your guess 1 !

restart:
fp:=diff(x^2+1,x);

fp2:=diff(x^2+1,x)-1;guess0:=0.1;

guess1:=evalf(guess0-subs(x=guess0,fp)/subs(x=guess0,limit((fp-fp2)/guess0-guess1,x=guess1)));
## it returns this error : 

Error, recursive assignment # 

this is your corrected 1 and 2 problem, but please correct the thrid !

restart:
Secant:=proc(f,x0,tol) local guess1,count,guess0;
fp=diff(f,x);
fp2=diff(f,x)-1;
guess0=x0;
guess1:=evalf(guess0-subs(x=guess0,fp)/subs(x=guess0,limit((fp-fp2)/guess0-guess1,x=guess1))); count:=1;
while abs(guess0-guess1)>tol do
guess0:=guess1;
guess1:=evalf(guess0-subs(x=guess0,fp)/subs(x=guess0,limit((fp-fp2)/guess0-guess1),x=guess1)); count:=count+1;
end;
guess1;count;
end:

restart:

int(exp(-z^2*sin(z)^2), z = 0 .. infinity, numeric, epsilon = 0.1e-1); #which returns 2.835068335#

exp(-z^2*sin(z)^2);

F:=convert(%,trig);convert(F,exp);simplify(convert(%,trig));

int(convert(F,exp), z = 0 .. infinity,numeric, epsilon = 0.1e-1); # which returns 2.259350091#

i do not know why the fire can not be uploaded :| . what's up in mapleprimes ?

 

when u assign sth to a symbol it gets its value and when u execute that,it will return the value not itself ! use eval instead ! 

 

restart

E := D*F

D*F

(1)

eval(E, {D = A*x}); eval(%, A = b^2*c)

A*x*F

b^2*c*x*F

(2)

%?

%?

 

Download eval.mws

here is one way :


``

restart

A := Matrix(6, 6, symbol = a)-Matrix(6, 6, symbol = a, shape = diagonal)+Matrix(6, 6, shape = identity)

A := Matrix(6, 6, {(1, 1) = 1, (1, 2) = a[1, 2], (1, 3) = a[1, 3], (1, 4) = a[1, 4], (1, 5) = a[1, 5], (1, 6) = a[1, 6], (2, 1) = a[2, 1], (2, 2) = 1, (2, 3) = a[2, 3], (2, 4) = a[2, 4], (2, 5) = a[2, 5], (2, 6) = a[2, 6], (3, 1) = a[3, 1], (3, 2) = a[3, 2], (3, 3) = 1, (3, 4) = a[3, 4], (3, 5) = a[3, 5], (3, 6) = a[3, 6], (4, 1) = a[4, 1], (4, 2) = a[4, 2], (4, 3) = a[4, 3], (4, 4) = 1, (4, 5) = a[4, 5], (4, 6) = a[4, 6], (5, 1) = a[5, 1], (5, 2) = a[5, 2], (5, 3) = a[5, 3], (5, 4) = a[5, 4], (5, 5) = 1, (5, 6) = a[5, 6], (6, 1) = a[6, 1], (6, 2) = a[6, 2], (6, 3) = a[6, 3], (6, 4) = a[6, 4], (6, 5) = a[6, 5], (6, 6) = 1})

(1)

X := Matrix(6, symbol = x, shape = diagonal)

X := Matrix(6, 6, {(1, 1) = x[1, 1], (1, 2) = 0, (1, 3) = 0, (1, 4) = 0, (1, 5) = 0, (1, 6) = 0, (2, 1) = 0, (2, 2) = x[2, 2], (2, 3) = 0, (2, 4) = 0, (2, 5) = 0, (2, 6) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = x[3, 3], (3, 4) = 0, (3, 5) = 0, (3, 6) = 0, (4, 1) = 0, (4, 2) = 0, (4, 3) = 0, (4, 4) = x[4, 4], (4, 5) = 0, (4, 6) = 0, (5, 1) = 0, (5, 2) = 0, (5, 3) = 0, (5, 4) = 0, (5, 5) = x[5, 5], (5, 6) = 0, (6, 1) = 0, (6, 2) = 0, (6, 3) = 0, (6, 4) = 0, (6, 5) = 0, (6, 6) = x[6, 6]})

