Maple 2019 Questions and Posts

These are Posts and Questions associated with the product, Maple 2019

Dill_ABC_Model_PDE_System_Solution.mw

The attached Maple 2019  document attempts to solve a non-linear system of two coupled, time-dependent first-order PDE's, given a list of initial and boundary conditions.  The system models the optical transmittance through a thin photoresist layer whose transmittance changes upon exposure to the incident exposure energy, and hence, the cumulative transmittance through the layer is itself a function of both the exposure time and the distance traveled through the resist layer.  The list of fixed parameters, P, defines the characteristics of a particular photoresist (hereafter "pr") and an assumed exposure irradiance.

My first attempt towards a general solution without initial or boundary conditions (hereafter "ics" & "bcs") apparently "succeeds" (in that no error messages are thrown), however, the form of the solution is quite complicated and difficult (for me at least) to interpret.  I think I understand that the _Cn are undefined constants that require supplying ics & bcs to determine the solutions for the transmitted intensity I(z,t) & the normalized molar fraction of the photo-active component in the pr, M(z,t).  However I do not understand what the symbol _f refers to in the returned solutions.

I make a second attempt to solve the system numerically, supplying a list of the [ics,bcs] as arguments to Pdesolve, however the error message "Error, (in pdsolve/numeric/process_PDEs) PDEs can only contain dependent variables with direct dependence on the independent variables of the problem, got {Iota(0, t), Iota(z, 0), Mu(0, t), Mu(z, 0)}" raises the question of whether I have misunderstood the required syntax in using Pdesolve or that the system as posed is in fact insoluble by Maple.

I would appreciate any insights that readers of this post can contribute, as my experience using Maple and PDesolve in particular must be considered embryonic at best.

Scott Milligan

Hello all,

I am fairly new to Maple and would like to programatically simplify the output form using Maple's pade function on an arbitrary function: Y := 1/(R__s + 1/(s*C__dl + 1/(R__ct + 1/(sqrt(s)/sigma + 1/R__w))))
I found that only Maple's pade function was able to convert my function into a rational expression which is quite interesting.

Now I would like to replicate using maple what was manually done in steps 2 - 4 of the attached solution pdf (which was done by hand).

I was only able to do step 1 (as shown in the attached maple worksheet) after which I got stuck.

kindly assist

restart

with(numapprox)

[chebdeg, chebmult, chebpade, chebsort, chebyshev, confracform, hermite_pade, hornerform, infnorm, laurent, minimax, pade, remez]

(1)

s = I*omega

s = I*omega

(2)

Y := 1/(R__s+1/(s*C__dl+1/(R__ct+1/(sqrt(s)/sigma+1/R__w))))

1/(R__s+1/(s*C__dl+1/(R__ct+1/(s^(1/2)/sigma+1/R__w))))

(3)

padey := pade(Y, x = sqrt(s), [1, 1])

(C__dl*s^(3/2)*R__ct*R__w+C__dl*R__ct*s*sigma+C__dl*R__w*s*sigma+s^(1/2)*R__w+sigma)/(C__dl*s^(3/2)*R__ct*R__s*R__w+C__dl*R__ct*R__s*s*sigma+C__dl*R__s*R__w*s*sigma+s^(1/2)*R__ct*R__w+s^(1/2)*R__s*R__w+R__ct*sigma+R__s*sigma+sigma*R__w)

(4)

collect((C__dl*s^(3/2)*R__ct*R__w+C__dl*R__ct*s*sigma+C__dl*R__w*s*sigma+s^(1/2)*R__w+sigma)/(C__dl*s^(3/2)*R__ct*R__s*R__w+C__dl*R__ct*R__s*s*sigma+C__dl*R__s*R__w*s*sigma+s^(1/2)*R__ct*R__w+s^(1/2)*R__s*R__w+R__ct*sigma+R__s*sigma+sigma*R__w), s)

(C__dl*s^(3/2)*R__ct*R__w+(C__dl*R__ct*sigma+C__dl*R__w*sigma)*s+s^(1/2)*R__w+sigma)/(C__dl*s^(3/2)*R__ct*R__s*R__w+(C__dl*R__ct*R__s*sigma+C__dl*R__s*R__w*sigma)*s+(R__ct*R__w+R__s*R__w)*s^(1/2)+R__ct*sigma+R__s*sigma+sigma*R__w)

(5)

padey2 := collect((C__dl*s^(3/2)*R__ct*R__w+C__dl*R__ct*s*sigma+C__dl*R__w*s*sigma+s^(1/2)*R__w+sigma)/(C__dl*s^(3/2)*R__ct*R__s*R__w+C__dl*R__ct*R__s*s*sigma+C__dl*R__s*R__w*s*sigma+s^(1/2)*R__ct*R__w+s^(1/2)*R__s*R__w+R__ct*sigma+R__s*sigma+sigma*R__w), sigma)

