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How do i best work with Polar vectors in Maple?...

Asked by: Mads758 10
vector polar vectorcalculus
June 18 2025
2  3

Hello,

I’m currently a student working with vectors as part of my electrical AC calculations. Up until now, I’ve been using GeoGebra to add and plot vectors, but I’m trying to transition fully to Maple, since I already use it for everything else in my studies.

All of my assignments are either given in — or require answers in — polar form (magnitude and angle), so I would really like to work directly in polar coordinates without converting everything to Cartesian and back.

I’ve already tried to figure this out on my own, but so far, I’ve only been able to make it work using Cartesian notation. I’ve attached a PDF with a typical example of the kind of tasks I work on, in case that helps clarify my needs.

Could you guide me on how to best set up and work with polar vectors in Maple — including how to define, add, and plot them directly in polar notation?

Vector_Help.pdf

Thanks in advance for your help!

Best regards,
Mads Bach Nielsen

- Yes this was written with the help of Chat GPT

ODE error in plots ...

Asked by: KIRAN SAJJAN 40
ode dsolve numeric
June 17 2025
0  13

why this error is getting. but in the published paper for the same parameter it is converging. what is the mistake in this worksheet please rectify it in sachin_base_paper.mw

Where is the "Stop Execution" icon?...

Asked by: WD0HHU 40
interrupt gui duplicate-question
June 17 2025
0  1

Maple 2024 had a very well defined "Stop Execution" symbol on the desktop.  

Maple 2025 doesn't have an obvious symbol somewhere.  Also, the two little "dots" that I once had in the lower left bottom in Maple 2025 have disappeared! There is only a bar at the bottom which seems to do nothing.

there is anyway for making fast the loop?...

Asked by: salim-barzani 1560
performance simplification conjugate
June 17 2025
2  4

i need a way for making my loop working fast, i need something for calculating such term fast without showing result but thus term make a lot of time for coming out ?

fasting.mw

substitute equation to equation...

Asked by: ashy 35
substitution incomplete-question
June 17 2025
0  4

I want to substitute equation to equation, how?

Download r.mw

Computation of left and right eigenvectors...

Asked by: Elisha 50
bifurcation eigenvector
June 17 2025
0  0

Someone should please help me compute the left and right eigenvectors of the system below. The purpose is to compute values for 'a' and 'b' in the bifurcation formula.

Thank you

``

> 

with(VectorCalculus)

 

 (1)
> 

interface(imaginaryunit = I)

I

 (2)
> 

I

I

 (3)
 
> 

diff(S(t), t) := `Λ__p`-(`#mrow(mi("ϕ",fontstyle = "normal"),mo("⋅"),msub(mi("θ",fontstyle = "normal"),mi("B")),mo("⋅"),msub(mi("I"),mi("B")))`/N[p]+µ__C)*S+`ω__B`*I__B

Lambda__p-(`#mrow(mi("ϕ",fontstyle = "normal"),mo("⋅"),msub(mi("θ",fontstyle = "normal"),mi("B")),mo("⋅"),msub(mi("I"),mi("B")))`/N[p]+µ__C)*S+omega__B*I__B

 (4)
> 

diff(I__B(t), t) := `#mrow(mi("ϕ",fontstyle = "normal"),mo("⋅"),msub(mi("θ",fontstyle = "normal"),mi("B")),mo("⋅"),msub(mi("I"),mi("B")))`*S/N[p]-`ω__B`*I__B-(`σ__B`+µ__C)*I__B

`#mrow(mi("ϕ",fontstyle = "normal"),mo("⋅"),msub(mi("θ",fontstyle = "normal"),mi("B")),mo("⋅"),msub(mi("I"),mi("B")))`*S/N[p]-omega__B*I__B-(sigma__B+µ__C)*I__B

 (5)
> 

NULL

``

 (6)
> 

diff(S__A(t), t) := `Λ__A`-(µ__A+`#mrow(mi("ϕ",fontstyle = "normal"),mo("⋅"),msub(mi("α",fontstyle = "normal"),mi("B")),mo("⋅"),msub(mi("I"),mi("B")))`/N[p])*S__A+`δ__A`*I__A

Lambda__A-(µ__A+`#mrow(mi("ϕ",fontstyle = "normal"),mo("⋅"),msub(mi("α",fontstyle = "normal"),mi("B")),mo("⋅"),msub(mi("I"),mi("B")))`/N[p])*S__A+delta__A*I__A

