Mathematica provides a unique capability for interactive learning. The possibility to combine program code and explanations in an interactive environment is well suited for teaching. The Chair of Microsystem Simulation at the University of Freiburg has developed a wide range of interactive simulation tutorials that have been distributed under the GNU Free Documentation License (FDL). The tutorials cover finite difference, finite volume and finite element methods, and multigrid and iterative solvers. Topics such as sparse matrices and derivatives recovery are also explained. Students are led through the topics assuming little or no prior knowledge. We found that the students gained a good understanding by experimenting with available parameters. In a subsequent step the tutorials are used for verifying other program code.