Maple 2019 Questions and Posts

These are Posts and Questions associated with the product, Maple 2019

I have loaded a series of worksheets into a help file using the makehelp command and installed in my toolbox package. Except for one of them, the worksheets appear in the help browser as worksheets instead of help files. Whenever I select one of them, it opens in maple as a worksheet. I would like to control whether a given help file opens as a worksheet or opens as a help.  I have read the helptools help and the help page for makehelp, but have been unable to identify the setting that determines which mode the help file operates in. Please advise what I am missing here.

How do I write this in logical notation in Maple? Is it even possible?

Show logical notation that expresses the following statement: If one dice shows an even number of spots and the second dice shows an odd number of spots, then the total for the pair is less than or equal to 9.

Hello

I solved these equations numerically but I need to solve it by Runge-Kutta fourth order Method. Kindly help me in the coding of the same.

 


restart;
N1 :=1:N2 :=1: N3 :=0.1 :R := -1:
EQ:={(1+N1)*diff(f(x),x$4)-N1*diff(g(x),x$2)-R*(-diff(f(x),x)*diff(f(x),x$2)+f(x)*diff(f(x),x$3))=0, N2*diff(g(x),x$2)+N1*(diff(f(x),x$2)-2*g(x))-N3*R*(f(x)*diff(g(x),x)-diff(f(x),x)*g(x))=0}:


IC:={D(D(f))(0)=0, D(f)(1)=0,f(0)=0,f(1)=1,g(0)=0,  g(1)=0}:

sol:= dsolve(EQ union IC, numeric,output=Array([0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1])):
 

I want to show the animation of the polar equation r=cos(2theta) be plotted from theta=0 to 2pi

I have a simple matrix, 11 rows x 3 columns, with header row.  <<

I multiply column 1 and 2 to get <<0.,0.031,0.218,0.657,1.084,1.095,0.654,0.217>>

Now, I just want to add up these elements, but 'sum' doesn't work 'Sum' doesn't work either. Is there a simpel way to do this?
 

m1 := `<|>`(`<,>`("# girls", 0, 1, 2, 3, 4, 5, 6, 7, 8), `<,>`("P(x)", 0.4e-2, 0.31e-1, .109, .219, .271, .219, .109, 0.31e-1, 0.4e-2), `<,>`("x*P(x)", 0, 0, 0, 0, 0, 0, 0, 0, 0))

Matrix(%id = 18446745635438952446)

(1)

m1[2 .. 9, 3] := `~`[`*`](m1[2 .. 9, 1], m1[2 .. 9, 2])

Vector[column](%id = 18446745635417541318)

(2)

"Sum?"

Vector[column](%id = 18446745635493441398)

(3)

"sum?"

Error, (in LinearAlgebra:-Multiply) invalid arguments

 

``


 

Download Untitled_(3).mw

I want to shade the area where the two polar curves overlap. The first curve is r=2 and the other curve is r=2(1-cos(theta)). How do I do this?

I want to find the surface area of this parametric curve revolving around the x-axis. I was able to plot the 2D rendering but I want to show the plot so that I can see the surface area. I suspect that would be the 3D rendering.

x=cos(t), y=2+sin(t), 0<=t<=2pi, x-axis

Hi,

It seems that plottools:-extrude doesn't support the "style" option: no error returned, just the extusion being always of surface style.
Am I correct ?

The solver seems to have a problem with some sets of boundary conditions. (See attached worksheet.)

Is there a way to get this numerical solution?
 

BC_test.mw

[differentiation of f and greek letter xi in bracket]

Hi,

I am trying to find q(t) from this 

ode1:=-diff(q(t), t) - 1.851851852*10^(-7)*q(t)*(2.042885233*10^10 - 3.517396152*10^18*(0.00001474262739*cos((1000*sqrt(1122)*t)/33) + 0.00001474262739*sin((1000*sqrt(1122)*t)/33))^2) + 9.259259260*10^(-7);

with initial condition

ics := q(0) = 2.45*10^(-12)

using

dsolve({ode1,ics})

but I cannot get the full solution. Is there any way I could find q(t)?

Thanks,

Baharm31

This is the source:

ode1.mw

 

 

 

Hello 

I am having equation y(x) in 5 variable c1, c2, A, R and x.

I am not able to plot graph in x and y(x) for A=1, c1 = 2.3, c2 = 2.4 and R=0,2 5,9.

Range of x: -1..1

Caption :graph of y(x) at different value of R.

Legend: R=0, R=1, R=2, R=3.

my equation is


 

"y(x):=0.0000148809523809523809 A^3 R^2 x^10-0.000334821428571428572 A^3 R^2 x^8+0.00156250000000000000 A^3 R^2 x^7+0.000133928571428571429 A^3 R^2 x^6-0.00312500000000000000 A^2 R^2 x^7+0.00156250000000000000 A^3 R^2 x^5-0.0156250000000000000 A^3 R^2 x^4-0.00312500000000000000 A^2 R^2 x^5-0.00625000000000000000 A^2 R x^6+0.00647321428571428572 A^3 R^2 x^3+0.0625000000000000000 A^2 R^2 x^4-0.0129464285714285714 A^2 R^2 x^3-0.0625000000000000000 A R^2 x^4+0.0625000000000000000 A c1 c2 x^4+0.125000000000000000 A^2 R x^3-0.00319293058132343847 A^3 R^2+0.00803571428571428571 A^2 R x^2-0.250000000000000000 A R x^3+0.0125000000000000000 A^2 R^2-0.00178571428571428571 A^2 R-0.0125000000000000000 A R^2+0.0125000000000000000 A c1 c2-0.750000000000000000 A x^2+0.500000000000000001 (0.0380078849721706865 A^3 R^2-0.150000000000000000 A^2 R^2+0.150000000000000000 A R^2-0.150000000000000000 A c1 c2) x^2+0.750000000000000000 A+1.00000000000000000 (-0.00959821428571428571 A^3 R^2+0.0191964285714285714 A^2 R^2) x+1.00000000000000000 (-0.125000000000000000 A^2 R+0.250000000000000000 A R) x:"