 (7)
> 

diff(I__A(t), t) := `#mrow(mi("ϕ",fontstyle = "normal"),mo("⋅"),msub(mi("α",fontstyle = "normal"),mi("B")),mo("⋅"),msub(mi("I"),mi("B")))`*S__A/N[p]-(µ__A+`δ__A`)*I__A

`#mrow(mi("ϕ",fontstyle = "normal"),mo("⋅"),msub(mi("α",fontstyle = "normal"),mi("B")),mo("⋅"),msub(mi("I"),mi("B")))`*S__A/N[p]-(µ__A+delta__A)*I__A

 (8)
> 

NULL

``

 (9)

Download CBD2.mw

remove the parentheses (for the dᵢ values)...

Asked by: jalal 435
table typesetting task
June 17 2025
0  6

Hi,

I’m trying to remove the parentheses (for the dᵢ values) to achieve optimal display. Ideas ? Thanks

S4_Droites_Implicite.mw

Problem with dsolve()...

Asked by: Rouben Rostamian 8506
ode dsolve differential-equations
June 16 2025
2  14

A colleage asked me for the solution of an elementary boundary value problem for an ODE that models the steady-state temperature distribution in a nonhomogeneous rod.  I solved it in Maple and passed the solution on to her without checking the result.  She struggled for a day or two, attempting to "debug" her finite element code whose result was not agreeing with Maple's.

Upon closer inspection, it turned out that her code was correct and the solution returned by Maple was not.  Here are the details.  I can't tell whether Maple's dsolve can be improved to provide correct solutions to this and similar problems.

Problem with dsolve()

> 

restart;
> 

kernelopts(version);

`Maple 2025.0, X86 64 LINUX, Mar 24 2025, Build ID 1909157`

A boundary value problem for an ODE

 

Let's solve the following boundary value problem:

> 

de := Diff(a(x)*Diff(u(x),x),x) = -1;

Diff(a(x)*(Diff(u(x), x)), x) = -1

> 

bc := u(-1)=0, u(1)=0;

u(-1) = 0, u(1) = 0

Maple's dsolve() fails to find a solution:

> 

dsolve({de,bc});

> 

 

Solution obtained by hand

 

The solution may be obtained by hand, as follows.

 

Integrate the DE once

a(x)*(diff(u(x), x)) = c-x.

where c is the integration constant.  Therefore

diff(u(x), x) = (c-x)/a(x) and (c-x)/a(x) = c/a(x)-x/a(x).

To determine the value of the constant c, integrate the above over [-1, 1]

and apply the boundary conditions:

c*(int(1/a(x), x = -1 .. 1))+int(x/a(x), x = -1 .. 1) = u(1)-u(-1) and u(1)-u(-1) = 0

whence
c = (int(x/a(x), x = -1 .. 1))/(int(1/a(x), x = -1 .. 1)).

Having thus determined c, we integrate the expression for diff(u(x), x) obtained above, and arrive at the solution
u(x) = int((c-xi)/a(xi), xi = -1 .. x).

Remark: The solution obtained here is valid for any a(x) as long as

the integrals encountered above make sense.  Note that there is
no requirement on the differentiability or even continuity of a(x).

Technically, a(x) can be any function such that 1/a(x) is integrable.

 

> 

 

Wrong solution returned by dsolve()

 

Let us consider a special choice of the coefficient a(x):

> 

a := x -> 1 + 2*Heaviside(x);

proc (x) options operator, arrow; 1+2*Heaviside(x) end proc

According the the calculations above, we have:

> 

c := int(x/a(x),x=-1..1) / int(1/a(x),x=-1..1) ;

-1/4

and therefore the correct solution is

> 

int((c-xi)/a(xi), xi=-1..x):
sol := u(x) = collect(%, Heaviside);

u(x) = ((1/6)*x+(1/3)*x^2)*Heaviside(x)-(1/4)*x-(1/2)*x^2+1/4

Here is what the solution looks like:

> 

plot(rhs(sol), x=-1..1, color=blue, thickness=3);

Let's attempt to solve the same boundary value problem with Maple's dsolve().