(2)

G := Matrix(6, 6, 6)

G := Matrix(6, 6, {(1, 1) = 6, (1, 2) = 6, (1, 3) = 6, (1, 4) = 6, (1, 5) = 6, (1, 6) = 6, (2, 1) = 6, (2, 2) = 6, (2, 3) = 6, (2, 4) = 6, (2, 5) = 6, (2, 6) = 6, (3, 1) = 6, (3, 2) = 6, (3, 3) = 6, (3, 4) = 6, (3, 5) = 6, (3, 6) = 6, (4, 1) = 6, (4, 2) = 6, (4, 3) = 6, (4, 4) = 6, (4, 5) = 6, (4, 6) = 6, (5, 1) = 6, (5, 2) = 6, (5, 3) = 6, (5, 4) = 6, (5, 5) = 6, (5, 6) = 6, (6, 1) = 6, (6, 2) = 6, (6, 3) = 6, (6, 4) = 6, (6, 5) = 6, (6, 6) = 6})

(3)

A.X

Matrix(6, 6, {(1, 1) = x[1, 1], (1, 2) = a[1, 2]*x[2, 2], (1, 3) = a[1, 3]*x[3, 3], (1, 4) = a[1, 4]*x[4, 4], (1, 5) = a[1, 5]*x[5, 5], (1, 6) = a[1, 6]*x[6, 6], (2, 1) = a[2, 1]*x[1, 1], (2, 2) = x[2, 2], (2, 3) = a[2, 3]*x[3, 3], (2, 4) = a[2, 4]*x[4, 4], (2, 5) = a[2, 5]*x[5, 5], (2, 6) = a[2, 6]*x[6, 6], (3, 1) = a[3, 1]*x[1, 1], (3, 2) = a[3, 2]*x[2, 2], (3, 3) = x[3, 3], (3, 4) = a[3, 4]*x[4, 4], (3, 5) = a[3, 5]*x[5, 5], (3, 6) = a[3, 6]*x[6, 6], (4, 1) = a[4, 1]*x[1, 1], (4, 2) = a[4, 2]*x[2, 2], (4, 3) = a[4, 3]*x[3, 3], (4, 4) = x[4, 4], (4, 5) = a[4, 5]*x[5, 5], (4, 6) = a[4, 6]*x[6, 6], (5, 1) = a[5, 1]*x[1, 1], (5, 2) = a[5, 2]*x[2, 2], (5, 3) = a[5, 3]*x[3, 3], (5, 4) = a[5, 4]*x[4, 4], (5, 5) = x[5, 5], (5, 6) = a[5, 6]*x[6, 6], (6, 1) = a[6, 1]*x[1, 1], (6, 2) = a[6, 2]*x[2, 2], (6, 3) = a[6, 3]*x[3, 3], (6, 4) = a[6, 4]*x[4, 4], (6, 5) = a[6, 5]*x[5, 5], (6, 6) = x[6, 6]})

(4)

Equate(Typesetting:-delayDotProduct(A, X), G);

