MaplePrimes Questions

I am trying to solve these equation using fsolve, but it returns the same valve. Please provide a solution.\

Please see the attachment. 

Hi, with Units[Simple] package loaded, I tried to differentiate a few functions using D[n] but it does not work. problem.mw

a := proc (x, y) options operator, arrow; exp(x*y) end proc

proc (x, y) options operator, arrow; exp(y*x) end proc

(1)

D[1](a)

proc (x, y) options operator, arrow; y*exp(y*x) end proc

(2)

D[2](a)

proc (x, y) options operator, arrow; x*exp(y*x) end proc

(3)

retart

retart

(4)

"with(Units[Simple]):"

a := proc (x, y) options operator, arrow; exp(x*y) end proc

proc (x, y) options operator, arrow; Units:-Simple:-exp(Units:-Simple:-`*`(x, y)) end proc

(5)

D[1](a)

Error, (in tools/gensym) too many levels of recursion

 

D[2](a)

Error, (in tools/gensym) too many levels of recursion

 

NULL

Download problem.mw

Hi! I've got a set of subsets S with Abeing the i-subset. I need to sum up all the x's in all the Ai's. How can this be achieved?

(ex):

sum( { {a, b, c}, {a, b, d} } )= 2a+2b+c+d

Hey I’m trying to define the antiderivative for a function:

g(x) = 1

G(x) = int(g(x),x)

When I then type:

G(x) and press enter Maple gives me G(x) = x which of course is correct

But I can’t type:

G(5)

Then it gives me the error message:

Error, (in int) integration range or variable must be specified in the second argument, got 5

How to fix this?

I know I can type G(x) = x manually but I’m not interested in doing so, because in my document I’m going to have a lot of antiderivatives.

Thanks in advance.

I have a student who then she uses tools/assistent/import data and then the file then Maple claims the Excel file is empty? She uses Maple 2021.2. File works on other my and other student computers. 

I would like to perform the following expansion up to an arbitrary order. The dots refer to higher-order terms. All the coefficients are symmetric except for the first one.

Thank you very much!

To Maple support:

I was investigating this pde from a different forum.

I noticed that when using an expanded version of the pde, Maple hangs. Without expanding the PDE, Maple gives an answer in 2 seconds. 

Why does expanding the PDE makes a difference? I do not have an earlier version of Maple on my new PC to check if this is a new issue or not.
 

interface(version);

`Standard Worksheet Interface, Maple 2022.0, Windows 10, March 8 2022 Build ID 1599809`

Physics:-Version()

`The "Physics Updates" version in the MapleCloud is 1230 and is the same as the version installed in this computer, created 2022, April 21, 9:8 hours Pacific Time.`

restart;
pde1:=VectorCalculus:-Laplacian(u(r,theta),'polar'[r,theta]);
pde1_expanded:=expand(pde1);
bc  := u(1,theta)=sin(theta)^4,u(3,theta)=1;
pdsolve([pde1=0,bc],u(r,theta))
 

(diff(u(r, theta), r)+r*(diff(diff(u(r, theta), r), r))+(diff(diff(u(r, theta), theta), theta))/r)/r

(diff(u(r, theta), r))/r+diff(diff(u(r, theta), r), r)+(diff(diff(u(r, theta), theta), theta))/r^2

u(1, theta) = sin(theta)^4, u(3, theta) = 1

u(r, theta) = (1/52480)*((328*r^6-26568*r^2)*ln(3)*cos(2*theta)+(-r^8+6561)*ln(3)*cos(4*theta)+19680*(ln(3)+(5/3)*ln(r))*r^4)/(ln(3)*r^4)

pdsolve([pde1_expanded=0,bc],u(r,theta)); #HANGS, Waited more than 40 minutes.