``


 

Download Ques1.mw


 

NULL

Restart:

pde := diff(w(x, t), x $ 4) + diff(w(x, t), t $ 2)/c^2 = 0;

diff(diff(diff(diff(w(x, t), x), x), x), x)+(diff(diff(w(x, t), t), t))/c^2 = 0

(1)

test1 := w(x, t) = W(x)*cos(omega*t); pde1 := expand((eval(pde, test1))/cos(omega*t))

w(x, t) = W(x)*cos(omega*t)

 

diff(diff(diff(diff(W(x), x), x), x), x)-W(x)*omega^2/c^2 = 0

(2)

ode := algsubs(omega^2/c^2 = alpha^4, pde1); sol := dsolve(ode); sol := convert(sol, trig)

-W(x)*alpha^4+diff(diff(diff(diff(W(x), x), x), x), x) = 0

 

W(x) = _C1*exp(-alpha*x)+_C2*exp(alpha*x)+_C3*sin(alpha*x)+_C4*cos(alpha*x)

 

W(x) = _C1*(cosh(alpha*x)-sinh(alpha*x))+_C2*(cosh(alpha*x)+sinh(alpha*x))+_C3*sin(alpha*x)+_C4*cos(alpha*x)

(3)

L_collection := [indets(sol, specfunc({cos, cosh, sin, sinh}))[]]

[cos(alpha*x), cosh(alpha*x), sin(alpha*x), sinh(alpha*x)]

(4)

``

temp := collect(sol, [sinh, cosh, sin, cos])

W(x) = (-_C1+_C2)*sinh(alpha*x)+(_C1+_C2)*cosh(alpha*x)+_C3*sin(alpha*x)+_C4*cos(alpha*x)

(5)

CL := [coeffs(rhs(temp), L_collection)]NULL

[-_C1+_C2, _C1+_C2, _C3, _C4]

(6)

R:=[seq(cat(_D,i)=CL[i], i=1..nops(CL))]

[_D1 = -_C1+_C2, _D2 = _C1+_C2, _D3 = _C3, _D4 = _C4]

(7)

MX:= subs((rhs=lhs)~(R), temp);

W(x) = _D1*sinh(alpha*x)+_D2*cosh(alpha*x)+_D3*sin(alpha*x)+_D4*cos(alpha*x)

(8)

boundary_condition_1 := simplify(rhs(eval(diff(MX, `$`(x, 1)), x = 0))/alpha = 0)

_D1+_D3 = 0

(9)

boundary_condition_2 := simplify(rhs(eval(MX, x = 0)) = 0)

_D2+_D4 = 0

(10)

boundary_condition_3 := simplify(rhs(eval(diff(MX, `$`(x, 1)), x = L))/alpha = 0)

cosh(alpha*L)*_D1+sinh(alpha*L)*_D2+cos(alpha*L)*_D3-sin(alpha*L)*_D4 = 0

(11)

boundary_condition_4 := simplify(rhs(eval(MX, x = L)) = 0)

_D1*sinh(alpha*L)+_D2*cosh(alpha*L)+_D3*sin(alpha*L)+_D4*cos(alpha*L) = 0

(12)

boundary_condition_solve := solve([boundary_condition_1, boundary_condition_2, boundary_condition_3, boundary_condition_4]); MX := eval(MX, boundary_condition_solve)

Warning, solutions may have been lost

 

{L = L, _D1 = -_D3, _D2 = -_D4, _D3 = _D3, _D4 = _D4, alpha = 0}, {L = 0, _D1 = -_D3, _D2 = -_D4, _D3 = _D3, _D4 = _D4, alpha = alpha}, {L = L, _D1 = 0, _D2 = 0, _D3 = 0, _D4 = 0, alpha = alpha}

 

Error, invalid input: eval received ({L = L, _D1 = -_D3, _D2 = -_D4, _D3 = _D3, _D4 = _D4, alpha = 0}, {L = 0, _D1 = -_D3, _D2 = -_D4, _D3 = _D3, _D4 = _D4, alpha = alpha}, {L = L, _D1 = 0, _D2 = 0, _D3 = 0, _D4 = 0, alpha = alpha}), which is not valid for its 2nd argument, eqns

 

``


 

Download Free_Vibration_Euler_Bernouli_Beam_1.mw

I have tried to solve these 4 equations to get the characteristic equation and finally the solution of the PDE.  But it shows some error. Can you please help with this issue?

I am trying to use this command

plot({0, 2*x^2, 2*x^2 - 2*x^3 + 8/3*x^4 - 4*x^5}, x = -10 .. 10, color = ["DarkGreen", "CornflowerBlue", "Burgundy"])

However, only the last function is showing up. 0 and 2x^2 is not showing up. I can't change the axes sizes because then the last function disappears.

I have the following question, plot the graph of mu=5*log_10(D_L/10) where D_L=(c/H_0)*\int_0^z dz'/[A(1+z')^4+B(1+z)^3+C]^{1/2} with resepct to z, where A,B,C are numerical values given beforehand, and c is the speed of light and H_0 is the current Hubble constant.

 

Can someone please help with this simple plotting assignment.

 

Thanks, just by experience, can I learnt these syntax languages.

 

Peace out!

 

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