Since plot and plot3d are not disturbed by undefined results there is no need for defining k for all values in the square [-1,1]x[-1,1].

With a definition of zero for points below the x-axis the plot is different and maybe not as intended.

Another minor comment. The two if- statements can be made into one by the use of 'elif' :

k := proc (x, y) if -1 <= x and x <= 0 and -1 <= y and y <= 0 then x^2+y^2 elif 0 <= x and x <= 1 and 0 <= y and y <= 1 then 3*x*y  end if end proc;
plot3d(k,  -1 .. 1,  -1 .. 1,axes=boxed);

And finally the answer to the original question: What is wrong with plot3d( k, x= -1..1,y=-1..1) is the same that is wrong with plot(sin, x = 0..2*Pi);

k and sin are procedures. So you have the choice between the variable free version plot(sin, 0..2*Pi) and the version plot(sin(x),x=0..2*Pi)

In your case you need unevaluation quotes around k(x,y), since your procedure doesn't handle symbolic input:

plot3d('k(x,y)', x= -1 .. 1, y= -1 .. 1,axes=boxed);
 

Preben Alsholm

There is nothing wrong with using (e.g.) s[1] and t together. The problem is with t[1] and t, i.e. the same letter 't' used in both names.

If you like the indexed name to resemble 't', you could use T[1] or tt[1], or whatever you like, just not t[1].

Preben Alsholm

There is nothing wrong with using (e.g.) s[1] and t together. The problem is with t[1] and t, i.e. the same letter 't' used in both names.

If you like the indexed name to resemble 't', you could use T[1] or tt[1], or whatever you like, just not t[1].

Preben Alsholm

In Maple 13.02:

F:= c -> evalf(Int(3*c*x^2 + c^2*x, x = 0 .. 1)):
  Optimization:-NLPSolve(F);

Error, (in Optimization:-NLPSolve) complex value encountered
 

Preben Alsholm

In Maple 13.02:

F:= c -> evalf(Int(3*c*x^2 + c^2*x, x = 0 .. 1)):
  Optimization:-NLPSolve(F);

Error, (in Optimization:-NLPSolve) complex value encountered
 

Preben Alsholm

Yes, the straightforward solve gave the warning (Maple 13.02).

Preben Alsholm

Yes, the straightforward solve gave the warning (Maple 13.02).

Preben Alsholm

Is "Extended Maintenance Program" equivalent in this regard to  "Elite Maintenance Plan"?

My university has received the following message from 
Adeptscience in the UK:
"We are working with MapleSoft to make sure that Elite Maintenance Plan customers, like yourselves are sent the new version by the end of May. This will be provided as a download link with new purchase codes unless you have a Site licence, in which case you will also receive physical product. This will take longer to arrive."       Preben Alsholm 

Thank you, indeed it does seem to be more efficient.

I tried in the previous simple example to compute the solution at t = 1 for 10000 values of (A, x0). The ratio between the times spent was roughly 3/1.
The actual test is below.

Preben Alsholm

restart;
ode := diff(x(t),t)=x(t)*(A-x(t)):
ic := x(0)=x0:
ivp:=unapply({ode,ic},A,x0):
sol := (A,x0)->dsolve( ivp(A,x0), numeric):
t0:=time():
for k from 1 to 100 do
  for j from 1 to 100 do
    sol(k,j)(1)
  end do
end do:
time()-t0;
                                   30.389
restart;
ode := diff(x(t),t)=x(t)*(A-x(t)):
ic := x(0)=x0:
sol := dsolve( {ode,ic}, numeric,parameters=[A,x0]):
t0:=time():
for k from 1 to 100 do
  for j from 1 to 100 do
    sol(parameters=[A=k,x0=j]);
    sol(1)
  end do
end do:
time()-t0;
                                    8.783
 

I still haven't seen any need for using the parameters version of dsolve/numeric.

What is wrong with the following?

restart;
ode := diff(x(t),t)=x(t)*(A-x(t)):
ic := x(0)=x0:
ivp:=unapply({ode,ic},A,x0);
sol := (A,x0)->dsolve( ivp(A,x0), numeric):
sol(2,1);
 

Preben Alsholm

When using sum, test[1,j] is evaluated at the indices [1,j] with j being the symbol j, therefore the error message.

You are better off using add, but if you do use sum, then put apostrophes around test[1,j] to ensure that the evaluation taking place before sum just consists in removing the apostrophes.

test:=Matrix([[1,2,3],[4,5,6],[9,8,7]]);
sum('test[1,j]',j=1..3);
add(test[1,j],j=1..3);
 

Preben Alsholm

When using sum, test[1,j] is evaluated at the indices [1,j] with j being the symbol j, therefore the error message.

You are better off using add, but if you do use sum, then put apostrophes around test[1,j] to ensure that the evaluation taking place before sum just consists in removing the apostrophes.

test:=Matrix([[1,2,3],[4,5,6],[9,8,7]]);
sum('test[1,j]',j=1..3);
add(test[1,j],j=1..3);
 

Preben Alsholm

Without actually seeing the system I don't have any other suggestions than the following.

Introduce g1 and g2 as new unknowns, so that the integration of f1 and f2 are done by dsolve directly.

restart;
sys:=diff(f1(t),t)=piecewise(t<=4,3*exp(-2*t),-1),diff(f2(t),t)=sin(t),diff(g1(t),t)=f1(t),diff(g2(t),t)=f2(t);
init:= f1(0)=1, f2(0)=1,g1(0)=0,g2(0)=0:
F:=dsolve({sys,init}, {f1(t), f2(t),g1(t),g2(t)}, numeric,output=listprocedure);
F1,F2,G1,G2:=op(subs(F,[f1(t),f2(t),g1(t),g2(t)]));
G2(5.5)/G1(5.5);
 

About the odeplot command: It doesn't solve your system, dsolve/numeric does.

Preben Alsholm

Without actually seeing the system I don't have any other suggestions than the following.

Introduce g1 and g2 as new unknowns, so that the integration of f1 and f2 are done by dsolve directly.

restart;
sys:=diff(f1(t),t)=piecewise(t<=4,3*exp(-2*t),-1),diff(f2(t),t)=sin(t),diff(g1(t),t)=f1(t),diff(g2(t),t)=f2(t);
init:= f1(0)=1, f2(0)=1,g1(0)=0,g2(0)=0:
F:=dsolve({sys,init}, {f1(t), f2(t),g1(t),g2(t)}, numeric,output=listprocedure);
F1,F2,G1,G2:=op(subs(F,[f1(t),f2(t),g1(t),g2(t)]));
G2(5.5)/G1(5.5);
 

About the odeplot command: It doesn't solve your system, dsolve/numeric does.

Preben Alsholm

You may also want to remove terms of the form 0.*I by using simplify:

s^5+3.236067976*s^4+(1.*10^(-10)*I)*s^4+5.236067975*s^3+(7.*10^(-10)*I)*s^3-(3.*10^(-10)*I)*s+5.236067975*s^2+3.236067977*s+1.000000000 :
fnormal(%);
simplify(%);
 

Preben Alsholm