Items tagged with functions functions Tagged Items Feed

has anybody any idea for this?  been stuck on it for a while now.


let f0 € V be any given function and define a sequence (fn)n€(No) of functions fn € V by 

f:= f0 and fn+1 =Af for all n € (N0)        #A could be the average of the four surrounding points to (i,j) or it could be an N x N matrix with spectral radius less than 1.  not entirely sure. I dont know what it should be but im sure one of you guys know.

prove that this sequence converges pointwise,

 i.e that for all i,j €  [N] x [N], foo(i,j) := limn-> oo fn(i,j) exists.   and that Δfoo=0 


it  says to be in the notation of ("")  but it doesnt matter if its not.  I can adapt to what its meant to be if I can get any way to prove it

Thanks in advance.




I am trying to write the following function in maple:

f(P(x)) = (x-1)*P'(x)-x*P(1) 

Where P(x) = 1 + x + x^2 


My approach thus far has yielded limited results; i am able to get some, but not all, of the results expected.

This is my code,( the relevant bits ):

p := x-> 1+x+x^2

f:= P -> (x-1)*P'(x)-x*P(1); 

if i then type f(1); in maple i get the expected result of -x

if however i type f(x) i get an equation that is unable to produce the expected result when simplified - seemingly, it doesn't parse for maple. The expected result would be -1 

Using unapply make's no difference. Either i have made a mistake typing in my functions - in which case i would like an ëxplanation as to what i did wrong, or seemingly there is a different approach here? Perhaps solving this problem with maple is simply not doable? - anyway my line of reasoning leads me to finally ask how i write a function within a function in this nice program :) 

Any help in this matter is greatly appreciated - i only just recently started using this program. 

firstly apologies in advance for stuff in this question such as "triangle symbol",  my computer is pretty old. 

ok so i was confused a bit here, what i'm trying to do is write a maple procedure that computes Af for a given f contained in V . except we only need to correct the bug in the script below. This script demonstrates such a procedure in the case that omega is a square. The domain is given here as the negative set of a function F contained in V .  I have left in notes where/what i think we need to do but i dunno how to...

N:=10 ; # Global Var
Average := proc(F, f0) local f, i, j;
f := f0; # !!!!!!!!!!!!!! something is bad here...
for i to N do for j to N do
if F(i, j) < 0 then
f[i, j] := (f0[i - 1, j] + f0[i + 1, j] + f0[i, j + 1] + f0[i, j - 1])/4 ;
end if;
end do;end do;
return f;
end proc;
f0:=Matrix(N,F); # just to have something to test the procedure
Average(F,f0); # does not return the expected average, modifies f0


the necessary information we were given to produce this so far was..

Let N be a positive integer and [N] = {i contained in N | 1<= i <=N }  Let "Omega" C {(i,j) contained in [N] x [N] | 2<=i,j<=N-1} be a subset. Let V = R^([N]x[N]) be the vector space of real valued functions [N]x[N] -> R
and A, "triangle symbol":V->V (average) and "triangle symbole" (Laplacian) be the linear maps such that
[Af](i; j) = f(i; j)      if (i; j) not contained in "Omega"   OR

                             [f(i, j + 1) + f(i, j - 1) + f(i + 1, j) + f(i - 1, j)]/4 if (i,j) is contained in "Omega"

["traingle symbol"f](i,j) =  0 if (i,j) isnt contained in "Omega"   OR

                            ( f(i,j) - [f(i, j + 1) + f(i, j - 1) + f(i + 1, j) + f(i - 1, j)]/4 )    if (i,j) is contained in "Omega"

 Please and thank you for any help in advance <3



convert any polynomial to Divide(Mult(x, Plus(y+z)), x)


I need to maximize two multivariate objective functions (f(x1,y1,z1,t1) and g(x2,y2,z2,t2)) with inequality and nonnegativity constraints (x1, x2>0 and y1, z1, t1, y2, z2, t2 >=0). I am looking for parametric not numerical solutions.

What is the best way to find the solution to such a problem using maple?

