## Evaluation of an expression...

Hello,

I am confused by the Syntax of maple. When does maple numerically evaluates an expression? I know that maple cannot distinguish the variable "e" from the exponential function "e". So I have to use the command palette or enter the 1-D sequence "exp(1)". Maple shows the symbols if not told otherwise. I can numerically evaluate the expression using "evalf(exp(1))".

But if I enter "I^2" for example maple behaves in a different way. It does not show "I^2" but it evaluates the expression. Same with "2+2". Maple shows me the result "4". So when does Maple numerically evaluate an expression and when does not?

Second question: When I enter "evalf(exp((I*2)*Pi))" I get "1.". What is the meaning of the point? Using "evalc(exp((I*2)*Pi))" I do not get the point - just "1".

## Consistency and stability of numerical calculation...

Hi

It seems when you run the code more than one time, various results are obtained each time.

What is the reason? How it can be fixed?

Thanks

 (1)

## help about taking real part...

hello guys, I can't take the real part of this formula that you can see in the picture that I upload for you.

## Can plot3d plot a parametric surface passed to it ...

Plot3d in this worksheet calls a procedure which conditionally returns the values for a parametrically defined ellipsoid, but the plot command fails. However the procedure passes the correct list of parametric values when it is called directly.

Is there a way to call a procedure within plot3d which successfully plots a parametrically defined surface?

Plot3d_proc_parametric.mw

## Plot a function in discrete form from analytical f...

Hello, everybody,

If I had the graph of a function just like plot(sin(x), x=-2..2)

The question is I want to plot this function is discrite form    by the pair of points (x[i], sin9x[i]) and i=1...N, where N is an integer number

## Can the edges of these surfaces be made smoother?...

The edges of the red and blue surfaces are ragged. Can they be made smoother when displayed?

Intersecting_surfaces.mw

## Series as Sigma summation representation...

Supposing as a nice simple example I use the power series command,

series(ex, x=0,8)

to get,

1+x+12x+ 16x+ 124x+ 1120x+ 1720x+ 15040x7

Is there automated anyway to get this as a Sigma representation?

## How to create an animation using a sequence of plo...

Hello, I have been attempting to plot a sequence of arrows in order to display how the vectors of the Frenet-Serret frame change throughout an helix-like trajectory. I came up with the following:

(With p1 being a plot I made earlier)

`for t from 0 by 0.1e-1 to 12.5663706144 do plots[display](p1, plottools[arrow](Vector([cos(t), sin(t), t/(7.5)]), Vector([-(1/2)*sqrt(2)*sin(t), (1/2)*sqrt(2)*cos(t), (1/2)*sqrt(2)]), .1, .2, .3, cylindrical_arrow)) end do`

This plots the desired arrow representing the tangent vector; however, it creates a plot for each step, while what I want is for it to display the arrow on each step in the same plot (as an animation).

I have attempted using the seq command, but I can't seem to get it right.

`plots[display](p1, plottools[arrow](seq([Vector([cos(t), sin(t), t/(7.5)]), Vector([-(1/2)*sqrt(2)*sin(t), (1/2)*sqrt(2)*cos(t), (1/2)*sqrt(2)]), .1, .2, .3, cylindrical_arrow], t = 0 .. 4*Pi, 0.1e-1)))`

With this code, the sequence won't be able to be executed.

Any ideas on how to do this? How can I use the sequence command in combination with plottools[arrow]?

## How do I correct this code?...

Hello everyone.and complements

Please I am trying to obtain series expansion of the expression below in u but encounter difficulties particularly when b=0. I am very optimistic that when b=0 there will be a result not division by 0. Can I get help on the code?

Thank you in anticipation of your quick and positive responses and suggestions

```# for k=2 CHEBY HYBRID WITH mu=(1-(1/2)*sqrt(2)))) AND v=(1+(1/2)*sqrt(2))))
restart:
omega:=u/h:
t:=(sum(a[j]*x^j,j=0..3)+a[4]*sin(omega*x)+a[5]*cos(omega*x)):
F:=diff(t,x):
G:=diff(t,x,x):
p1:=simplify(eval(t,x=q))=y[n]:
p2:=simplify(eval(t,x=q+(1-(1/2)*sqrt(2))*h))=y[n+mu]:
p3:=simplify(eval(t,x=q+h))=y[n+1]:
p4:=simplify(eval(t,x=q+(1+(1/2)*sqrt(2))*h))=y[n+v]:
p5:=simplify(eval(F,x=q+2*h))=f[n+2]:
p6:=simplify(eval(G,x=q+2*h))=g[n+2]:

vars:= seq(a[i],i=0..5):
Cc:=eval(<vars>, solve({p||(1..6)}, {vars})):
for i from 1 to 6 do
a[i-1]:=Cc[i]:
end do:
Cf:=t:

K:=collect(combine(simplify(eval(Cf,x=q+2*h),size),trig),{y[n],y[n+mu],y[n+1],y[n+v],f[n+2], g[n+2]},factor):

Num := numer(K):
Den := denom(K):

N := 20:   # order of expansion
Num_N :=(convert(series(Num, u, N),polynom)):
Den_N := (convert(series(Den, u, N),polynom)):
b:=y[n+2]=(convert(series(Num_N/Den_N, u, N),polynom)):

eval(b,u=0); ```

## nonlinear integral eq...

how can solve this nonlinear integral eq?

## How do I solve stiff nonlinear ODE coupled with in...

Hi there

I am trying to solve the ODE below

 >
 (1)
 >
 (2)
 >
 (3)
 >

 >
 >
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 >

My questions are:

1. Why does the solution for the longer time span (t<10) looks different from the shorter time span (t<0.1)? I have read about stiff ODEs and probably this has something to do with it. I am trying to figure out what is going on with the solutions.

2. I tried dsolve with stiff methods (lsode and rosenbrock) and both gave me the same solutions as above. I have not tried the advance options yet. How do I set dsolve so that the solution for the longer span (t>10) looks similar to shorter span?

## Why does procedure P perform differently inside th...

I would like procedure P to perform inside the map statement exactly as it does outside the map statement. Can this be done?

Map_Procedure.mw

## LPSolve doesnt register constraint...

Can anyone tell me why maple wont accept my constraint?

Code:

LPSolve(3*x__1+14*x__2+18*x__3+6*x__4+2*x__5, {3*x__1+5*x__2+6*x__3+2*x__4+x__5 <= 10}, x__1 = 0 .. 1, x__2 = 0 .. 1, x__3 = 0 .. 1, x__4 = 0 .. 1, x__5 = 0 .. 1, maximize = true)

It returns the error "Warning, problem appears to be unbounded", when i can clearly see that it is bounded!

Im trying to solve the LP-relaxation of a binary problem which is why i have a 0..1 bound on every variable. Running Maple 2016.1 on windows if thats a help.

## Solution for integration...

Request help in solving the equation:

Eq_H_1 := C[11*m]*(int((t-(j-1)*T)*alpha*(-alpha*(K*T*beta+T*beta*j-K*T-T*beta-T*j-beta*t+T+t))^(-beta/(beta-1))*exp(-R[m]*t), t = (j-1)*T .. (K+j-1)*T))

Thanks

## How do i sum over indexes [Solved]...

Hey mapleprimes

I am trying to get the sum function to give me n variables, well not sure how to explain it, so let me show:

`sum(x__i, i = 0 .. 2)`

I was expecting to get x__0 + x__1 + x__2