[x[1, 1] = 6, a[1, 2]*x[2, 2] = 6, a[1, 3]*x[3, 3] = 6, a[1, 4]*x[4, 4] = 6, a[1, 5]*x[5, 5] = 6, a[1, 6]*x[6, 6] = 6, a[2, 1]*x[1, 1] = 6, x[2, 2] = 6, a[2, 3]*x[3, 3] = 6, a[2, 4]*x[4, 4] = 6, a[2, 5]*x[5, 5] = 6, a[2, 6]*x[6, 6] = 6, a[3, 1]*x[1, 1] = 6, a[3, 2]*x[2, 2] = 6, x[3, 3] = 6, a[3, 4]*x[4, 4] = 6, a[3, 5]*x[5, 5] = 6, a[3, 6]*x[6, 6] = 6, a[4, 1]*x[1, 1] = 6, a[4, 2]*x[2, 2] = 6, a[4, 3]*x[3, 3] = 6, x[4, 4] = 6, a[4, 5]*x[5, 5] = 6, a[4, 6]*x[6, 6] = 6, a[5, 1]*x[1, 1] = 6, a[5, 2]*x[2, 2] = 6, a[5, 3]*x[3, 3] = 6, a[5, 4]*x[4, 4] = 6, x[5, 5] = 6, a[5, 6]*x[6, 6] = 6, a[6, 1]*x[1, 1] = 6, a[6, 2]*x[2, 2] = 6, a[6, 3]*x[3, 3] = 6, a[6, 4]*x[4, 4] = 6, a[6, 5]*x[5, 5] = 6, x[6, 6] = 6]

(5)

``

``


Download matrix.mw


restart:q:=x+y;

x+y

(1)

f := unapply(q, x, y);c:=10^(-1):

proc (x, y) options operator, arrow; x+y end proc

(2)

 G(x,y,xi,eta,t):=(1+2*(sum((exp(-Pi^(2)*n^(2)*c*t))*cos(n*Pi*x)*cos(n*Pi*xi),n=1..10)))*(1+2*(sum((exp(-Pi^(2)*m^(2)*c*t))*cos(m*Pi*y)*cos(m*Pi*eta),m=1..10)));

(1+2*exp(-(1/10)*Pi^2*t)*cos(Pi*x)*cos(Pi*xi)+2*exp(-(2/5)*Pi^2*t)*cos(2*Pi*x)*cos(2*Pi*xi)+2*exp(-(9/10)*Pi^2*t)*cos(3*Pi*x)*cos(3*Pi*xi)+2*exp(-(8/5)*Pi^2*t)*cos(4*Pi*x)*cos(4*Pi*xi)+2*exp(-(5/2)*Pi^2*t)*cos(5*Pi*x)*cos(5*Pi*xi)+2*exp(-(18/5)*Pi^2*t)*cos(6*Pi*x)*cos(6*Pi*xi)+2*exp(-(49/10)*Pi^2*t)*cos(7*Pi*x)*cos(7*Pi*xi)+2*exp(-(32/5)*Pi^2*t)*cos(8*Pi*x)*cos(8*Pi*xi)+2*exp(-(81/10)*Pi^2*t)*cos(9*Pi*x)*cos(9*Pi*xi)+2*exp(-10*Pi^2*t)*cos(10*Pi*x)*cos(10*Pi*xi))*(1+2*exp(-(1/10)*Pi^2*t)*cos(Pi*y)*cos(Pi*eta)+2*exp(-(2/5)*Pi^2*t)*cos(2*Pi*y)*cos(2*Pi*eta)+2*exp(-(9/10)*Pi^2*t)*cos(3*Pi*y)*cos(3*Pi*eta)+2*exp(-(8/5)*Pi^2*t)*cos(4*Pi*y)*cos(4*Pi*eta)+2*exp(-(5/2)*Pi^2*t)*cos(5*Pi*y)*cos(5*Pi*eta)+2*exp(-(18/5)*Pi^2*t)*cos(6*Pi*y)*cos(6*Pi*eta)+2*exp(-(49/10)*Pi^2*t)*cos(7*Pi*y)*cos(7*Pi*eta)+2*exp(-(32/5)*Pi^2*t)*cos(8*Pi*y)*cos(8*Pi*eta)+2*exp(-(81/10)*Pi^2*t)*cos(9*Pi*y)*cos(9*Pi*eta)+2*exp(-10*Pi^2*t)*cos(10*Pi*y)*cos(10*Pi*eta))

(3)

w:=int(int(f(xi,eta)*G(x,y,xi,eta,t), eta=0..1), xi=0..1);W:=unapply(w,x,y,t);