Which book is the starting point and have examples

Good time friends,

Recently, I saw this link There we asked to find the functions f(x) ang g(x) by having both composition functions fog(x) and gof(x). I know what to do to find any of f(x) (or g(x)) if I am given fog(x) (or gof(x)) respectively, but I confess I don't know what to do with this one. Can Maple overcome this knid of problem? Thanks for your time.

Hi MaplePrimers,

I'm trying to solve a system of algebraic equations using 'solve' [float].  I'd prefer to use 'solve' over 'fsolve', as 'solve' solves my system in about 0.05s, whereas fsolve takes about 5 seconds.  I need to solve the system repeatedly at a different points, so time is important.  I don't know why there is such a large difference in time ... 

I have a few piecewise functions of order 3 to 5.  It solves fine with the other (piecewise) equations, but adding one piecewise function which gives me an error while trying to solve:

Error, (in RootOf) _Z occurs but is not the dependent variable.

I think this is due to solve finding multiple solutions.  Is there a way to limit solve to only real solutions?

Thanks in advance!


Apologies if this is a very simple question and I am being a bit stupid, but how do I plot two functions of r on one graph, if they operate over different values of r? 

Say I have the functions:

FOO = r→APOT*exp(-r/rho)-CPOT/r^6+4*E2/r 

g = r→(c1*exp(d1*r)+c2*exp(d2*r)+c3*exp(d3*r)+c4*exp(d4*r))/r 

where FOO takes values of r between 0.5 and 2, and g takes values of r between o.2 and 0.5. 


Any help would be appreicated!

I have following expression


which is 1 solution of the ODE

ode2 := -(diff(y(t), t, t))+(4-12/(1+s*cosh(2*t))+(8*(-s^2+1))/(1+s*cosh(2*t))^2)*y(t) = 0

Now I wanted to construct 2 linear independent solutions via:



and calculate the Wronskian:

with(LinearAlgebra); with(VectorCalculus)

Determinant(Wronskian([f(t_b-t), f(t-t_a)], t))

Since I know these functions are solutions of the second order ODE which does not contain any first order derivative the Wronskian should be a constant. Unfortunately Maple has a hard time to simplify it since the epxression is a little big. Is it my fault or has anyone an idea what to do?

Hello there,


I have some troubles with plotting implicit functions , aswell with plotting polar ones.

When I ask the plot of my function it's not ''smooth'' , it has edgdes everywhere that aren't suposed to be there (I think).


These are 2 examples:



Both curbes




Can somebody help me out on how to draw them smoothly?

Maybe I have to change settings?


Thanks alot!



In connection with recent developments in the Physics package, we now have mathematical typesetting for all the inert functions of the mathematical language. Hey! This is within the Physics update available on the Maplesoft Physics: Research & Development webpage

I think this is an interesting development that will concretely change the computational experience with these functions: it is not the same to compute with something you see displayed as %exp(x) instead of the same computation but flowing with it nicely displayed as an exponential function with the e in grey, reflecting that Maple understands this object as the exponential inert function, with known properties (all those of the active exp function), and so Maple can compute with the inert one taking these properties into account while not executing the function itself - and this is the essence of the inert function behaviour.

Introducing mathematical display, copy and paste for all these inert functions of the mathematical language concretely increases the mathematical expressiveness of the system, for teaching, working and also for presenting ideas.

Attached is a brief illustration.

Edgardo S. Cheb-Terrab
Physics, Maplesoft  InertMathematicalFun.pdf

I am trying to find what values of x f(x) is increasing without estimating from the graph



I have entered two functions and got a solotion for them:

Now i want to know if there is someway Maple can do this automaticly:


So that i not have to do like i did here, manuel copy-paste the values into the function, or re-enter them.


Using Maple 17.02 on Windows 64-bit, but i guess that makes no differance, since it's java :) 


Try makeing it simple, i'm new with Maple.


Thanks in advance!

Emil Kristensen


Can you please graph this function, as well as find the domain and range in interval notation?


1 2 3 4 5 6 7 Last Page 1 of 40