## How to plot gyroid surface by Maple...

Greeting for all

, How to plot gyroid surface by Maple where its equation is

Amr

## How expand in perturbation series in maple?...

I have the following ODE perturbation problem which I want maple to solve for me:

q'(\tau)=f(p(eps*\tau)+eps*q(\tau),r(eps*\tau)+s(\tau))-f(p(eps*\tau,r(eps*\tau)+s(\tau))-f(p(eps*\tau),r(eps*\tau))

where q(\tau)=q_0(\tau)+eps*q_1(\tau)

p(eps*\tau)=p_0(eps*\tau)+eps*p_1(eps*\tau)

s(\tau)=s_0(\tau)+eps*s_1(\tau)

r(eps*\tau)=r_0(eps*\tau)+eps*r_1(eps*\tau)

I want maple to expand every function that depends on eps in its arguments by a Taylor series around eps=0, i.e h(eps)=h(0)+eps*h'(0)

and also expand the difference above the fs with an eps-expansion around eps=0.

I did all this manually now I want to check if my calculations are correct, eventaully I want to equate same powers of eps of the RHS and LHS of the first ODE I wrote above.

Then how to use maple for this?

Thnaks.

## residual standard error command?...

Does there exist a Maple command that on its own calculates the residual standard error of two regression lists?

## Need help on this ...

Given the following functions, graph them and identify relative and absolute extrema (if any).

f(x)=3x^3-2x^2+5x-7     [-3,6]

## Doing some Substitution ...

How I can do ?

Thank you.

Substitution of . 5,6,7) into Eqs. 1–(4), gives the new equation as functions of the generalized coordinates,
u_m,n(t);  v_m,n ( t), and w_m,n ( t). These expressions are then inserted in the Lagrange equations (see Eq. 8)) a set of N second-order coupled ordinary differential equations with both quadratic   and cubic nonlinearities.

In Eq (8) q are generalized coordinate such as uvw  and .

\where the elements of the vector, are the time-dependent generalized coordinates.

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## How to calculate Vector[row] y2 using spline fit F...

Hi,

I was able to determine a cubic spline fit, F(v), to x1 and y1. Now I have vector x2 which I would like to use F(v) to calculate y2 as another Vector[row]. I am having trouble accomplishing this task. Any help is greatly appreciated. Thanks.

x1 := Vector[row]([0.8e-1, .28, .48, .68, .88, 1, 1.2, 1.4, 1.6, 1.8, 2, 2.2, 2.4, 2.6, 2.8, 3, 3.2, 3.4, 3.6, 3.8, 4, 4.2]);

y1 := Vector[row]([-10.081, -10.054, -10.018, -9.982, -9.939, -9.911, -9.861, -9.8, -9.734, -9.659, -9.601, -9.509, -9.4, -9.293, -9.183, -9.057, -8.931, -8.806, -8.676, -8.542, -8.405, -8.265]);

m := ArrayTools[Dimensions](x1);

maxx := rhs(m[1]);

F := proc (v) options operator, arrow; CurveFitting:-Spline(x1, y1, v, degree = 3) end proc;

x2 := Vector[row]([seq(log10(2*10^x1[k]), k = 1 .. maxx)])

y2:=?

Pts1 := plot(x1, y1, style = point, symbol = diamond, gridlines = true, color = red);

plt_sp := plot(F(v), v = x1[1] .. x1[maxx], color = blue);

plots:-display(Pts1, plt_sp)

## Why am I getting this strange result when calculat...

In Maple 2018, I was playing around with some sums of infinite series, and I came across a result that made me wonder if Maple was perhaps using some other definition or understanding of the sum of a series in its calculation. Take a look at the screenshot linked below:

https://ibb.co/hMdkQHn

That first series is most certainly divergent since the limit as n approaches infinity of n^2/(n+1) is not equal to 0. And just to confirm my own sanity, I even checked some of the partial sums of the series, which sure enough are diverging. And yet for the infinite sum, Maple is giving this finite result.

I even checked a more familiar alternating series, the alternating harmonic series, which Maple does correctly calculate to be ln(2).

What am I missing here? Is Maple using a different definition for the sum of the series than the limit of the partial sums as n approaches infinity? Or is there a mistake with how I've written something that I'm not noticing?

