Hi,

I need taylor expasion of

A(w):=M/sqrt(M^2+2*w)-mup*sqrt(((mu*M^2+3*sigmap-2*w)-sqrt((mu*M^2+3*sigmap-2*w)^2-12*mu*sigmap*M^2))/(6*sigmap))

I used taylor(A,w,4), but I had a problem!

If I know that A(w) is a real function, how can I remove ‘csgn’ from the  ‘taylor(A,w,4)’ command:

Thanks.

12.mws

There are discrepancies between Maple's solution of Fourier transforms and the results printed in USA NIST Handbook of Mathematical Functions, page 30

fourier(exp(-a*abs(x))/sqrt(abs(x)),x,s) assuming a>0;
            /   /   (1/2)   (1/2)                (1/2)  
        1   |   |2 2      Pi      signum(s - _U1)       
       ---- |int|-------------------------------------,
       2 Pi |   |       /   2    \                      
            |   |       |_U1     |          (1/2)       
            |   |     a |---- + 1| (s - _U1)            
            |   |       |  2     |                      
            \   \       \ a      /                      

                                    \\
                                    ||
         _U1 = -infinity .. infinity||
                                    ||
                                    ||
                                    ||
                                    ||
                                    //

For this transform of
                 "exp(-a*abs(x))/sqrt(abs(x))"

 the result in the NIST table is
          "sqrt(a + sqrt(a^2 + s^2))/sqrt(a^2 + s^2)"

 .
fourier(sinh(a*t)/sinh(Pi*t),x,s) assuming a>-Pi, a<Pi;
                    2 sinh(a t) Pi Dirac(s)
                    -----------------------
                          sinh(Pi t)       

For this transform of sinh(a*x)/sinh(Pi*x)   the result in the NIST table is
                         "1/sqrt(2*Pi)"  "sin(a)/(cosh(s) + cos(a))"

 
fourier(cosh(a*t)/cosh(Pi*t),x,s) assuming a>-Pi, a<Pi;
                    2 cosh(a t) Pi Dirac(s)
                    -----------------------
                          cosh(Pi t)       

For this transform of cosh(a*x)/cosh(Pi*x) the result in the NIST table is  
                          "sqrt(2/Pi) cos(a/2)*cosh(s/2)/(cosh(s) + cos(a))"

These disparities are significant, apart from the fact that Maple failed to solve the first example above.

 

Hi, 

Is it possible to define a linear idempotent operator in Maple?
I found no clue in the define help page.
To fix the ideas, an example could be the transposition operator on the ring of matrices

Thanks in advance

Hi,

I'm only getting one Answer instead of two (see below).

Thanks in Advance

 

Example 4: Solving Equations Involving Radicals   (1.1) (1.2) (1.3) (1.4) (1.5) (1.6) (1.7) (1.8)

 

Download Radicals.mw

Hello. Please help me. I set the function as "spline". The resulting function is shown in the figure. Is there any way to find the extremum points of this function? I will need to investigate many such functions, so searching separately for local minima and maxima will be a difficult long job for my research. Thank you for your answers.

Doing a routine simplification but got an error...Dont know where the mistake comes from.

 

simplification_error.mw

Is it possible to make notes above and next to a matrix like in the image above? How?

I'm sorry if this is really obvious but I'm new to Maple.

Thank you in advance :)

I want to solve the following problem in Maple:

I used the following Maple code. I am unsure whether this is the correct way of entering the assumptions for the initial and boundary conditions though.

 

>  (1) >  (2) >  (3) >  (4) >  >

Download IVP_with_inequalities.mw

Hi, I have a problem that needs excessive use of symbolic matrix-vector manipulation. I'm using maple physics vector package. my first problem is that it seems this package don't support symbolic vector transpose and the related rules is there a way to implement this, for example, I want to write in symbolic form: V_*Transpose(V_) but maple eliminate the Transpose head function and evaluate this as V_^2 which is wrong, or I want maple automatically simplify the transpose rule which state that (ab)'=b'a' which a and b are symbolic matrices if maple doesn't understand this, so is there a way I can implement this.
my second question is how can I state that for example, A*B is not equal to B*A with just assuming A and B are Matrix with Airbtrary dimension and not define A and B indices so that whenever i type: A*B+B*A it doesn't evaluate it as 2*AB

I need to plot a model of the amount of internet users starting from 1995 - 2024 in the US.

 

Example : Quadratic Modeling: Internet Users   number of users of internet t = time i.e 5 = 1995 year

 

Download Modeling_graph.mw

 

How can i sove further to get exact value

 

I am new to maple. I am trying to plot3d  the following differential eq:

eq1 := diff(c(x, t), t) - 1.5*diff(c(x, t), x, x) + 0.05/(x + 0.001) = 0

With these initial conditions:

ics := c(x, 0) = 0, c(0, t) = 10, D[1](c)(20, t) = 0

And then I slove and plot this:

sol := rhs(dsolve({eq1, ics}, c(x, t)))

plot3d(sol, x = 0 .. 20, t = 0 .. 100, labels = [x, t, c])

But I only get an empty coordinate system with no plot. I don't have this problem when in the last line of the eq, I have 0.05*x instead of 0.05/(x + 0.001).

Could someone help me with what might be the problem?

 

 

 

Hi,

How to change Maple symbol " I " to mathematical symbol " i " ?

Thanks

How to do this in Maple please?

Iterate an array and select x items so that the sum of the selected items equal or are above a value.

Eg. 10 real numbers in an array, random for example between 0..10 and select some of them so the value is equal or greater than y, e.g 5.2 , as close as possible to optimize the selection.

restart; with(plots):with(LinearAlgebra):unprotect(O); alias(conj = conjugate); conj z = lambda*v+a; La droite D est représentée par son équation complexe Appelons H l'affixe h le pied de la perpendicukaire abaissée de O sur (D) Les vecteurs OH et V sont orthogonaux donc z = lambda v + a h*conj(v)+conj(h)*v = 0; Le point H appartient à la droite (D) donc : h = lambda*v+a; conj(h) = conj(a)+lambda*conj(v); (lambda*v+a)*conj(v)+(conj(a)+lambda*conj(v))*v = 0; solve(%, lambda); h := simplify(subs(lambda = %, lambda*v+a)); a := 3-I*4; v := -2/3+4*I; evalc(h); H := [Re(h), Im(h)]; Représentation graphique d'un cas particulier : f := proc (x) options operator, arrow; -3*x+5 end proc: a := 3: A := [a, f(a)]:O:=[0,0]: zo := [8/3+I*f(8/3)]; ze := [2+I^(eval(diff(f(x), x), x = 2))]; Zo := [8/3, f(8/3)]; Ze := [2, f(2)]; ex := -3*x+5; V := `