I wasn't able to reproduce your example with a constant μ1. Can you post that code ? 

I wasn't able to reproduce your example with a constant μ1. Can you post that code ? 

Sorry, please ignore what I said about the subs() in my first answer. However, there is a problem with those:

R1 := subs(w = w1, 2*Z0*(1-S21)/S21):

S21 is an expression involving R1, so this assignment is recursive and that's why you get those errors. The same applies to the next lines. I had a little look at the paper, but I don't know anything about the application. It does seem that there is a recurrance relation so perhaps you need to reformulate your code and use Maple's recurance equation solver rsolve()

Also, this doesn't do anything, as you don's assign it to anything

solve({2*Z0/sqrt(4*Z0+1/(wc*C1-1/(wc*L1))+1/(wc*C2-1/(wc*L2))) = 1/sqrt(2)}, {wc}):

Sorry, please ignore what I said about the subs() in my first answer. However, there is a problem with those:

R1 := subs(w = w1, 2*Z0*(1-S21)/S21):

S21 is an expression involving R1, so this assignment is recursive and that's why you get those errors. The same applies to the next lines. I had a little look at the paper, but I don't know anything about the application. It does seem that there is a recurrance relation so perhaps you need to reformulate your code and use Maple's recurance equation solver rsolve()

Also, this doesn't do anything, as you don's assign it to anything

solve({2*Z0/sqrt(4*Z0+1/(wc*C1-1/(wc*L1))+1/(wc*C2-1/(wc*L2))) = 1/sqrt(2)}, {wc}):

Thanks, roman_pearce, pagan and Markiyan Hirnyk

Thanks, roman_pearce, pagan and Markiyan Hirnyk

@pagan Thank you. That's very interesting !

@Markiyan Hirnyk Thanks for the code improvements and the linked reference :)

Personally I've never have any problems with MS Access either, but then I don't use it for things that are intensive - it's just a data repository for me. Without intimate knowledge of your data I can't really comment on your use of it; but I had the impression from your post above that you were just wanted to use it as data repository too. Anyway.....

The last time I used maple with database access I was checking some statistical analysis - it was around 5000 records I think; each record had around 10 columns. I really can't tell you how long it took but I was not consious of it taking an enormous time. Probably it was done before I could make a cup of coffee. 

Before spending money on a dedicated server, another possibility is to test it with a database in the cloud - I've been using a cloud for SQL Server for nearly a year now and they  gave me a free 14 day trial prior to sign up. If you can find one that is physically near you, and offeres this, and you have fast local internet then network bandwidth may not be a problem. And if network bandwidth is the limiting factor, then you also have some crude idea of a possible increase in speed if you had a dedicated database server at your site instead. 

@alex_01 Running SQL Server on your laptop is probably not a good idea, performance will definitely be sub-par. I've only ever run it on a machine dedicated to it. In my experience I didn't notice any significant difference in speed between loading data into Maple and loading it into excel from the database, though I can't give you any actual timings.  If you want to run the database on your laptop, have you considered using MS Access ? 

I am confused that you say "the databases them self did not handle the large amount of data very well" - I have a lot of experience with SQL Server and it is perfectly suited to handle large amounts of data (I don't really consider 10,000 records to be large). Of course, this assumes that the database schema has been designed with your usage patterns in mind along with appropriate views, stored procedures and triggers. Also, it goes without saying that the database needs to be running on appropriate hardware.

In that case, have you considered using a different underlying distribution for the positive reals, such as lognormal or gamma ? May I ask what data you are modelling ?

Edit: or a truncated normal distribution.

As per @Markiyan Hirnyk we need to be clear about what you are trying to achieve, so it would be helpful if you can write your formulas in Maple code or at least define the functions and variables you use. Personally I find the integrand difficult to understand; in particular, it may be a good idea not to use Pi as the name of one of the normal variables since the constant Pi is usually part of the PDF of a normal variate, so I don't know what you mean by Pi(Xi-Q) in the integrand.

@Pseudomodo Thanks, that's very useful. Are these things documented somewhere ?

@Pseudomodo Thanks, that's very useful. Are these things documented somewhere ?