Is it possible to determine an analytic solution to the following system of two differential equations for $A$ and $B$ using Maple.  My suspicion is that trial and error would find an analytic solution in theory and so that Maple could find the solution.  M is a constant and \sigma is some arbitrary function of t and the spatial coordinates. 

\[ \Bigg( \frac{\partial^2}{\partial x^2} + \frac{\partial^2}{\partial y^2} + \frac{\partial^2}{\partial z^2} + \frac{1}{2} \Bigg( 1 + \frac{M}{2 \sqrt{x^2 + y^2 + z^2}} \Bigg) \Bigg( \frac{\partial \sigma}{\partial x }\frac{\partial}{\partial x} +\frac{\partial \sigma}{\partial y}\frac{\partial}{\partial y} +\frac{\partial \sigma}{\partial z}\frac{\partial}{\partial z} \Bigg) \Bigg)B=0, \]

\[\frac{d A}{dt} = AB.\]

Furthermore, the boundary conditions are 

\[B \rightarrow -1  \: \text{as}  \: \sqrt{x^2 + y^2 + z^2} \rightarrow \infty,\]

\[A \rightarrow e^{-t} \: \text{as} \: \sqrt{x^2 + y^2 + z^2} \rightarrow \infty \]

System_of_Equations.pdf

Hi, I have this graph and i am trying to find a method that will only look at the second gradient change. I want it to adjust list A that it takes out the coordinates for the first gradient and the last 2. I have tried to find a way to make it work but i have no idea how to get maple to sense that there is a gradient change (basically i want to split the graph in 4 bits each of which contains a constant gradient if that makes sense!)

Dear Users!

Hope you would be fine. I have some problem in execution the last loops (highlighted as red) where sumation is present. When NN>3 it takes alot of time more than 12 hours. Is there any alternative command to reduce the query. I am waiting for your response. Thanks in advance. 

restart; with(LinearAlgebra); Digits := 30; NN := 2; nu := 1; M1 := NN; M2 := NN; M3 := NN;

for k1 from 0 while k1 <= M1-1 do for k2 from 0 while k2 <= M2-1 do for k3 from 0 while k3 <= M3-1 do

SGP[M3*(M2*k1+k2)+k3+1] := simplify(sum((-1)^(k1-i1)*GAMMA(k1+i1+2*nu)*x^i1*(sum((-1)^(k2-i2)*GAMMA(k2+i2+2*nu)*y^i2*(sum((-1)^(k3-i3)*GAMMA(k3+i3+2*nu)*z^i3/(GAMMA(i3+nu+1/2)*factorial(k3-i3)*factorial(i3)), i3 = 0 .. k3))/(GAMMA(i2+nu+1/2)*factorial(k2-i2)*factorial(i2)), i2 = 0 .. k2))/(GAMMA(i1+nu+1/2)*factorial(k1-i1)*factorial(i1)), i1 = 0 .. k1)) end do end do end do;

SGPxyz := `<,>`(seq(seq(seq(SGP[M3*(M2*(i-1)+j-1)+k], k = 1 .. M3), j = 1 .. M2), i = 1 .. M1));

Lambda := `<,>`(seq(seq(seq(chi[M3*(M2*(i-1)+j-1)+k], k = 1 .. M3), j = 1 .. M2), i = 1 .. M1));

for i while i <= NN^3 do for j while j <= NN^3 do for k while k <= NN^3 do

q[i, j, k] := int(int(int(SGP[i]*SGP[j]*SGP[k]*(-x^2+x)^(nu-1/2)*(-y^2+y)^(nu-1/2)*(-z^2+z)^(nu-1/2), z = 0 .. 1), y = 0 .. 1), x = 0 .. 1) end do end do end do;

U := Matrix(NN^3, NN^3, 0);

for j while j <= NN^3 do for k while k <= NN^3 do U[j, k] := simplify(sum(chi[i1]*q[i1, j, k], i1 = 1 .. NN^3)) end do end do;

F := simplify(evalm(U));

Special request to @acer @Carl Love @Kitonum @Preben Alsholm

Using library is very easy to plot the graph. But how to do this question by using spacecurve rather than the library

I do not quite understand why prof asks this question. Or I am doing right? Where can I improve? Or I understand this question completely wrong. To be honest, I did not get the point 

Why the least square of my calculation is different from the library. Where I am wrong? And how to plot this graph without the library? just use the function mentioned in the content

Hi,

I am struggling with an issue of the solutions produced by the "fsolve" command for a polynomial with multiple solutions. I am running the commands that are represented as follows:

f := x^2-x+0.25:

fsolve({f=0}, x=0..1);

It produces multiple solutions as follows:

{x = 0.5000000000}, {x = 0.5000000000}

What I am looking for is as follows:

1. Store multiple solutions separately.

2. For each solution, separate the variable "x=" and the numerical value "0.50000000". 

I would appreciate inputs from the team. 

Thank you,

Omkar

# uname -a

Linux p9x79 5.4.0-48-generic #52-Ubuntu SMP Thu Sep 10 10:58:49 UTC 2020 x86_64 x86_64 x86_64 GNU/Linux

I use X with TWM.

When minized, the maple icon is about 1/4" diameter.  How do I change this to a larger icon?

Hi, 

I'm trying to calculate the inner product of these two vectors. 

|a> = (1 + i) i, (1) j, (i) k

|b> = (4 - 1) i, (0) j, (2 -2i)k

where bold i, j, k, are the orthonormal bases. 

I can calculate it on paper, the problem I'm having is figuring out how to calculate it using maple. I want to be able to use dirac notation. I've tried using the physics library but none of the example use actual vectors but instead use quantum numbers. 

Thanks, 

Poiseuill's law: the formula is correct if both sides has the same dimension, so it is required that 

     [v]=[(P*R^m*nⁿ)/L]

find n and m that make the above equation dimensionally correct

It might seem like a small thing, but is there a way to separate the text from the numbers? It's only for optical purposes, as i think it looks better. 

Thank you,

MO

When I type the command

sum(2^n, n=0..N)

Maple calculates it correctly. However, if I then go back to that expression and click on it to change the value of N, Maple tries to execute something before I hit enter. It won't stop unless I press the Interrupt button, and after that I have to insert some other calculation, e.g. 1+1, for it to work once again.

This happens even on completely new files and for any explicit values of N.

Why is this happening?

Hello! I am trying to plot a parabola given by the equation x=y^2. I used the following code

plot(y^2, y = -1 .. 1, color = blue, thickness = 3, title = "T1.1 x=y^2 [ECE]")

but my plot looks like this

I want it to have the x-axis horizontally displayed and the y-axis to be vertically displayed. Something like this

Any advice? 

Thank you!

I think I am doing this question right. Is there anything to improve the code?