In-Jee Jeong

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These are questions asked by In-Jee Jeong


What I want is quite simple but I have not seen it implemented anywhere yet. 

I have an explicit map F from the plane into itself. (not an ODE but simply a map) 

Then I have a set X, (something like a line segment or a rectangle in the plane) for which I 

really need to keep track of the images $F(X), F^2(X), F^3(X)$, and so on.

Is there a way to plot the image of a set in Maple? 

Thank you very much for your interests in the question. 




I am solving a large system of ODEs, using the following command,

> Sol := dsolve({seq(ode[j], j = 0 .. 21), seq(v[j](0) = 0, j = 1 .. 21), v[0](0) = 1}, [seq(v[j](t), j = 0 .. 21)]);



and then plot the quantities I want by something like

> plots:-odeplot(Sol, [t, v[3](t)+v[5](t)], t = 0 .. 1.5);

My problem is that, I do not know a priori which quantity I want to plot, and plotting using above method requires solving the ODEs each time separately, which takes a long time.


So I was curious if there is a scheme that I can solve my system for once and for all, and then plot any quantities that I would like to see.

Let N be an integer. 


For each pair of integers (n,m) where 1<= n,m <= N, we have a variable f_{n,m}(t). 


Then for these we have a system of ODEs 


d/dt f_{n,m}(t) = \sum_{n', m'} f_m'n' * f_m''n'' * (m'n'' - m''n') 


where m''=m-m', n''=n=n', and the sum is simply over for all pairs (n',m'). 


I simply do not know how to put these set of equations into Maple in a nice way. 


I will really appreciate any help!

Hi, I want to define functions recursively... 

I don't know how to do it with the for loop in Maple.

I have a[0](t)=0, a[1](t)=t, and then some recursion connecting a[j+1](t) = f( a[j](t), a[j-1](t)) for some explicit function f. 

Then I want to plot the graph of a[N](t) as a function of t. 



I have numerically solved a system of ODEs and plotted the graphs of a[j](t) for each j=0..21.

It was clear from the picture that each a[j] has a unique zero. Is there a maple command to

locate these zeroes?

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