Seeking Recommendations for an Ebook on Dynamical ...

I'm looking for a comprehensive ebook on mathematical modeling, specificaly focused on dynamical systems and how to use Maple for simulations and analysis. Does anyone have any recommendations for a good resource or textbook that covers these topics thoroughly?

How do i resolve my code which encountering error ...

i am trying to make code for automatic differentiation method. kindly help me out with that. i have asked chatgpt too. i am going to attach my file alongwith chatgpt code kindly help meautomatic_differentiation.mw

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 u_1 = -alpha*u[1]*(20*u[2]-20*u[0])+1600*u[0]-3200*u[1]+1600*u[2] u_2 = -alpha*u[2]*(20*u[3]-20*u[1])+1600*u[1]-3200*u[2]+1600*u[3] u_3 = -alpha*u[3]*(20*u[4]-20*u[2])+1600*u[2]-3200*u[3]+1600*u[4] u_4 = -alpha*u[4]*(20*u[5]-20*u[3])+1600*u[3]-3200*u[4]+1600*u[5] u_5 = -alpha*u[5]*(20*u[6]-20*u[4])+1600*u[4]-3200*u[5]+1600*u[6] u_6 = -alpha*u[6]*(20*u[7]-20*u[5])+1600*u[5]-3200*u[6]+1600*u[7] u_7 = -alpha*u[7]*(20*u[8]-20*u[6])+1600*u[6]-3200*u[7]+1600*u[8] u_8 = -alpha*u[8]*(20*u[9]-20*u[7])+1600*u[7]-3200*u[8]+1600*u[9] u_9 = -alpha*u[9]*(20*u[10]-20*u[8])+1600*u[8]-3200*u[9]+1600*u[10] u_10 = -alpha*u[10]*(20*u[11]-20*u[9])+1600*u[9]-3200*u[10]+1600*u[11] u_11 = -alpha*u[11]*(20*u[12]-20*u[10])+1600*u[10]-3200*u[11]+1600*u[12] u_12 = -alpha*u[12]*(20*u[13]-20*u[11])+1600*u[11]-3200*u[12]+1600*u[13] u_13 = -alpha*u[13]*(20*u[14]-20*u[12])+1600*u[12]-3200*u[13]+1600*u[14] u_14 = -alpha*u[14]*(20*u[15]-20*u[13])+1600*u[13]-3200*u[14]+1600*u[15] u_15 = -alpha*u[15]*(20*u[16]-20*u[14])+1600*u[14]-3200*u[15]+1600*u[16] u_16 = -alpha*u[16]*(20*u[17]-20*u[15])+1600*u[15]-3200*u[16]+1600*u[17] u_17 = -alpha*u[17]*(20*u[18]-20*u[16])+1600*u[16]-3200*u[17]+1600*u[18] u_18 = -alpha*u[18]*(20*u[19]-20*u[17])+1600*u[17]-3200*u[18]+1600*u[19] u_19 = -alpha*u[19]*(20*u[20]-20*u[18])+1600*u[18]-3200*u[19]+1600*u[20] u_20 = -alpha*u[20]*(20*u[21]-20*u[19])+1600*u[19]-3200*u[20]+1600*u[21] u_21 = -alpha*u[21]*(20*u[22]-20*u[20])+1600*u[20]-3200*u[21]+1600*u[22] u_22 = -alpha*u[22]*(20*u[23]-20*u[21])+1600*u[21]-3200*u[22]+1600*u[23] u_23 = -alpha*u[23]*(20*u[24]-20*u[22])+1600*u[22]-3200*u[23]+1600*u[24] u_24 = -alpha*u[24]*(20*u[25]-20*u[23])+1600*u[23]-3200*u[24]+1600*u[25] u_25 = -alpha*u[25]*(20*u[26]-20*u[24])+1600*u[24]-3200*u[25]+1600*u[26] u_26 = -alpha*u[26]*(20*u[27]-20*u[25])+1600*u[25]-3200*u[26]+1600*u[27] u_27 = -alpha*u[27]*(20*u[28]-20*u[26])+1600*u[26]-3200*u[27]+1600*u[28] u_28 = -alpha*u[28]*(20*u[29]-20*u[27])+1600*u[27]-3200*u[28]+1600*u[29] u_29 = -alpha*u[29]*(20*u[30]-20*u[28])+1600*u[28]-3200*u[29]+1600*u[30] u_30 = -alpha*u[30]*(20*u[31]-20*u[29])+1600*u[29]-3200*u[30]+1600*u[31] u_31 = -alpha*u[31]*(20*u[32]-20*u[30])+1600*u[30]-3200*u[31]+1600*u[32] u_32 = -alpha*u[32]*(20*u[33]-20*u[31])+1600*u[31]-3200*u[32]+1600*u[33] u_33 = -alpha*u[33]*(20*u[34]-20*u[32])+1600*u[32]-3200*u[33]+1600*u[34] u_34 = -alpha*u[34]*(20*u[35]-20*u[33])+1600*u[33]-3200*u[34]+1600*u[35] u_35 = -alpha*u[35]*(20*u[36]-20*u[34])+1600*u[34]-3200*u[35]+1600*u[36] u_36 = -alpha*u[36]*(20*u[37]-20*u[35])+1600*u[35]-3200*u[36]+1600*u[37] u_37 = -alpha*u[37]*(20*u[38]-20*u[36])+1600*u[36]-3200*u[37]+1600*u[38] u_38 = -alpha*u[38]*(20*u[39]-20*u[37])+1600*u[37]-3200*u[38]+1600*u[39] u_39 = -alpha*u[39]*(20*u[40]-20*u[38])+1600*u[38]-3200*u[39]+1600*u[40]
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resolve the issue

