maple2015

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These are questions asked by maple2015

Hi

I use Maple 2016.

The following command calculates semicircle perimeter, but it returns infinity.

`assuming`([int(sqrt(1+(diff(sqrt(R^2-(x-R)^2), x))^2), x = 0 .. 2*R)], [R > 0])

Please download 1.txt.

Integrand := parse(FileTools[Text][ReadFile]("1.txt")):

int(Integrand, [z = -R .. R, y = 0 .. R], numeric);

plots[implicitplot3d](Phi = phi, z = -R .. R, y = 0 .. R, Phi = 0 .. 0.1e-1, color = ColorTools[Gradient]("Red" .. "Blue", best)[4], grid = [50, 50, 20]);

Why the integrand has positive real amounts in the domain [z = -R .. R, y = 0 .. R] for R=0.5, but the integral value is negative?

Hi

I got an square matrix (70×70) from MATLAB (please download attached text file 1.txt). Following codes are used in MAPLE, but an unknown error is occurred. It seems that matrix is divided in two submatrices. Please hint me or run the codes to obtain fiirst three minimum real positive roots of the determinant. 

Thank you for taking your time

Maple codes

Digits:=150:

M:=parse(FileTools[Text][ReadFile]("1.txt")):

LinearAlgebra:-Determinant(M):

fsolve(%,P=0..0.5)*100;

Hi

Please download the attachment.

 

I try to find a relation between EL and Lap(EL) in polar coordinate for one variable function w(r), where Lap is laplacian and EL is Euler Lagrange equation. Please check the Maple code and help me to do some manipulations to find a general relation (if any relation exists!).

In fact I need the inverse of Euler Lagrange equation to obtain f(r) for an arbitrary function g(r) in equation below

EL(f) = Lap(EL(g))

Or f=inverseEL(Lap(EL(g)))

Thank you for taking your time

 

 

 

restart; s := proc (f) subs(d[0] = w(r), seq(d[n] = diff(w(r), `$`(r, n)), n = 1 .. 10), f) end proc; ss := proc (f) subs(seq(diff(w(r), `$`(r, 11-n)) = d[11-n], n = 1 .. 10), w(r) = d[0], f) end proc; EL := proc (eq) s(diff(ss(eq), d[0]))+add((diff(s(diff(ss(eq), d[n])), `$`(r, n)))*(-1)^n, n = 1 .. 10) end proc

f := (diff(w(r), r, r))^2*r^4+4*r^6*(diff(w(r), r, r, r))^2:

a1 := EL(F):

a2 := VectorCalculus:-Laplacian(EL(f), 'polar[r, t]'):

simplify(a1-a2)

8*r^6*(diff(diff(diff(diff(diff(diff(diff(diff(w(r), r), r), r), r), r), r), r), r))+248*r^5*(diff(diff(diff(diff(diff(diff(diff(w(r), r), r), r), r), r), r), r))+2582*r^4*(diff(diff(diff(diff(diff(diff(w(r), r), r), r), r), r), r))+10910*r^3*(diff(diff(diff(diff(diff(w(r), r), r), r), r), r))+17786*r^2*(diff(diff(diff(diff(w(r), r), r), r), r))+8192*r*(diff(diff(diff(w(r), r), r), r))-92*(diff(diff(w(r), r), r))

(1)

``


 

Download EL.mw

 

Hi

I want to write a code to show that

Please check the following code:

restart;
with(VectorCalculus):
SetCoordinates(cartesian[x, y, z]): 
g1 := proc (u1, u2, u3, s)
local N, u, n, intr1, intr2, intr3, R1, R2:
u := VectorField([u1, u2, u3]): 
N := Gradient(s): 
n := N/sqrt(add(N[k]^2, k = 1 .. 3)): 
intr1 := solve(subs(z = 0, s), y): 
intr2 := solve(subs(z = 0, y = 0, s)): 
R1 := int(int(subs(z = solve(s, z)[1], u . n), y = intr1[1] .. intr1[2]), x = intr2[1] .. intr2[2], numeric):
intr1 := solve(s, z): 
intr2 := solve(subs(z = 0, s), y):
intr3 := solve(subs(z = 0, y = 0, s)): 
R2 := evalf(int(int(int(Del . u, z = intr1[1] .. intr1[2]), y = intr2[1] .. intr2[2]), x = intr3[1] .. intr3[2])):
print(R1, R2) 
end proc

It seems that different answers are obtained.

g1(x, 1, z, x^2+y^2+z^2-2);
                   6.664324407, -23.69537567
 

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