> 

dsolve({de,bc}):
bad_sol := collect(%, Heaviside);

u(x) = ((1/3)*x^2+x/(3*exp(-2)+3)-exp(-2)*x/(3*exp(-2)+3))*Heaviside(x)-(1/2)*x^2-x/(3*exp(-2)+3)+(3*exp(-2)+1)/(6*exp(-2)+6)

That's very different from the correct solution obtained above.   To see the problem with it, let's recall that according to the DE, the expression a(x)*(diff(u(x), x))NULLshould evaluate to  c-x for some constant c,  but what we get through bad_sol is nothing like c-x;  in fact, it's not even continuous:

> 

a(x)*diff(rhs(bad_sol), x):
collect(%, Heaviside, simplify);
plot(%, x = -0.5 .. 0.5);

((4*x-2)*exp(-2)+4*x+2)*Heaviside(x)^2/(3*exp(-2)+3)+(-(4/3)*x-1/3)*Heaviside(x)-x-1/(3*exp(-2)+3)

It appears that dsolve goes astray by attempting to expand the expression diff(a(x)*(diff(u(x), x)), x).   It shouldn't.

 

 

Download dsolve-bug.mw

 

How do i print an index of integrals?...

Asked by: paulmcquad 105
integration education student
June 14 2025
1  3

Hi.

So I get this ->

int(x^2, x = 0 .. a)

(1/3)*a^3

 (1)

NULL


But i would like this ->

Download 5.3-Definite-Integral.mw

 

And maybe something similar for indefinite integrals.

This would really help me with education in calculus so thanks everybody.

Mapleflow worksheets in Maple 2025...

Asked by: Christopher2222 6030
worksheet
June 14 2025
0  2

It would appear being able to run Mapleflow worksheets in Maple is only useful to those who have Mapleflow.

Just wondering without being able to see what variables are in the mapleflow worksheet how would I know what values to pass to it?

What does this sum result mean?...

Asked by: paulmcquad 105
sum symbolic summation
June 14 2025
1  1

Hi.

I have been learning Integration for calculus. I came about on output that i not know what it means.

See for yourself. ->
If anyone can help make this mess.

Thanks in advance.

sum((-2)^j/(j-2)^2, j = 3 .. n)

4*polylog(2, -2)+2^(n+1)*(1+(-2*n^2+4*n-2)*LerchPhi(-2, 2, n))*(-1)^n/(-1+n)^2

 (1)

NULL

Download ex5sigma.mw

there is anyway to export the table from maple to ...

Asked by: salim-barzani 1560
table matrix latex
June 13 2025
0  1

i want to do export  the table to latex there is command to do?

table.mw

How do I shrink the "useless" white area...

Asked by: rlewis 40
worksheet animation 3d
June 13 2025
1  5

In the screen shot below taken from a 3D animation I want to vastly shrink the area I have stippled with spots (it's actually white on the worksheet).  It's outside the cube defining the 3D animation and inside the square that defines the part of the worksheet used for an image.

How make it error be small in iteration and how a...

Asked by: salim-barzani 1560
June 13 2025
0  4

in my iteration when i got answer the error is so big and the method is powerfull i don't know i did mistake or my exact function i have to change it, becuase error is so big , how i can make error be smaller i did any mistake ?
and how i can plot them together exact and approximate in one graph also 3D and 2D

Num-e1.mw

How to simplify an exponential expression into hy...

Asked by: Ahmed111 135
simplify simplification approximation
June 13 2025
1  2

I am working with a symbolic expression in Maple that combines exponential terms. How can exponential terms be fully converted into hyperbolic functions? 

> 

restart
> 

with(Student[Precalculus])
> 

interface(showassumed = 0)
> 

assume(x::real); assume(t::real); assume(lambda1::complex); assume(lambda2::complex); assume(a::real); assume(A__c::real); assume(B1::real); assume(B2::real); assume(delta1::real); assume(delta2::real); assume(`ω__0`::real); assume(g::real); assume(l__0::real)
> 