-(1/99225)*(-99225*exp(20*Pi^2*t)*Pi^2+1254400*cos(Pi*x)^9*exp((119/10)*Pi^2*t)-2822400*cos(Pi*x)^7*exp((119/10)*Pi^2*t)+518400*cos(Pi*x)^7*exp((151/10)*Pi^2*t)+2116800*cos(Pi*x)^5*exp((119/10)*Pi^2*t)-907200*cos(Pi*x)^5*exp((151/10)*Pi^2*t)+254016*cos(Pi*x)^5*exp((35/2)*Pi^2*t)-588000*cos(Pi*x)^3*exp((119/10)*Pi^2*t)+453600*cos(Pi*x)^3*exp((151/10)*Pi^2*t)+176400*cos(Pi*x)^3*exp((191/10)*Pi^2*t)-317520*cos(Pi*x)^3*exp((35/2)*Pi^2*t)+44100*cos(Pi*x)*exp((119/10)*Pi^2*t)-56700*cos(Pi*x)*exp((151/10)*Pi^2*t)-132300*cos(Pi*x)*exp((191/10)*Pi^2*t)+79380*cos(Pi*x)*exp((35/2)*Pi^2*t)+396900*cos(Pi*x)*exp((199/10)*Pi^2*t)+396900*cos(Pi*y)*exp((199/10)*Pi^2*t)-317520*cos(Pi*y)^3*exp((35/2)*Pi^2*t)+453600*cos(Pi*y)^3*exp((151/10)*Pi^2*t)-588000*cos(Pi*y)^3*exp((119/10)*Pi^2*t)+518400*cos(Pi*y)^7*exp((151/10)*Pi^2*t)-2822400*cos(Pi*y)^7*exp((119/10)*Pi^2*t)+44100*cos(Pi*y)*exp((119/10)*Pi^2*t)+1254400*cos(Pi*y)^9*exp((119/10)*Pi^2*t)-907200*cos(Pi*y)^5*exp((151/10)*Pi^2*t)+2116800*cos(Pi*y)^5*exp((119/10)*Pi^2*t)+176400*cos(Pi*y)^3*exp((191/10)*Pi^2*t)-132300*cos(Pi*y)*exp((191/10)*Pi^2*t)+79380*cos(Pi*y)*exp((35/2)*Pi^2*t)-56700*cos(Pi*y)*exp((151/10)*Pi^2*t)+254016*cos(Pi*y)^5*exp((35/2)*Pi^2*t))*exp(-20*Pi^2*t)/Pi^2

 

proc (x, y, t) options operator, arrow; -(1/99225)*(518400*cos(Pi*x)^7*exp((151/10)*Pi^2*t)+2116800*cos(Pi*x)^5*exp((119/10)*Pi^2*t)-907200*cos(Pi*x)^5*exp((151/10)*Pi^2*t)+254016*cos(Pi*x)^5*exp((35/2)*Pi^2*t)-588000*cos(Pi*x)^3*exp((119/10)*Pi^2*t)+453600*cos(Pi*x)^3*exp((151/10)*Pi^2*t)+176400*cos(Pi*x)^3*exp((191/10)*Pi^2*t)-317520*cos(Pi*x)^3*exp((35/2)*Pi^2*t)+44100*cos(Pi*x)*exp((119/10)*Pi^2*t)-56700*cos(Pi*x)*exp((151/10)*Pi^2*t)-132300*cos(Pi*x)*exp((191/10)*Pi^2*t)+79380*cos(Pi*x)*exp((35/2)*Pi^2*t)+396900*cos(Pi*x)*exp((199/10)*Pi^2*t)+396900*cos(Pi*y)*exp((199/10)*Pi^2*t)-317520*cos(Pi*y)^3*exp((35/2)*Pi^2*t)+453600*cos(Pi*y)^3*exp((151/10)*Pi^2*t)-588000*cos(Pi*y)^3*exp((119/10)*Pi^2*t)+518400*cos(Pi*y)^7*exp((151/10)*Pi^2*t)-2822400*cos(Pi*y)^7*exp((119/10)*Pi^2*t)+44100*cos(Pi*y)*exp((119/10)*Pi^2*t)+1254400*cos(Pi*y)^9*exp((119/10)*Pi^2*t)-907200*cos(Pi*y)^5*exp((151/10)*Pi^2*t)+2116800*cos(Pi*y)^5*exp((119/10)*Pi^2*t)+176400*cos(Pi*y)^3*exp((191/10)*Pi^2*t)-132300*cos(Pi*y)*exp((191/10)*Pi^2*t)+79380*cos(Pi*y)*exp((35/2)*Pi^2*t)-56700*cos(Pi*y)*exp((151/10)*Pi^2*t)+254016*cos(Pi*y)^5*exp((35/2)*Pi^2*t)-99225*exp(20*Pi^2*t)*Pi^2+1254400*cos(Pi*x)^9*exp((119/10)*Pi^2*t)-2822400*cos(Pi*x)^7*exp((119/10)*Pi^2*t))*exp(-20*Pi^2*t)/Pi^2 end proc