any one gets their Maple desktop become shuffled u...

I noticed very serious problem in Maple 2024.1

This is new windows 10  22H2  installation. With Maple 2024.1. I've only seen this using Maple and no other windows applications. I have 2 monitors and NVIDIA GeForce RTX 3060 graphics card.

What happens is that sometimes (may be 2-3 times each day), Maple frontend gets all mangled up. I could not figure what causes it. it could be when I move the window from one terminal to the other. sometimes it happens when I open a debugger window.

Only way to fix this is to close all of Maple and start it again.

Here is a movie. I use only worksheets. I have 3-4 open at the time.  When I move the mouse over the worksheet it keeps shuffling and duplicating as you see.

Just wondering if anyone seen anything like this and what can cause it. Again, it is only Maple that shows this problem, no other windows application does this. Have 128 GB Ram and PC is only 2 years old.

This is the very first time I see this in Maple and used Maple for long time and on this same PC before and had two terminals also before all the time. I have no idea what causes it.

Could it be Java problem in Maple 2024.1 ?

Why simplify is needed after limit?...

someone deleted my question or forum did.

Why is simplify needed to evaluate limit? Is this documented somewhere?

 > interface(version);

 > e:=-tanh(sqrt(2)*(a*x+b))

 > limit(e,x=0)

 > simplify(%);

 >

Why doesn't solve give any indication that there c...

I created the following worksheet to illustrate my question.

We have two equations.  and  are parameters and we wish to solve for  and .

=

=

=

Maple says the only solution is the trivial solution.

If we check the determinant of the matrix of the system we see it can be zero for certain values of  given .

=

=

 (1)

If  is one of these values then the system of equations is singular and has non-zero solutions.

For example, subbing the first value above into the equations and solving Maple gives us non-trivial solutions.

 (2)

Why didn't Maple give us any indication that there could be non-zero solutions in the first call to ?

For context, the system of equations comes from a calculation involving coupled oscillators.

I had a system of differential equations, guessed at a solution, plugged it in and got the equations shown in the worksheet. The guess isn't a correct solution in general, but it is a solution if w is one of the values computed in the worksheet (the values of the variable "solutions").

how to force maple to give final expression...

hw8.mw

I am struggling to find the answer how to force maple to give finakl answer and not some expression. Actually i am trying to solve for a

show variable in outcome ...

i have a generator function but in out come i have phi(p_1,p_2,p_3, so on )=** result is clear but this p_1 and p_2 in not shown i want to be shown in my outcome

generate_solution.mw

It happens from time to time that context menus do not appear. Normally, they appear at mouse-over (i.e. when the cursor is moved over an menu item).

