Hi!

Let F(z) (with z complex) a given function. I want to compute F^n(z0), i.e. the composition of F with itself n-times, where z0 is a given point (complex).

Is correct the following procedure to compute F^k(z0)?

App := proc (k, z0) local z1, z2, j; z1 := z0; z2 := NULL; for j to k do z2 := F(z1); z1 := z2 end do; return z2 end proc

Many thanks in advance for your comments.

Hi

Consider the piecewise function

f:=x->piecewise(x≤0,−3,0<x≤1,x^2,1<x,-x)

can Maple solve the inequation  in R:   f(x)> a

where "a" is a given number in R

Of course the results depend on parameter a

Many thanks for your help

Hello!! Please help me,I need to solve a system of linear algebraic equations by running, and I solved the built-in command solve

restart;
with(plots):
f:=unapply(-x^2+1,x);
mu[1]:=unapply(1/(t^2+1),t);
mu[2]:=unapply(1/(t-5),t); 
g:=unapply(t^3-7*x,[t,x]);
l:=2; T:=3;
n:=10: m:=n: 
h:=evalf(l/n); 
tau:=evalf(T/m);
for k from 0 to n do 
x[k]:=h*k:
end do: 
for j from 0 to m do 
t[j]:=tau*j: 
end do:
ss:=evalf({seq(seq((y[k,j+1]-y[k,j])/tau=(y[k-1,j]-2*y[k,j]+y[k+1,j])/h^2+g(t[j],x[k]),k=1..n-1),j=0..m-1),seq(y[0,j]=mu[1](t[j]),j=1..m),seq(y[k,0]=f(x[k]),k=0..n),seq(y[n,j]=mu[2](t[j]),j=1..m)});
#s:=evalf(solve(ss,{seq(seq(y[k,j],k=0..n),j=0..m)}));

 We know the following facts: 

The SequenceGraph command returns a graph with the specified degree sequence given as input, if such a graph exists. It raises an exception otherwise. 
 But  If I  want to get more graphs  that satisfy this condition of degree sequence ? (If graphs are not many ,I want get all graphs better)
what should I do.?
For example: DrawGraph(SequenceGraph([3, 2, 2, 1, 1, 1]));  It returns the first graph below, but it is obvious that the second graph also fits the condition.

squenceGraph.mw

Download MltxPLOTS.mw

Hello Dear,

I have the following equation

 This equation is satisfied if the coefficients are zero.

So I need an order in Maple to write that

Good evening!!! I have a task to implement the task of Cauchy by the method of Milne, wrote the code, but did not understand it until the end, help to understand? what's wrong?
First calculate four "initial" values by the method of Runge-Kutta methods, then use the method of Milne, the Fact that two times running, perhaps extra?

restart;
with(plots):
a:=0; b:=1; eps:=evalf(10^(-3)):
f:=unapply(2*x*(x^2+y),x,y);
G:=simplify(dsolve({diff(y(x),x)=f(x,y(x)),y(a)=1}));                    
N:=15: h:=(b-a)/N:
for i from 0 to N do 
x[i]:=a+i*h: 
end do:
y[0]:=1;
s[0]:=1;
for i from 0 to 2 do 
t[1]:=evalf(h*f(x[i],y[i])):
t[2]:=evalf(h*f(x[i]+h/2,y[i]+t[1]/2)): 
t[3]:=evalf(h*f(x[i]+h/2,y[i]+t[2]/2)):
t[4]:=evalf(h*f(x[i]+h,y[i]+t[3])):
y[i+1]:=evalf(y[i]+(t[1]+2*t[2]+2*t[3]+t[4])/6):
q[1]:=evalf(h*f(x[i],s[i])):
q[2]:=evalf(h*f(x[i]+h/2,s[i]+q[1]/2)): 
q[3]:=evalf(h*f(x[i]+h/2,s[i]+q[2]/2)):
q[4]:=evalf(h*f(x[i]+h,s[i]+q[3])):
s[i+1]:=evalf(s[i]+(q[1]+2*q[2]+2*q[3]+q[4])/6):
end do;
for i from 3 to N-1 do 
y[i+1]:=evalf(y[i-3]+((4*h)/3)*(2*f(x[i],y[i])-f(x[i-1],y[i-1])+2*f(x[i-2],y[i-2]))):
s[i+1]:=evalf(s[i-1]+(h/3)*(f(x[i+1],y[i+1])+4*f(x[i],s[i])+f(x[i-1],s[i-1]))):
d[i+1]:=abs(y[i+1]-s[i+1])/29:
if abs(d[i+1]) < eps then y[i]:=y[i]:
else y[i]:=s[i];
end if: end do;
s1:=plot(rhs(G),x=a..b,color=yellow):
s2:=pointplot({seq([x[k],y[k]],k=0..N)}): 
display(s1,s2);

So I have this expression

f:=(coth(x)^(1/3)-tanh(x)^(1/3))*(coth(x)^(2/3)+tanh(x)^(2/3)+1)

which Maple can not simplify?

I need to do it like this

`assuming`([expand(simplify(add(`~`[simplify]([op(combine(expand((coth(x)^(1/3)-tanh(x)^(1/3))*(coth(x)^(2/3)+tanh(x)^(2/3)+1))))]))))], [x > 1])

Is this actually true or what is happening here?

Hi

I have a first oder PDE, I use pdsolve I obtained a solution depend on function F

condition_unique_solution.mw

My question: The boundary condition  f(x,y) = 1 is supplied on the line y = k x, where k is a constant. For which k
does there exist a unique solution for f(x, y)?

Many thanks for your help

Let there be an infinite sequence of real numbers: A=a[0], a[1], ... .
Let P = (n -> sum(a[i]*x^i, i=0..n)).
What is A if for all n: P(n) has n real roots.

Hi there

I'm an old user of Maple, but I've never been able to plot functions with unit. You can see my latest attempt down below

b := 120*Unit('mm');
h := 200*Unit('mm');
V := 8*Unit('kN');

I__x := (1/12)*b*h^3

Q(x):=(1/2)*((1/4)*h^2-(100*Unit('mm')-x)^2)*b 
tau(x):=V*Q(x)/(I__x*b)

plot(Q(x(Unit('mm')), units), x = 0*Unit('mm') .. 100*Unit('mm'))

Plot_function_with_units.mw

If anyone is able to help me with this problem, I would greatly appreciate it.

Hi 

I solve the laplace equation written in polar coordinates in annular domain.
The code run without any error 

But there is no solution displayed after running the code, note that I use Maple 18

Laplace_annulardomain.mw

Many thinks for your help

I want to divide each row of Marix A by diagonal element. In for loop, when I assign dividing results to the letter A , the type of A still remains matrix, but if I choose another letter (like B) results are stored in Table. Why? How can I assign to a matrix?

Also I can't figure out why maple doesn't show elements of table(see worksheet file).

I should notice that my main problem is assigning not dividing.

worksheet.mw

Hi everyone;

I want to generate the Matlab code from the Maple code but I obtained an error message as shown below. Can anyone tell me please what does this error message mean?

MatlabCode.mw
 

Download MatlabCode.mw

Thank you ^^

i want to design a packaging container to hold 320 sphere-shaped chocolates that each has a diameter 1.8 cm and weights about 3.2g each. i hope can get all posible shape using maple18 .