expr := A__c*exp(-(2*I)*(A__c^2*g*l__0^2-1/2)*`ω__0`*t)+(2*I)*exp(-I*(A__c^2*g*l__0^2-1/2)*`ω__0`*t)*(sqrt(delta1+I*delta2-sqrt(-A__c^2*g+(delta1+I*delta2)^2))*exp(-2*sqrt(-A__c^2*g+(delta1+I*delta2)^2)*(l__0^2*(I*delta1-delta2)*t*`ω__0`+(1/2)*x))-sqrt(delta1+I*delta2+sqrt(-A__c^2*g+(delta1+I*delta2)^2))*exp(sqrt(-A__c^2*g+(delta1+I*delta2)^2)*(x+(2*I)*`ω__0`*l__0^2*(delta1+I*delta2)*t)))*(sqrt(-delta1+I*delta2-sqrt(-A__c^2*g+(delta1-I*delta2)^2))*exp((2*(l__0^2*(I*delta1+delta2)*t*`ω__0`-(1/2)*x))*sqrt(-A__c^2*g+(delta1-I*delta2)^2))-sqrt(-delta1+I*delta2+sqrt(-A__c^2*g+(delta1-I*delta2)^2))*exp(-(2*(l__0^2*(I*delta1+delta2)*t*`ω__0`-(1/2)*x))*sqrt(-A__c^2*g+(delta1-I*delta2)^2)))*delta2/(exp(I*(A__c^2*g*l__0^2-1/2)*`ω__0`*t)*(((-sqrt(delta1+I*delta2-sqrt(-A__c^2*g+(delta1+I*delta2)^2))*sqrt(-delta1+I*delta2+sqrt(-A__c^2*g+(delta1-I*delta2)^2))-sqrt(delta1+I*delta2+sqrt(-A__c^2*g+(delta1+I*delta2)^2))*sqrt(-delta1+I*delta2-sqrt(-A__c^2*g+(delta1-I*delta2)^2)))*exp((2*(l__0^2*(I*delta1+delta2)*t*`ω__0`-(1/2)*x))*sqrt(-A__c^2*g+(delta1-I*delta2)^2))+exp(-(2*(l__0^2*(I*delta1+delta2)*t*`ω__0`-(1/2)*x))*sqrt(-A__c^2*g+(delta1-I*delta2)^2))*(sqrt(delta1+I*delta2-sqrt(-A__c^2*g+(delta1+I*delta2)^2))*sqrt(-delta1+I*delta2-sqrt(-A__c^2*g+(delta1-I*delta2)^2))+sqrt(-delta1+I*delta2+sqrt(-A__c^2*g+(delta1-I*delta2)^2))*sqrt(delta1+I*delta2+sqrt(-A__c^2*g+(delta1+I*delta2)^2))))*exp(-2*sqrt(-A__c^2*g+(delta1+I*delta2)^2)*(l__0^2*(I*delta1-delta2)*t*`ω__0`+(1/2)*x))+exp(sqrt(-A__c^2*g+(delta1+I*delta2)^2)*(x+(2*I)*`ω__0`*l__0^2*(delta1+I*delta2)*t))*((sqrt(delta1+I*delta2-sqrt(-A__c^2*g+(delta1+I*delta2)^2))*sqrt(-delta1+I*delta2-sqrt(-A__c^2*g+(delta1-I*delta2)^2))+sqrt(-delta1+I*delta2+sqrt(-A__c^2*g+(delta1-I*delta2)^2))*sqrt(delta1+I*delta2+sqrt(-A__c^2*g+(delta1+I*delta2)^2)))*exp((2*(l__0^2*(I*delta1+delta2)*t*`ω__0`-(1/2)*x))*sqrt(-A__c^2*g+(delta1-I*delta2)^2))-exp(-(2*(l__0^2*(I*delta1+delta2)*t*`ω__0`-(1/2)*x))*sqrt(-A__c^2*g+(delta1-I*delta2)^2))*(sqrt(delta1+I*delta2-sqrt(-A__c^2*g+(delta1+I*delta2)^2))*sqrt(-delta1+I*delta2+sqrt(-A__c^2*g+(delta1-I*delta2)^2))+sqrt(delta1+I*delta2+sqrt(-A__c^2*g+(delta1+I*delta2)^2))*sqrt(-delta1+I*delta2-sqrt(-A__c^2*g+(delta1-I*delta2)^2)))))*(-delta1+I*delta2)*(delta1+I*delta2))

