Lean Programming Language

A Theorem-Proving Language

https://lean-lang.org/

AI & Mathematics Research

https://www.quantamagazine.org/the-ai-revolution-in-math-has-arrived-20260413/

Free Microsoft eBooks

"Introducing Windows Server 2012" @ http://blogs.msdn.com/b/microsoft_press/archive/2012/06/04/free-ebook-introducing-windows-server-2012.aspx "Introducing MS SQL Server 2012" @ http://www.microsoft.com/sqlserver/en/us/default.aspx

SpaceTime 3.0

Check out this neat mathematics software for PC, MAC, and mobile devices called SpaceTime @ http://www.spacetime.us/windows/.

It is available on Windows, LINUX, Pocket PC, MAC, Smart Phones etc.

Price is right too: $10 to $ 30!

Data Analysis Software for Excel

Crystal Ball v. 7.3 enables Monte Carlo simulation and analysis with MS Excel spreadsheets. It enables the creation of scatter plots, displays correlations, dependencies, and other relationships between pairs of forecasts and assumptions plotted against each other.

Find it @ http://www.decisioneering.com/.

Solver for Partial Differential Equations

FlexPDE is a scripted finite element model builder and numerical solver. The software is available @ http://www.flexpde.com/sdmenu5.html

and a Student License @ http://www.flexpde.com/student5.html

and sample books @ http://www.flexpde.com/bookstore.html


Consider solving the following PDE problem with the specified boundary conditions:


You have to develop the script first.

FlexPDE equations must be second order or less in space and first order or less in time, so one has to split this equation into a system of three equations:

w: dt(w)=u
v: dxx(w)=v
u: EI*dxx(v)+rho*A*dt(u)=0

Now for the boundary conditions

w=0 is a boundary condition on w,
dxx(w)=0 is boundary condition on v,
dxx(w)=M/EI is boundary condition on v,

and

EI*dx(v)=EI*dxxx(w)=F is the natural BC for the u equation.