(4)

plot(W(.51086, .49427, t), t = 0 .. 1);

 

plottools:-getdata(%); M := %[-1]; #ExportMatrix("new2.dat", M);

["curve", [0. .. 1., 1.00243326872752547 .. 1.00544209665487538], Vector(4, {(1) = ` 200 x 2 `*Matrix, (2) = `Data Type: `*float[8], (3) = `Storage: `*rectangular, (4) = `Order: `*Fortran_order})]

 

M := Vector(4, {(1) = ` 200 x 2 `*Matrix, (2) = `Data Type: `*float[8], (3) = `Storage: `*rectangular, (4) = `Order: `*Fortran_order})

(5)

M(1..5,1..2);

Matrix(5, 2, {(1, 1) = 0., (1, 2) = 1.00544209665488, (2, 1) = 0.525760502512563e-2, (2, 2) = 1.00531367935084, (3, 1) = 0.983221904522613e-2, (3, 2) = 1.00524476661193, (4, 1) = 0.149768509547739e-1, (4, 2) = 1.00519694709506, (5, 1) = 0.201555848241206e-1, (5, 2) = 1.00516850310343})

(6)

for i to 200 do
X||i := M(i,1);Y||i:=M(i,2);od;

HFloat(0.0)

 

HFloat(1.0054420966548754)

 

HFloat(0.005257605025125628)

 

HFloat(1.005313679350836)

 

HFloat(0.009832219045226132)

 

HFloat(1.0052447666119306)

 

HFloat(0.01497685095477387)

 

HFloat(1.0051969470950588)

 

HFloat(0.020155584824120606)

 

HFloat(1.0051685031034252)

 

HFloat(0.025309705075376884)

 

HFloat(1.0051519809528207)

 

HFloat(0.030088234321608037)

 

HFloat(1.0051429646370702)

 

HFloat(0.03503612457286432)

 

HFloat(1.005137449011675)

 

HFloat(0.04015323974874372)

 

HFloat(1.005134170141501)

 

HFloat(0.04525394427135678)

 

HFloat(1.0051323235512175)

 

HFloat(0.050500645829145735)

 

HFloat(1.005131261067313)

 

HFloat(0.05512194341708543)

 

HFloat(1.005130719877206)

 

HFloat(0.06032442994974875)

 

HFloat(1.0051303453485858)

 

HFloat(0.0655482783919598)

 

HFloat(1.0051300820437188)

 

HFloat(0.07058242432160805)

 

HFloat(1.0051298442180068)

 

HFloat(0.07515391110552763)

 

HFloat(1.0051295854399453)

 

HFloat(0.08058985105527638)

 

HFloat(1.0051291645879956)

 

HFloat(0.08519480522613065)

 

HFloat(1.0051286662079586)

 

HFloat(0.09055146165829146)

 

HFloat(1.0051278696661838)

 

HFloat(0.09529301025125628)

 

HFloat(1.005126926199813)

