MaplePrimes Questions

Hi there

I'm an old user of Maple, but I've never been able to plot functions with unit. You can see my latest attempt down below

b := 120*Unit('mm');
h := 200*Unit('mm');
V := 8*Unit('kN');

I__x := (1/12)*b*h^3

Q(x):=(1/2)*((1/4)*h^2-(100*Unit('mm')-x)^2)*b 
tau(x):=V*Q(x)/(I__x*b)

plot(Q(x(Unit('mm')), units), x = 0*Unit('mm') .. 100*Unit('mm'))

Plot_function_with_units.mw

If anyone is able to help me with this problem, I would greatly appreciate it.

Hi 

I solve the laplace equation written in polar coordinates in annular domain.
The code run without any error 

But there is no solution displayed after running the code, note that I use Maple 18

Laplace_annulardomain.mw

Many thinks for your help

I want to divide each row of Marix A by diagonal element. In for loop, when I assign dividing results to the letter , the type of A still remains matrix, but if I choose another letter (like B) results are stored in Table. Why? How can I assign to a matrix?

Also I can't figure out why maple doesn't show elements of table(see worksheet file).

I should notice that my main problem is assigning not dividing.

worksheet.mw

 

i want to design a packaging container to hold 320 sphere-shaped chocolates that each has a diameter 1.8 cm and weights about 3.2g each. i hope can get all posible shape using maple18 .

 

Good morning everyone, 

I have a problem, when I try to evaluate the definite integral below, Maple can not provide a result. What can I do so that the Maple can calculate this integral?

This is the Maple code with the result:

 

 

restart

with(VectorCalculus):

with(LinearAlgebra):

with(CodeGeneration):

N := 1:

M := 2:

``

for i to N do rpv1 || i := 0; rpv2 || i := 0; rpv3 || i := 0; for j to M do rpv1 || i := VectorCalculus:-`+`(rpv1 || i, Typesetting:-delayDotProduct(diff(VectorCalculus:-`*`(VectorCalculus:-`+`(s, VectorCalculus:-`-`(xi || i)), 1/L || i)^j, s), Phi || i || j)); rpv2 || i := VectorCalculus:-`+`(rpv2 || i, Typesetting:-delayDotProduct(diff(VectorCalculus:-`*`(VectorCalculus:-`+`(s, VectorCalculus:-`-`(xi || i)), 1/L || i)^j, s), `ϕ` || i || j)); rpv3 || i := VectorCalculus:-`+`(rpv3 || i, Typesetting:-delayDotProduct(diff(VectorCalculus:-`*`(VectorCalculus:-`+`(s, VectorCalculus:-`-`(xi || i)), 1/L || i)^j, s), gamma || i || j)) end do; rp || i := Matrix([[rpv1 || i], [rpv2 || i], [rpv3 || i]]) end do:

``

for i to N do rppv1 || i := 0; rppv2 || i := 0; rppv3 || i := 0; for j to M do rppv1 || i := VectorCalculus:-`+`(rppv1 || i, Typesetting:-delayDotProduct(diff(diff(VectorCalculus:-`*`(VectorCalculus:-`+`(s, VectorCalculus:-`-`(xi || i)), 1/L || i)^j, s), s), Phi || i || j)); rppv2 || i := VectorCalculus:-`+`(rppv2 || i, Typesetting:-delayDotProduct(diff(diff(VectorCalculus:-`*`(VectorCalculus:-`+`(s, VectorCalculus:-`-`(xi || i)), 1/L || i)^j, s), s), `ϕ` || i || j)); rppv3 || i := VectorCalculus:-`+`(rppv3 || i, Typesetting:-delayDotProduct(diff(diff(VectorCalculus:-`*`(VectorCalculus:-`+`(s, VectorCalculus:-`-`(xi || i)), 1/L || i)^j, s), s), gamma || i || j)) end do; rpp || i := Matrix([[rppv1 || i], [rppv2 || i], [rppv3 || i]]) end do:

``

``

for i to N do for j from 0 to 0 do U || i || j := 0 end do end do:

for i to N do for j from 0 to 0 do V || i || j := 0 end do end do:

for i to N do for j from 0 to 0 do W || i || j := 0 end do end do:

for i to N do for j from 0 to VectorCalculus:-`+`(M, -2) do U || i || (VectorCalculus:-`+`(j, 1)) := VectorCalculus:-`+`(U || i || j, VectorCalculus:-`*`(VectorCalculus:-`+`(s, VectorCalculus:-`-`(xi || i)), 1/L || i)^VectorCalculus:-`+`(j, 1)) end do end do:

for i to N do for j from 0 to VectorCalculus:-`+`(M, -2) do V || i || (VectorCalculus:-`+`(j, 1)) := VectorCalculus:-`+`(V || i || j, VectorCalculus:-`*`(VectorCalculus:-`+`(s, VectorCalculus:-`-`(xi || i)), 1/L || i)^VectorCalculus:-`+`(j, 1)) end do end do:

for i to N do for j from 0 to VectorCalculus:-`+`(M, -2) do W || i || (VectorCalculus:-`+`(j, 1)) := VectorCalculus:-`+`(W || i || j, VectorCalculus:-`*`(VectorCalculus:-`+`(s, VectorCalculus:-`-`(xi || i)), 1/L || i)^VectorCalculus:-`+`(j, 1)) end do end do:

for i to N do f || i := VectorCalculus:-`+`(Typesetting:-delayDotProduct(VectorCalculus:-`*`(Typesetting:-delayDotProduct(E, A), 1/mu), VectorCalculus:-`+`(VectorCalculus:-`+`(rpp || i, VectorCalculus:-`-`(VectorCalculus:-`*`(rpp || i, 1/evalc(norm(Re(rp || i), 2))))), VectorCalculus:-`*`(Typesetting:-delayDotProduct(rp || i, Typesetting:-delayDotProduct(rp || i^%T, rpp || i)), 1/evalc(norm(Re(rp || i), 2))^3))), Typesetting:-delayDotProduct(g, e3)) end do:

for i to N do for j to VectorCalculus:-`+`(M, -1) do fun || i || j := int(VectorCalculus:-`*`(U || i || j, Row(f || i, 1)), s = xi || i .. L || i) end do end do;

fun11

(int((s-xi1)*(E*A*(2*Phi12/L1^2-2*Phi12/(sqrt((gamma11/L1+2*gamma12*s/L1^2-2*gamma12*xi1/L1^2)^2+(`ϕ11`/L1+2*`ϕ12`*s/L1^2-2*`ϕ12`*xi1/L1^2)^2+(Phi11/L1+2*Phi12*s/L1^2-2*Phi12*xi1/L1^2)^2)*L1^2)+(Phi11/L1+(2*(s-xi1))*Phi12/L1^2)*((2*(Phi11/L1+(2*(s-xi1))*Phi12/L1^2))*Phi12/L1^2+(2*(`ϕ11`/L1+(2*(s-xi1))*`ϕ12`/L1^2))*`ϕ12`/L1^2+(2*(gamma11/L1+(2*(s-xi1))*gamma12/L1^2))*gamma12/L1^2)/((gamma11/L1+2*gamma12*s/L1^2-2*gamma12*xi1/L1^2)^2+(`ϕ11`/L1+2*`ϕ12`*s/L1^2-2*`ϕ12`*xi1/L1^2)^2+(Phi11/L1+2*Phi12*s/L1^2-2*Phi12*xi1/L1^2)^2)^(3/2))/mu+g*e3)/L1, s = xi1 .. L1))*e[x]

(1.1)

``

NULL

``


 

Download integral.mw

 

Thank you !

If I have checked the Editable button just below the working window, then the temperature would be very high in the next time when I start Maple 2019. I do not what is going on. But when I unchecked the Editable button, and wait for several seconds, then the temperature and the load of my laptop are on the normal state.  Is this a bug for Maple 2019? My OS is Debian Stretch, that is,

$ uname -a
Linux debian 4.9.0-9-amd64 #1 SMP Debian 4.9.168-1 (2019-04-12) x86_64 GNU/Linux

 

Hi

I try to solve the laplace equation with some special boundary conditions.