((C__dl*R__ct*s+C__dl*R__w*s+1)*sigma+C__dl*s^(3/2)*R__ct*R__w+s^(1/2)*R__w)/((C__dl*R__ct*R__s*s+C__dl*R__s*R__w*s+R__ct+R__s+R__w)*sigma+C__dl*s^(3/2)*R__ct*R__s*R__w+s^(1/2)*R__ct*R__w+s^(1/2)*R__s*R__w)

(6)

Download maple_attempt.mw

solution.pdf

Hi All,

I solved a high degree polynomial equation for two variables and obtained a list of solutions as under:

{s = 0.01291429045, t = 0.06099359500}, {s = -0.6944124361, t = 0.8895072341}, {s = 0.3000821715, t = -0.06855860577}, {s = 0.1246366197, t = -0.06899397557}, {s = 43.29465387, t = -10.98020355}, {s = 7.400522990*10^6, t = -1.879497900*10^6}, {s = 7.442623977*10^6, t = -1.890190214*10^6}

In the second stage, I have to plug these solutions into another expression andsolve for second stage decision variables. However, I am only interested in the solutions where both s and t are non negative. How can I reduce the set to have a smaller subset?

Thanks for help

Hello everybody!

Im working on my great great (not great at all.. ) Dutch math book. Im really considering getting a copy of "Advanced Engineering Mathematics, by Robert Lopez". But hey, i worked through the first book, and now im at the half of the other second book. So i will finish it.

They left me with no clue on how to get the deal done, that is what is so perfect about this book i guess (i did a lot of books, but these Dutch books, yeah they do me like that) they will leave you in the dark, while they get all the grandeur because they know how to get it done, and you as the reader, well as a first timer, dont know how. Ive talked to a lot of students about this book. Yes it sucks. Classes full of students did agree on that, the majority did. So yeah, im trying to get a book delivered from the university library to a university libary closer to me, so i can get the book that does have good reviews.

The things i did learn from the Dutch math book did work great in statics and mechanics. That made short work of all the questions like a hot knife through butter.

THE ACTUAL QUESTION:
I cant prove this, because i dont know how. The translation says: a. Prove that the inverse of A exists for all values of p.

b. Determine the inverse of A

My take on it thusfar:

#Opdracht 9

#a.

with(LinearAlgebra)

A := `<,>`(`<|>`(1, 1, 1, 1), `<|>`(p, p+2, p+3, p+4), `<|>`(p^2, (p+2)^2, (p+3)^2, (p+4)^2), `<|>`(p^3, (p+2)^3, (p+3)^3, (p+4)^3))

Matrix(%id = 18446747008253355422)

(1)

``

``

``

#b.

B := MatrixInverse(A)

Matrix(%id = 18446747008306226350)

(2)

``

Thank you!

Greetings,

The Function

Download Mapleprimes_Question_Book_2_Paragraph_4.4_Question_9a.mw

Dear everyone,

Ive been looking at this problem ive got, but i cant find out what would make it work. I can put numbers in a matrix, i can solve 3 unknowns with 3 equations. But now there is a variable, and the variable causes the solution to give either: 1 solution, no solution, or more than one solution. 

I can "brush the matrix" as they say it in Dutch, but im learning Maple so it can go a lot faster than manual labor. So is there a way to do it with Maple? 

Figure 4.1 gives from left to right: 1 solution, no solution, and an indefinite amount of solutions.

Questions: For what value of p, a. gives 1 solution? b. gives no solution? c. gives more than 1 solution?

Now i got Maple to tell me how much p x1, x2, and x3 was, but its not bringing me anywhere to where i can get to a solution. 

A manual method is given in this example. Manual is way way to slow for what i need to achieve, ive got some large big books with mechanics, dynamics, statics, fluid mechanics, concrete calcutions, chemistry etc. waiting for me. I can never achieve that manually in the same time as i could do it with maple. :S 

#example of how to do a solve of a matrix with 3 variables:

stelsel := {x1+x2+x3 = 4, 3*x1+x2-5*x3 = -10, 3*x1+2*x2-x3 = 1}

{x1+x2+x3 = 4, 3*x1+x2-5*x3 = -10, 3*x1+2*x2-x3 = 1}

(1)

solve(stelsel, {x1, x2, x3})

{x1 = -7+3*x3, x2 = 11-4*x3, x3 = x3}

(2)

#now the example number 15

stelsel := {(2-p)*x2+x3 = 2, -x1+2*x2+(2-p)*x3 = 0, (1-p)*x1+2*x2+2*x3 = p+3}

{(2-p)*x2+x3 = 2, -x1+2*x2+(2-p)*x3 = 0, (1-p)*x1+2*x2+2*x3 = p+3}

(3)

solve(stelsel, {x1, x2, x3})

{x1 = -(p^2-6)/(p^2-4*p+4), x2 = -(2*p-5)/(p^2-4*p+4), x3 = 1/(-2+p)}

(4)

``

Thank you!