 


 

Download hangs_pde.mw

DirectSearch finds nonexisting roots....     DirectSearch_finds_nonexisting_roots.mw

 

restart

plot([cos(x), 0.001*x*x],x=-40..40,y=0..2)     ### test function plot

 

eq:= cos(x)= 0.001*x*x;     ###   float

cos(x) = 0.1e-2*x^2

(1)

use RealDomain in solve(eq,x,explicit) end use   ## lacking some of the roots

-7.793210110, 7.793210110, -11.11953559, 11.11953559, -4.734809278, 4.734809278, -1.568336644, 1.568336644

(2)

use RealDomain in solve(eq,x) end use

-7.793210110, 7.793210110, -11.11953559, 11.11953559, -4.734809278, 4.734809278, -1.568336644, 1.568336644

(3)

fsolve(eq,x=-30)

-31.17938383

(4)

plot([cos(x), 0.001*x*x],x=-32..-31,y=0.9..1)

 

fsolve(eq,x=-32..-30);  fsolve(eq,x=-31.7..-31.4)

-31.17938383

 

-31.52634294

(5)

with(DirectSearch)

[BoundedObjective, CompromiseProgramming, DataFit, ExponentialWeightedSum, GlobalOptima, GlobalSearch, Minimax, ModifiedTchebycheff, Search, SolveEquations, WeightedProduct, WeightedSum]

(6)

eq;
SolveEquations(eq,AllSolutions):

cos(x) = 0.1e-2*x^2

(7)

interface(rtablesize=90);
SolveEquations(eq, AllSolutions)

90

 

Matrix(%id = 4800942722)

(8)

DirectSearch finds nonexisting roots!!!

Dr. Ali GÜZEL

 

Download DirectSearch_finds_nonexisting_roots.mw

Hello!

How do I get the plot of P(t) and C(t) and also a table with the values of P(t) for each t? Itried but I couldn't...

``

restart; beta := 0.7e-2; Lambda := 0.2e-4; `ρ__o` := 0.3e-2; lambda := 0.8e-1; h := 0.1e-1; n := 100

Error,

restart; beta := 0.7e-2; Lambda := 0.2e-4; `ρ__o` := 0.3e-2; lambda := 0.8e-1; h := 0.1e-1; n := 100

 

for i from 0 to n-1 do P[i+1] := (1+h*(`ρ__o`-beta)/Lambda)*P(i)+h*lambda*C(i); C[i+1] := h*beta*P(i)/Lambda+(-h*lambda+1)*C(i) end do:

seq(i, i = 0 .. 30); seq(P[i], i = 0 .. 30)

Error,

seq(i, i = 0 .. 30); seq(P[i], i = 0 .. 30)

 

with(plots); with(DEtools); p1 := plot([P(t)], t = 0 .. 100, [[P(0) = 1]], scene = [t, P(t)], thickness = 2, linecolor = red, stepsize = .1); p2 := plot([C(T)], t = 0 .. 100, [[C(0) = beta/(Lambda*lambda)]], scene = [t, C(t)], thickness = 2, linecolor = red, stepsize = .1); display([p1, p2])

``

Download System_Recursive_Equations.mw

Thank!!!

Dear all

How can I add more terms, in taylor approximation of odes. 

Attached the code well written for only second order approximatiom, how can i get the fourth order approximation in taylor expansion to approximate an IVP

taylor_fourth_order.mw

thank you

Backspacing at the end of a few math containers on one row will shift them upwards beyond the top screen out of view and out of existence.  Your last chance of retrieval is when you can still see the bottom half portions of the letters/equations before you need to go to the first point and press enter to bring them down.  Once they're out of view, there's no chance to bring back what you wrote - the assignments are still valid.  Also note CRTL-Z will not bring them back. 

This worksheet displays an intersection between two spheres based on a test which seems unrelated to the display.

How can this be explained?

Intersecting_spheres.mw

Using the hide command after displaying a plot in MapleFlow2022 prevents that plot from being moved.

If you create another plot, then both plots are movable until you use the hide command again, at which point you need to create another plot to allow plots to be positioned.

Hello,

I am writing an arrow procedure and will like to know if there is a way to implement the following 
 

bj := (G, y) ->  (`@`(seq((t -> u -> v -> G(u, t) - v)(args[1 + nargs - i]), i = 1 .. nargs - 2)))(y)
bj(F, y, a, b, c, d);
v:=[p, q, r, s]
the output

My question is, how can I replace the v with each element of the list to get the following as output
F(F(F(F(y,a)-p),b)-q,c)-r,d)-s

Aany suggestion will be highly appreciated

 

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