## algebraic equations...

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How can I find A and B explicitly

## Derivative and Differentiability ...

Using the definition of a derivative as a limit i.e., lim h->0  f(x+h)-f(x)/h  .Find the derivative of the following functions:

a) f(x)=3x^3-2x^2+5x-7

## Plot graph from array...

Hi, I've created an array from a do loop, where the number in the array is the number of degrees for which I've calculated the answer, I now wish to graph the angle against the value in the array. i.e. the value a[50]=156.21 should graph to the point (50,156.21). Ideally as well I'd like for it to be joined up by a smooth curve of best fit, but I'll take what I can get, I can't seem to figure out how to plot it at all at the moment.

See code below:

restart;

for i from 50 by 5 to 85 do
ThetaBn := (1/180)*i*Pi;
s := cos(2*ThetaBn)*x+(2*sin(ThetaBn)*sin(ThetaBn))*sin(x);
a[i] := 180.0*fsolve(s = 0, x, 1 .. 6)*(1/Pi)
end do;

Thanks

## Why cannot 'solve' find the solution of some trivi...

I would like to understand why the 'solve' command is unable to find any solution to the system of equation { x^2=2, x^3=2*sqrt(2) }  (which obviously has a unique solution x=sqrt(2) ). The syntax that I used is
> solve({x^2 = 2, x^3 = sqrt(2)^3}, [x]);
and the output is the empty list.

I suspect that this is related to the presence of the algebraic number sqrt(2). Does anyone have a better understanding ?

I am using Maple version 2018.0, build ID 1298750.

Thank you.

## Shortcut or implicit operation?...

I discovered incidentally that the command  Matrix(3, 3, -) (the number 3 is purely illustrative) returned the same result than the command Matrix(3, 3, (i,j) -> i-j).
In the same way + realizes (i,j) -> i+j), * realizes (i,j) -> i*j), ...

More surprisingly . realizes (i,j) -> i*j while I'm in worksheet mode, with "old" maple input style, and that the command 2.3 does not answer 6 but concatenates 2 and 3.

Is this a known behaviour or an undocumented feature?

## Odetest only partially simplifies system of equati...

Hello,

I am attempting to check solutions to a system of ODEs using odetest. However, odetest only appears to partially substitute the provided solution. Furthermore, it appears to be related to the alphabetical order of the functions.

For instance, here I have two functions, phiL and phiM, that satisfy Laplace's equation and are coupled through the boundary conditions, BCs.

laplace := {-phiL(z) + diff(phiL(z),z$2)=0, -phiM(z) + diff(phiM(z),z$2)=0}:
BCs := {phiL(d1)=0,phiM(-d1)=0,phiL(0)=phiM(0), D(phiL)(0)-D(phiM)(0)=-n}:
sol := {
phiM(z) = n/2/coth(d1)*(cosh(z)+coth(d1)*sinh(z)),
phiL(z) = n/2/coth(d1)*(cosh(z)-coth(d1)*sinh(z))
}:

odetest(sol, laplace union BCs,{phiL(z),phiM(z)});

This returns

{0, 1/2*(2*phiL(0)*coth(d1)-n)/coth(d1), D(phiM)(0)-1/2*n}

Here, phiL(0) and phiM(0) are unevaluated even though the provided solutions are valid there.

Furthermore, while renaming phiL to an alphabetically earlier name (eg, phiJ) causes the corresponding change in the output. However, renaming it to something alphabetically after phiM (eg, phiN) causes the terms in the output to switch. That is, changing phiL to phiN in the above code results in

{0, 1/2*(2*phiM(0)*coth(d1)-n)/coth(d1), D(phiN)(0)+1/2*n}

Therefore, it seems to be related to the way Maple internally stores the list of variables.

Is this a bug? Or is there something I'm missing?

Thanks!

## Calculating the outer product matrix...

My question has two steps:

STEP 1:  The multiplication  of is defined as follows

if n<>l, then

.

if n=l and m<=s,

Question 1: I wrote a code for calculating the multiplication  of. Is it right?

The code for Step 1

restart;

multiply:=proc(n,m,l,s) local g,a:
a:=unapply(doublefactorial(2*j-1)/factorial(j),j):
g:=unapply((a(m-j)*a(j)*a(s-j)/a(m+s-j))*(2*m+2*s-4*j+1)/(2*m+2*s-2*j+1),j):

if n<>l then 0 else
end if
end proc:

n:=2:
l:=2:
m:=1:
s:=1:
multiply(n,m,l,s);


when I compared the results which I got and the results which is given in the book as follows, I think it is right.

Step 2:

We know that the outer product matrix is calculated as follows

We found the elements of the outer product matrix in Step 1.

Question 2 : I want to write the elements which are derived in step 1 to the outer product matrix in step 2. In here, the outer product matrix is NxN matrix. N=(M+1).2^(K-1) where K, M are any integers.