Hi,

I would be really grateful if someone can help me in solving the below attached problem in maple.

Thanks in advance.

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January 10 2021

1
1

Hi,

I would be really grateful if someone can help me in solving the below attached problem in maple.

Thanks in advance.

Plot the wedge cut from the cylinder x²+y²=1 by the planes z=-y and z=0.

December 30 2020

2
1

Hey everyone,

f_1 and f_2 are satisfying the set of non-linear integral equations I have attached to this message.

I know that I need to solve them numerically by iterations. Probably, the first guest of the function f_1 and f_2 is the driving term. a is just a parameter which can be fixed (I guess smaller than \pi/4). * is the convolution product and k is the momentum space parameter. I learnt that in order to solve them I should solve them in the Fourier space. I know also that I need to discretize these function in the “real ” space between {-L,+L} before applying the FFT or one of its relatives. Thank you for any suggestions or leads.

December 27 2020

0
2

Hi,

I noticed that, in Maple 2020.2, the caracters seem smaller. As if the zoom had somewhat been reduced (a bit).

However, in the preferences, the default zoom level I would like is between 100 and 125% (something like 110%) (since the default zoom level is adjusted by steps of +/- 25%). I wondered if there was a way to set the default zoom level to an arbitrary value. In fact I thought it would be great to have a field instead of a list of choices, so we can choose a custom value.

Thank you

December 23 2020

0
18

Here is my try to integrate the expression L with trapozoid or simpson

December 18 2020

1
0

restart; V:=x->piecewise(0<=x and x<=a,0,infinity): ic:=f(x,0)=piecewise(0<=x and x<=a,A*x*(a-x),0): pde :=I*h*diff(f(x,t),t)=-h^2/(2*m)*diff(f(x,t),x$2) +V(x)*f(x,t): sol:=pdsolve([pde,ic],f(x,t)) assuming a>0; Latex(sol)

gives

f \! \left(x , t\right) = \left(\left\{\begin{array}{cc}A x \left(a -x \right) & 0\le x \le a \\0 & \mathit{otherwise} \end{array}\right.\right)+\left(\Mapleoverset{\infty}{\Mapleunderset{n =1}{\textcolor{gray}{\sum }}}\! \frac{t^{n} \left(\textbf{proc} (U) \\ \textbf{option} \,operator,\,arrow; \\ \mapleIndent{1} r-1 st I \ast (-1/2 \ast h\hat{~}{2} \ast m\hat{~}{-1} \ast \mathit{diff} (\mathit{diff} (U,\,x),\,x) + \mathit{piecewise} (0&lex \, \textbf{and} \, x&lea,\,0,\,infinity) \ast U) \ast h\hat{~}{-1}\\ \textbf{end\ proc};\right)^{\left(n \right)}\! \left(\left\{\begin{array}{cc}A x \left(a -x \right) & 0\le x \le a \\0 & \mathit{otherwise} \end{array}\right.\right)}{n !}\right)

Notice, non-printable characters. I think it should have been **\ast **there but it gives ** st**

Maple 2020.2 and Physics 897.

FYI, this is what latex() command gives

latex(sol) f \left( x,t \right) = \begin{cases}Ax \left( a-x \right) & 0\leq x \land x\leq a\\0 & \text{otherwise}\end{cases} +\sum _{n=1}^{\infty }{\frac {{t}^{n} \left( U\mapsto {\frac {-i \begin{cases}0 & 0\leq x \land x\leq a\\\infty & \text{otherwise}\end{cases} U}{h}}^{ \left( n \right) } \right) \left( \begin{cases}Ax \left( a-x \right) & 0\leq x \land x\leq a\\0 & \text{otherwise}\end{cases} \right) }{n!}}

Which compiles with no problem

\documentclass[11pt]{article} \usepackage{amsmath} \begin{document} \[ f \left( x,t \right) = \begin{cases}Ax \left( a-x \right) & 0\leq x \land x\leq a\\0 & \text{otherwise}\end{cases} +\sum _{n=1}^{\infty }{\frac {{t}^{n} \left( U\mapsto {\frac {-i \begin{cases}0 & 0\leq x \land x\leq a\\\infty & \text{otherwise}\end{cases} U}{h}}^{ \left( n \right) } \right) \left( \begin{cases}Ax \left( a-x \right) & 0\leq x \land x\leq a\\0 & \text{otherwise}\end{cases} \right) }{n!}} \] \end{document}

Thank you

December 15 2020

0
0

Dear all

I have Lie commutations for vectors e1, e2, e3, e4, e5, e6 as follow:

[e1, e3] = e3, [e1, e4] = e4, [e1, e5] = e5, [e1, e6] = e6, [e2, e3] = -e5, [e2, e4] = e6, [e3, e5] = e6

for which the command

Query("Jacobi")

returns the false result, which means, the vectors are not closed under Jacobi's identity. How can I find vector triplets for which Jacobi's identity does not hold?

Please find Maple file.Jacobi_identity.mw

Dear all,

I have a time-fractional PDE as follows. ( denotes Caputo fractional derivative with respect to t)

**for alpha=1**, this is **a classical PDE **and the exact solution is given as follows (in a book)

**Question: **

**1) for alpha=1**, I want to find the L2 errors and L∞ errors in a table.

**2) for alpha=0.5**,** **Can Maple find a solution (numeric or exact)?

**MY TRY: (MAPLE 2020.2)**

restart: with(plots): PDE:=diff(y(x,t),t)=y(x,t)*diff(y(x,t),x$3)+y(x,t)*diff(y(x,t),x)+3*diff(y(x,t),x)*diff(y(x,t),x$2) ; #c is an arbitratry constant c:=4: exact_sol:=(x,t)->-8*c/3*(cos ((x-c*t)/4))^2; # I selected initial and boundary conditions as follows IBC := { y(x,0)=exact_sol(x,0),y(0,t)=exact_sol(0,t),D[1](y)(0,t)=D[1](exact_sol)(0,t),y(1,t)=exact_sol(1,t)}; numeric_sol := pdsolve(PDE,IBC,numeric); num3d:=numeric_sol:-plot3d(t=0..1,x=0..1,axes=boxed, color=[0,0,y]); exact3d:=plot3d(exact_sol(x,t),t=0..1,x=0..1,axes=boxed); display(exact3d,num3d); pdetest(y(x,t)=exact_sol(x,t),PDE,IBC);

December 15 2020

0
0

Hi

I have a system of pde that it is solved with pdsolve procedure.

This procedure takes a few time, but when I need to do plots, especially 3d plot the software takes a lot of time (several hours).

How can I make plots faster?

Thanks.

December 13 2020

3
7

It's been about a year since I've been able to display *any* worksheet at all on MaplePrimes. In the example below, I took a very simple worksheet that had been displayed in an Answer to another recent Question and tried to upload it. So, we know that it's *somehow* possible to display this particular worksheet on MaplePrimes.

Maple Worksheet - Error

Failed to load the worksheet **/maplenet/convert/prove.mw **.

Download prove.mw

December 11 2020

1
0

Given a metric, to compute quantities in the NP formalism one needs to specify a null tetrad. In the various examples in the help pages, sometimes the tetrad is specified simply as a list of 4 vectors, e.g., NT := [...] and sometimes evalDG is applied as in NT := evalDG({...]). Using the first format, Maple accepted NT as argument in NPSpinCoefficients but NPCurvatureScalars(SpinCoefficients,NT) complained that the second argument wasn't a list of four vectors. When I used the second format, both commands returned the expected results. Why the difference?

December 11 2020

0
0

I am facing difficulty to realize this double iterative process.

The equations in question are