But, i get the follwoing error

Error, (in pdsolve/sys) the given system is not polynomial in the variables {f}

 

 laplace_equation.mw

Thank you for any help

 

This worksheet is a modification to Kitonum's excellent http://www.mapleprimes.com/posts/202222-Contour-Curves-With-Labels.

The mod adds the ability to display labelled contours for expressions in x and y defined parametrically.

Your comments are welcome.

Contourplot_with_labels.mw


 

with(LinearAlgebra)

A := Matrix(4, 4, {(1, 1) = 1, (1, 3) = -1, (1, 4) = 3, (2, 2) = 2, (2, 3) = 1, (3, 1) = -1, (3, 2) = 1, (3, 3) = 6, (3, 4) = -1, (4, 1) = 3, (4, 3) = -1, (4, 4) = 10}, fill = 0)

Matrix(%id = 18446746512315154430)

(1)

b := Matrix(4, 1, {(1, 1) = 0, (2, 1) = -2, (3, 1) = -1, (4, 1) = -1})

Matrix(%id = 18446746512315153574)

(2)

x := Matrix([[x1], [x2], [x3], [x4]])

Matrix(%id = 18446746512315146838)

(3)

f := proc (x) options operator, arrow; (1/2)*Transpose(x).A.x+Transpose(b).x end proc

proc (x) options operator, arrow; Typesetting:-delayDotProduct(Typesetting:-delayDotProduct((1/2)*LinearAlgebra:-Transpose(x), A), x)+Typesetting:-delayDotProduct(LinearAlgebra:-Transpose(b), x) end proc

(4)

(1/2)*Transpose(x).A.x+Transpose(b).x

Matrix(%id = 18446746512315132494)

(5)

while g(vk) < 10^(-6) do k end do

Error, cannot determine if this expression is true or false: (Matrix(4, 4, {(1, 1) = 1, (1, 2) = 0, (1, 3) = -1, (1, 4) = 3, (2, 1) = 0, (2, 2) = 2, (2, 3) = 1, (2, 4) = 0, (3, 1) = -1, (3, 2) = 1, (3, 3) = 6, (3, 4) = -1, (4, 1) = 3, (4, 2) = 0, (4, 3) = -1, (4, 4) = 10})) . vk+(Matrix(4, 1, {(1, 1) = 0, (2, 1) = -2, (3, 1) = -1, (4, 1) = -1})) < 1/1000000

 

v0 := Matrix([[0], [1], [0], [0]])

Matrix(%id = 18446746512315172734)

(6)

g := proc (x) options operator, arrow; A.x+b end proc

proc (x) options operator, arrow; Typesetting:-delayDotProduct(A, x)+b end proc

(7)

alpha0 := solve(diff(f(v0-g(v0)*alpha)[1, 1], alpha) = 0)

1/10

(8)

v1 := v0-alpha0*g(v0)

Matrix(%id = 18446746512315163582)

(9)

v(k+1) := vk-`&alpha;k`*g(vk)

vk-`&alpha;k`*(Matrix(%id = 18446746512315154430).vk+Matrix(%id = 18446746512315153574))

(10)

`&alpha;k` := solve(diff(f(vk-g(vk)*alpha)[1, 1], alpha) = 0)

Hi, 
Essentially i am trying to programe an iterative loop where v(K+1) can be found fro v(K), I'm not sure how to programe a loop but I know this is not a hard thing to do so I am struggling, any help would be appreciated! Thanks. 
Edit: Also alpha K must be found at each stage by optimising f(v(k+1))
 

Download Optimisation_coursework.mw

Hello everyone!

I'm having some problem with this equation:

solve(0.1 = 23.714*(-0.93205)^2/(20.3+61.4*.884^x), x)

I'm trying to solve for x, but i keeps saying "Warning, solutions may have been lost."