 

HFloat(0.10049524055276382)

 

HFloat(1.0051255863130446)

 

HFloat(0.10544899402010051)

 

HFloat(1.0051239719350966)

 

HFloat(0.11061771608040202)

 

HFloat(1.0051218938794964)

 

HFloat(0.11536421643216081)

 

HFloat(1.0051195986698855)

 

HFloat(0.12048395829145729)

 

HFloat(1.0051166762056676)

 

HFloat(0.12580193120603014)

 

HFloat(1.005113119600027)

 

HFloat(0.13043124226130653)

 

HFloat(1.0051095706328173)

 

HFloat(0.13543102502512563)

 

HFloat(1.0051052467852606)

 

HFloat(0.14059628984924621)

 

HFloat(1.0051002301125815)

 

HFloat(0.14564949376884423)

 

HFloat(1.0050947712106035)

 

HFloat(0.1505387283919598)

 

HFloat(1.0050889645007863)

 

HFloat(0.15596738984924624)

 

HFloat(1.0050819090048029)

 

HFloat(0.16084528361809045)

 

HFloat(1.0050750237196298)

 

HFloat(0.16605347638190956)

 

HFloat(1.0050671053553928)

 

HFloat(0.17077287311557787)

 

HFloat(1.0050594295490034)

 

HFloat(0.17593242030150755)

 

HFloat(1.005050500926828)

 

HFloat(0.18078715211055274)

 

HFloat(1.0050415964935862)

 

HFloat(0.18586174567839198)

 

HFloat(1.0050317780888274)

 

HFloat(0.19082308844221105)

 

HFloat(1.0050216860556584)

 

HFloat(0.19601715452261306)

 

HFloat(1.005010612685916)

 

HFloat(0.2010196574874372)

 

HFloat(1.0049994709394743)

 

HFloat(0.20613543929648243)

 

HFloat(1.0049876085677374)

 

HFloat(0.21120885984924626)

 

HFloat(1.0049753926185856)

 

HFloat(0.2158708064321608)

 

HFloat(1.0049637847322237)

 

HFloat(0.22121392331658293)

 

HFloat(1.0049500469843557)

 

HFloat(0.22599287075376884)

 

HFloat(1.0049373824178167)

 

HFloat(0.23108822547738694)

 

HFloat(1.004923503126965)

 

HFloat(0.23596513010050252)

 

HFloat(1.0049098704131825)

 

HFloat(0.24138030592964826)

 

HFloat(1.0048943517388513)

 

HFloat(0.24606945030150754)

 

HFloat(1.004880604308175)

 

HFloat(0.2513916711055276)

 

HFloat(1.0048646697368173)

 

HFloat(0.2562422975879397)

 

HFloat(1.0048498552014418)

 

HFloat(0.2615481206532663)

 

HFloat(1.0048333480625111)

 

HFloat(0.26612614864321604)

 

HFloat(1.0048188641259044)

 

HFloat(0.27133998814070354)

 

HFloat(1.0048021110729248)

 

HFloat(0.2763762996984925)

 

HFloat(1.0047856820024907)

 

HFloat(0.28140932115577894)

 

HFloat(1.00476903545311)

 

HFloat(0.2864238270351759)

 

HFloat(1.0047522363264243)

 

HFloat(0.2912411973366834)

 

HFloat(1.0047359083463425)

 

HFloat(0.2964489022110553)

 

HFloat(1.004718061378617)

 

HFloat(0.3014122225628141)

 

HFloat(1.0047008741895227)

 

HFloat(0.30663588351758797)

 

HFloat(1.0046826104334023)

 

HFloat(0.3113645545728643)

 

HFloat(1.0046659326871892)

 

HFloat(0.31659062130653265)

 

HFloat(1.0046473517637455)

 

HFloat(0.3215962825628141)

 

HFloat(1.004629418177737)

 

HFloat(0.3265897598994975)

 

HFloat(1.0046114051786545)

 

HFloat(0.3318054663316583)

 

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``


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