Greetings,

The Function

Download Mapleprimes_Question_Book_2_Paragraph_4.2_Example_15.mw

Hi
Can someone help me write the program for this equation?
I really need this program.
With respect

 

I hava a recursive formula with variable n. The answer has the variable n and also N1.  What doe N1 mean?

How_to_collect_Coefficent.mw

Kindly help me to find the coefficients from the equation. I have attached the MAPLE file here.

Thank You 

It may seem like a stupid question, but why is the first answer not complete, but the second imput is the same as what the book states?

I know you dont need to be able to read Dutch to understand that A = amplitude (amplitude), Omega = Hoekfrequentie (Angular frequency), and Varphi= Fasehoek (phase angle). 

They state that fc(0)= A*e^i*varpi, but it clearly shows that the equation on the left of the equal sign gives a "2" and on the right it gives "2+ 2*i*sqrt3".

Why is this so? It does not make things more easy if you can make "mistakes" like that by just asking the answer, but maple spits out half an answer... 

He thanks a lot guys!

Greetings,

The Function 

p.s.
I scanned my math books, i like it, i can search in the book now with the "ctrl+f" function in Adobe reader. Get a scanner. Mine is a Canon Lide 400. Not regretting it.. :) 
Download Mapleprimes_Book_2_Question_3.6.mw
 

omega := 5

5

(1)

`&varphi;` := (1/3)*Pi

(1/3)*Pi

(2)

A := 4

4

(3)

"f(t):=A*cos(omega*t+`&varphi;`)""+A*I*sin(omega*t+`&varphi;`)"
 

proc (t) options operator, arrow, function_assign; A*cos(omega*t+varphi) end proc

 

(4*I)*sin((1/3)*Pi+5*t)

(4)

f(0)

2

(5)

A*exp(I*`&varphi;`)

2+(2*I)*3^(1/2)

(6)

NULL

``

Download Mapleprimes_Book_2_Question_3.6.mw

What is the procedure to add global optima package in maple?

Dear power users, could someone be so kind to help me out with this file and give me some explanation on what I did wrong?

QuestionMaplePrimes.mw Thank you for you time and help

I am still learning Maple and so I would like to rely on you power users to help me out. I probably doing something which is not allowed or not using the best method. I would appreciate any advice. Thank you in advance    ProcQuestion.mw 

Fitting procedures in Maple are self explaning and easy to perform. However, I was wondering if it is possible to fit data vectors with units. For example one vector would have units of seconds and the other units of length. Thank you for your help.

Maple code for finding optimum maximum value of function TOTP given below when D is kept in the range of 300 to 2000?Also give maple code to find 3Dplot to determine the convexity of function TOTP with respect to y and Sr?

I want the resulting shape of the 3D matrix M (ٍExcel file) to be placed in below grids codes.
The range of x and y is between 0 and 1 and the range of z is 1/1 e-4 to 1/1 e-10.

PlotTest.xlsx


 

``

grids := proc (M, x_min, x_max, y_min, y_max) local z_min, z_max, plot_f, xz, yz, xy; z_min := 0.11e-6; z_max := 0.1e-2; plot_f := plot3d(M, x = x_min .. x_max, y = y_min .. y_max); xz := plot3d([x, y_min, z], x = x_min .. x_max, z = z_min .. z_max, style = line, color = blue, thickness = 0, grid = [6, 6]); yz := plot3d([x_min, y, z], y = y_min .. y_max, z = z_min .. z_max, style = line, color = blue, thickness = 0, grid = [6, 6]); xy := plot3d([x, y, z_min], x = x_min .. x_max, y = y_min .. y_max, style = line, color = blue, thickness = 0, grid = [6, 6]); return plots:-display(plot_f, xz, yz, xy, lightmodel = none, tickmarks = [6, 6, 6], labels = [x, y, "Error"], labeldirections = [horizontal, horizontal, vertical], axes = frame, orientation = [45, 70, 0], view = 0.11e-6 .. 0.1e-2) end proc

grids(M, 0, 1, 0, 1)

Warning, expecting only range variables [x, y] in expression M to be plotted but found name M

 

 

``

``


 

Download eeeeeee.mw

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