A__c*exp(-(2*I)*(A__c^2*g*l__0^2-1/2)*omega__0*t)+(2*I)*exp(-I*(A__c^2*g*l__0^2-1/2)*omega__0*t)*((delta1+I*delta2-(-A__c^2*g+(delta1+I*delta2)^2)^(1/2))^(1/2)*exp(-2*(-A__c^2*g+(delta1+I*delta2)^2)^(1/2)*(l__0^2*(I*delta1-delta2)*t*omega__0+(1/2)*x))-(delta1+I*delta2+(-A__c^2*g+(delta1+I*delta2)^2)^(1/2))^(1/2)*exp((-A__c^2*g+(delta1+I*delta2)^2)^(1/2)*(x+(2*I)*omega__0*l__0^2*(delta1+I*delta2)*t)))*((-delta1+I*delta2-(-A__c^2*g+(delta1-I*delta2)^2)^(1/2))^(1/2)*exp(2*(l__0^2*(I*delta1+delta2)*t*omega__0-(1/2)*x)*(-A__c^2*g+(delta1-I*delta2)^2)^(1/2))-(-delta1+I*delta2+(-A__c^2*g+(delta1-I*delta2)^2)^(1/2))^(1/2)*exp(-2*(l__0^2*(I*delta1+delta2)*t*omega__0-(1/2)*x)*(-A__c^2*g+(delta1-I*delta2)^2)^(1/2)))*delta2/(exp(I*(A__c^2*g*l__0^2-1/2)*omega__0*t)*(((-(delta1+I*delta2-(-A__c^2*g+(delta1+I*delta2)^2)^(1/2))^(1/2)*(-delta1+I*delta2+(-A__c^2*g+(delta1-I*delta2)^2)^(1/2))^(1/2)-(delta1+I*delta2+(-A__c^2*g+(delta1+I*delta2)^2)^(1/2))^(1/2)*(-delta1+I*delta2-(-A__c^2*g+(delta1-I*delta2)^2)^(1/2))^(1/2))*exp(2*(l__0^2*(I*delta1+delta2)*t*omega__0-(1/2)*x)*(-A__c^2*g+(delta1-I*delta2)^2)^(1/2))+exp(-2*(l__0^2*(I*delta1+delta2)*t*omega__0-(1/2)*x)*(-A__c^2*g+(delta1-I*delta2)^2)^(1/2))*((delta1+I*delta2-(-A__c^2*g+(delta1+I*delta2)^2)^(1/2))^(1/2)*(-delta1+I*delta2-(-A__c^2*g+(delta1-I*delta2)^2)^(1/2))^(1/2)+(-delta1+I*delta2+(-A__c^2*g+(delta1-I*delta2)^2)^(1/2))^(1/2)*(delta1+I*delta2+(-A__c^2*g+(delta1+I*delta2)^2)^(1/2))^(1/2)))*exp(-2*(-A__c^2*g+(delta1+I*delta2)^2)^(1/2)*(l__0^2*(I*delta1-delta2)*t*omega__0+(1/2)*x))+exp((-A__c^2*g+(delta1+I*delta2)^2)^(1/2)*(x+(2*I)*omega__0*l__0^2*(delta1+I*delta2)*t))*(((delta1+I*delta2-(-A__c^2*g+(delta1+I*delta2)^2)^(1/2))^(1/2)*(-delta1+I*delta2-(-A__c^2*g+(delta1-I*delta2)^2)^(1/2))^(1/2)+(-delta1+I*delta2+(-A__c^2*g+(delta1-I*delta2)^2)^(1/2))^(1/2)*(delta1+I*delta2+(-A__c^2*g+(delta1+I*delta2)^2)^(1/2))^(1/2))*exp(2*(l__0^2*(I*delta1+delta2)*t*omega__0-(1/2)*x)*(-A__c^2*g+(delta1-I*delta2)^2)^(1/2))-exp(-2*(l__0^2*(I*delta1+delta2)*t*omega__0-(1/2)*x)*(-A__c^2*g+(delta1-I*delta2)^2)^(1/2))*((delta1+I*delta2-(-A__c^2*g+(delta1+I*delta2)^2)^(1/2))^(1/2)*(-delta1+I*delta2+(-A__c^2*g+(delta1-I*delta2)^2)^(1/2))^(1/2)+(delta1+I*delta2+(-A__c^2*g+(delta1+I*delta2)^2)^(1/2))^(1/2)*(-delta1+I*delta2-(-A__c^2*g+(delta1-I*delta2)^2)^(1/2))^(1/2))))*(-delta1+I*delta2)*(delta1+I*delta2))

 (1)

NULL

Download simplify.mw

  1. Further simplify the expression under three physical scenarios, assuming delta__1 > 0:

    • Case (i): When A__c = 0

    • Case (ii): When delta__1 > g * A__c

    • Case (iii): When delta__1 < g * A__c

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