@vshyam But I am still curious to know: Do you have an integral for which Maple's default quadrature routines failed? Perhaps some tweaking of the optional parameters to Int is all that is needed. See ?int,numeric.

Could you show me an example of using the command Inverse? What packages do you have loaded? Show me an example that indicates to you that it is some sort of approximation to MatrixInverse.

MatrixInverse on a 4x4 totally symbolic matrix takes 125 milliseconds on my computer.

To avoid confusion for other readers, you should say if you have the Physics package loaded, or perhaps some other package that changes the behaviour of diff. Your subs command would certainly not work with the ordinary diff.

@vshyam Did Maple's default quadratures not work on your problem? Is this the same integral as we discussed in your "Fsolve in an integral" Question from last week?

Let me know if you need higher precision and/or higher speed. I could make some small adjustments for both.

@vshyam Did Maple's default quadratures not work on your problem? Is this the same integral as we discussed in your "Fsolve in an integral" Question from last week?

Let me know if you need higher precision and/or higher speed. I could make some small adjustments for both.

@Paul 4.33 seems close to 4.49. How close is it when measured in standard deviations?

I would guess that they have not used the same batting order in every game.

It would be interesting to run the model for all the teams---just for their current lineups, not all permuations---and compare with actual performance. That would give some credence to the validity of the Markov model. I'd make a rough guesstimate that if a majority of teams come within 1/2 a standard deviation of actual performance, then the model is good.

The baseball data is probably available for free download online. Access to that could be built right into the worksheet.

If the boundary condition f(1) = 0 is changed to f(1) = c, and then you test out various values of c, dsolve seems to have serious objections to any value of c less than about 0.485. Changing option values abserr or maxmesh doesn't seem to help. So, are you sure about f(1) = 0?

@emma hassan In your colleague's code, A is the band matrix. In your code, A is a vector, and B is the band matrix. You need to multiply either

(row vector) . matrix = (new row vector)

or

matrix . (column vector) = (new column vector)

And the left-right order of those products matters! To switch a row vector to a column vector, use Transpose, or a shortcut is to use %T as an exponent.

@emma hassan In your colleague's code, A is the band matrix. In your code, A is a vector, and B is the band matrix. You need to multiply either

(row vector) . matrix = (new row vector)

or

matrix . (column vector) = (new column vector)

And the left-right order of those products matters! To switch a row vector to a column vector, use Transpose, or a shortcut is to use %T as an exponent.

@Preben Alsholm Thank you, Preben, for the memory jog. I've updated the main Answer to incorporate your suggestion.

@Preben Alsholm Thank you, Preben, for the memory jog. I've updated the main Answer to incorporate your suggestion.

@vshyam Wikipedia and crowd-sourcing are great.

Are you trying some special numerical integration that Maple can't otherwise handle? Or are you just studying the method?

@vshyam Wikipedia and crowd-sourcing are great.

Are you trying some special numerical integration that Maple can't otherwise handle? Or are you just studying the method?

Note that Maple does allow for an empty Matrix, Matrix(0,0) or simply Matrix(), whose determinant is 1. So you don't need to treat n = 0 as a separate case.

Note that Maple does allow for an empty Matrix, Matrix(0,0) or simply Matrix(), whose determinant is 1. So you don't need to treat n = 0 as a separate case.