Any ideas?
 

Hello,

What is the minimum period of the following equation.


 

d := evalf(expand((100+100*cos(6*t)+200*cos(12*sqrt(2)*t))^2))

40000.-2580480000.*cos(t)^2*cos(1.414213562*t)^6+604800000.*cos(t)^2*cos(1.414213562*t)^4-51840000.*cos(t)^2*cos(1.414213562*t)^2+2621440000.*cos(t)^6*cos(1.414213562*t)^12-7864320000.*cos(t)^6*cos(1.414213562*t)^10+8847360000.*cos(t)^6*cos(1.414213562*t)^8-4587520000.*cos(t)^6*cos(1.414213562*t)^6+1075200000.*cos(t)^6*cos(1.414213562*t)^4-92160000.*cos(t)^6*cos(1.414213562*t)^2-3932160000.*cos(t)^4*cos(1.414213562*t)^12+0.1179648000e11*cos(t)^4*cos(1.414213562*t)^10-0.1327104000e11*cos(t)^4*cos(1.414213562*t)^8+6881280000.*cos(t)^4*cos(1.414213562*t)^6-1612800000.*cos(t)^4*cos(1.414213562*t)^4+138240000.*cos(t)^4*cos(1.414213562*t)^2+1474560000.*cos(t)^2*cos(1.414213562*t)^12-4423680000.*cos(t)^2*cos(1.414213562*t)^10+4976640000.*cos(t)^2*cos(1.414213562*t)^8+720000.*cos(t)^2+274560000.*cos(1.414213562*t)^4-5125120000.*cos(1.414213562*t)^6+0.4942080000e11*cos(1.414213562*t)^8-0.2811494400e12*cos(1.414213562*t)^10+0.1013841920e13*cos(1.414213562*t)^12+0.1677721600e12*cos(1.414213562*t)^24-0.1006632960e13*cos(1.414213562*t)^22+0.2642411520e13*cos(1.414213562*t)^20-0.3984588800e13*cos(1.414213562*t)^18+0.3810263040e13*cos(1.414213562*t)^16-0.2406481920e13*cos(1.414213562*t)^14-5760000.*cos(1.414213562*t)^2+10240000.*cos(t)^12-30720000.*cos(t)^10+34560000.*cos(t)^8+1320000.*cos(t)^4-16000000.*cos(t)^6

(1)

``


 

Download period

 

 

When typing 

z:=exp(I*2*Pi/3);
convert(z,'sincos')

Maple evaluates the intermediate result which is cos(2*Pi/3)+I*sin(2*Pi/3) and  gives

Is there a way to tell it not to do this? I'd like to see the result as when typing

'cos(2*Pi/3)+I*sin(2*Pi/3)'

Is there an option or method to tell Maple not to immediate evaluation in the above? it can do evaluate next time the expression is used.

 


How to solve a system of partial equations with boundary conditions.I used this formula

restart;
sys_Pde := diff(V(x, t), x, x) = 0, diff(T(x, t), x, x) = 0;
          
BC := eval(diff(V(x, t), x), x = 1) = 0, eval(V(x, t), x = 0) = 1+cos(w*t), eval(T(x, t), x = 0) = 0, eval(T(x, t), x = 1) = 1;
pdsolve({sys_Pde});
   {T(x, t) = _F1(t) x + _F2(t), V(x, t) = _F3(t) x + _F4(t)}
pdsolve({BC, sys_Pde});


Error, (in PDEtools:-ToJet) found functions to be rewritten in jet notation, {V(1, t)}, having different dependency than the indicated in [V(x, t)]

 

I

have the following function phi(x,y) which depends on two unknown functions F1 and F2 which are differentiable.

Phi(x,y)=y sin(x y) + F1(y) + y^2 F2(x y)

Note that F1 and F2 are obtained by hand when I solve a partial differential equation

I would like to find  phi(x,y)  that satisfies phi=1 and diff(phi(x,y),y)=1-x^2*cos(x^2) on line y=x

 

constraint.mw

Thanks for your help

 

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