Example: Right-click on input line

A Maple restart is required to get the normal behaviour back.

Recently I noticed that repeatedly clicking at different location on the menu item make the contex menus appear again.

This can be workarround if a restart is not acceptable.

It seems that the new Java IDE, which was introduced with Maple 2021, is more susceptible to this phenomen.

All on Windows 10.

Since this behaviour is rare I could not identify a clear pattern which system state or event could be responsible for the appearance of this phenomen.

I would be interested if someone else has observed it and found another solution how to get the menus back without restarting Maple.

internal error (in is/internal) type does not ex...

Any idea why calling solve(eqs,unknowns) gives Error, (in is/internal) type does not exist when the unknowns are in a set, but the error goes away when the unknowns are in a list? Is this expected or is this a bug?

 > interface(version);

 > Physics:-Version()

 > restart;
 > eqs:={0 = ln(2)+ln(-a*sech(1/2*2^(1/2)*b)^2), 1 = -tanh(1/2*2^(1/2)*b)*a^(1/2)*2^(1/2)}; unknown:={a, b};

 > solve(eqs,unknown)

Error, (in is/internal) type a does not exist

 > solve(eqs,unknown)

Error, (in is/internal) type a does not exist

 > restart;
 > eqs:=[0 = ln(2)+ln(-a*sech(1/2*2^(1/2)*b)^2), 1 = -tanh(1/2*2^(1/2)*b)*a^(1/2)*2^(1/2)]; unknown:={a, b};

 > solve(eqs,unknown)

Error, (in is/internal) type a does not exist

 > restart;
 > eqs:=[0 = ln(2)+ln(-a*sech(1/2*2^(1/2)*b)^2), 1 = -tanh(1/2*2^(1/2)*b)*a^(1/2)*2^(1/2)]; unknown:=[a, b];

 > solve(eqs,unknown)

 >

Update

Reported to Maplesoft support.

limit not evaluating...

Any idea why limit(e,x=0) fail to evaluate but  eval(e,x=0) does in this example?

 > interface(version);

 > Physics:-Version();

 > restart;
 > e:=-tanh(sqrt(2)*(a*x+b))

 > limit(e,x=0)

 > eval(e,x=0)

 >

I tried the above using some other software, and there both evaluate to same result as expected:

In Maple, I found that by removing the sqrt(2) from inside the tanh, then limit now works

e:=-tanh((a*x+b));
limit(e,x=0)


Is this a bug?

Turning points of 3d plane...

Dear all, I have the following issue:

Goal is to calculate saddle, turning point, etc.

As you can see in the code above only in case of a second restart x2 is calculated correctly.

Thanks for help.

I have created a document on my computer that runs normally in Maple 2024.1. However, when I upload this document to MaplePrimes, it shows an error or behaves unexpectedly. The document contains a system of differential equations, which I solved numerically and plotted, but the plots and equilibrium points do not display correctly after uploading.

When I run this code on my local machine, it works perfectly. However, after uploading the document to MaplePrimes, it does not run as expected. What could be causing this issue? Is there a known problem with Maple 2024.1 when uploading documents, or could there be a compatibility issue with MaplePrimes?

Any help or suggestions would be greatly appreciated. Thank you!

This project discusses the predator-prey system, particularly the Lotka-Volterra equations, which model the interaction between two species: prey and predators. Let's solve the Lotka-Volterra equations numerically and visualize the results.

 (1)

Now, we need to handle a modified version of the Lotka-Volterra equations. These modified equations incorporate logistic growth fot the prey population.

 (2)

Improving the performance in series summation...

