If you're into science or design engineering, you should probably check out Elmer. Among a host of other great applications, this free, Finland-born software can help you design airplanes, predict the temperature distribution of a heat exchanger, and do your quantum mechanics homework.
At its core, Elmer is an open source finite element solver of partial differential equations. Development of Elmer began in 1995 as a collaboration between Finnish universities, research institutes and private industry, and was primarily developed by Finland's CSC IT Center for Science. Elmer was released as open source in 2005. According to the Elmer FAQ page, Elmer has hundreds of regular users worldwide and thousands of Elmer test users annually.
Click here for a 3-minute video introduction to Elmer.
Elmer processes partial differential equations in a descrete form, and handles coupled systems, non-linearities, and time-dependencies. The Elmer GUI allows the user to either import meshes or create simple ones in a variety of file types, and generates output in .grd, .mesh, and .ep files. The source code of Elmer is written in Fortran 90, C, and C++, and is distributed under the GNU Public License (GPL). The Elmer source code is here on sourceforge.
Here is a 10-minute Elmer tutorial from Elmer's YouTube Channel.
Thank you, Finland. It appears that your song needs a new verse.