Hello, I am trying to evaluate the following series (summing up to 100), but due to the binomial factor, the summation is very slow, can anybody suggest some better code to speed up the summation?

n1 = 423; x = 16; n2 = 81; y = 35; s1 = 0.1; b1 = 7; beta1 = 2.1;

Mysum := (r, xx, k, b, s, beta) -> b*beta^s*sum(sum(binomial(k - xx, j)*(-1)^(j + h)*GAMMA(s + h + 1)*(beta - 1)^h/(h!*(r + xx + b*s + j + b*h)), h = 0 .. 100), j = 0 .. k - x)/GAMMA(s);

Mysum(0, x, n1, b1, s1, beta1);

Combining standard font and Greek symbols in a plo...

I can't combine standard font and Greek symbols in a plot legend. I want to type:

"Limit of X_{i}^{\rho=0} (\alpha\mapsto+\infty)>0"

where I used LaTeX notation to emphasise that I want (1) superscript and subscript of X displayed as aligned exactly on top of each other, (2) rho, alpha, mapsto-style arrow, and infinity typed in their respective symbolic forms.

thanks!

why dsolve gives division by zero on this ode? ...

I do not have earlier Maple version to check now. But Maple 2024.1 gives division by zero on this second order ode with missing x. This looks like new problem in Maple. Would someone who have access to earlier version of Maple be able to check if this problem shows there also? I solved this and get y=x+3 as solution which Maple verifies.

 > interface(version);

 > restart;
 > ode:=diff(y(x),x\$2)=(diff(y(x),x))^3-(diff(y(x),x))^2; IC:=y(0)=3,D(y)(0)=1;

 > dsolve([ode,IC])

Error, (in dsolve) numeric exception: division by zero

 > sol:=y(x)=3+x; odetest(sol,[ode,IC])

 > infolevel[dsolve]:=5;

 > dsolve([ode,IC])

Methods for second order ODEs:

--- Trying classification methods ---

trying 2nd order Liouville

trying 2nd order WeierstrassP

trying 2nd order JacobiSN

differential order: 2; trying a linearization to 3rd order

--- trying a change of variables {x -> y(x), y(x) -> x}

differential order: 2; trying a linearization to 3rd order

trying 2nd order ODE linearizable_by_differentiation

trying 2nd order, 2 integrating factors of the form mu(x,y)

trying differential order: 2; missing variables

-> Computing canonical coordinates for the symmetry [0, 1]

-> Rewriting ODE in canonical coordinates by means of differential invariants

Try computing 1 more symmetries for ODE written in canonical coordinates

-> Computing symmetries using: way = 3

Found another symmetry:

Found another symmetry:

Computing a convenient ordering to use the 3 symmetries available

<- differential order: 2; canonical coordinates successful

<- differential order 2; missing variables successful

Error, (in dsolve) numeric exception: division by zero

 > dsolve(ode)

Methods for second order ODEs:

--- Trying classification methods ---

trying 2nd order Liouville

trying 2nd order WeierstrassP

trying 2nd order JacobiSN

differential order: 2; trying a linearization to 3rd order

--- trying a change of variables {x -> y(x), y(x) -> x}

differential order: 2; trying a linearization to 3rd order

trying 2nd order ODE linearizable_by_differentiation

trying 2nd order, 2 integrating factors of the form mu(x,y)

trying differential order: 2; missing variables

-> Computing canonical coordinates for the symmetry [0, 1]

-> Rewriting ODE in canonical coordinates by means of differential invariants

Try computing 1 more symmetries for ODE written in canonical coordinates

-> Computing symmetries using: way = 3

Found another symmetry:

Found another symmetry:

Computing a convenient ordering to use the 3 symmetries available

-> Calling odsolve with the ODE diff(_b(_a) _a) = _b(_a)^3-_b(_a)^2 _b(_a) HINT = [[1 0] [-_a+y -_b*(_b-1)]]

*** Sublevel 2 ***

symmetry methods on request

1st order, trying reduction of order with given symmetries:

1st order, trying the canonical coordinates of the invariance group

<- 1st order, canonical coordinates successful

<- differential order: 2; canonical coordinates successful

<- differential order 2; missing variables successful