Arrays & Tensors
Continuum Mechanics   (Cabrera's short version)
Dirac Equation
Flat and Curved
Maxwell in Schwarzschild
Oblique Coordinates

Tensorial Packages

Tensorial is a general purpose tensor calculus package for Mathematica 5.0 or higher. Easy to learn and convenient for students and researchers. The authors are Renan Cabrera,  David Park, and Jean-François Gouyet. Some of the features of Tensorial  are:

• Complete freedom in choosing tensor labels, indices and base indices.
• Flavored (colored or annotated) indices for various coordinate systems.
• Differently flavor indices may have different dimensions and base index sets.
• Minimum keystroke tensor input and formatted output that can be copied and pasted.
• Detailed set of index manipulation routines.
• Easy routines for setting tensor values or rules and expanding tensor sums and arrays.
• Zero tensors balance free indices, behave like zero and expand to zero arrays.
• CircleTimes and dot product routines.
• Routines to declare and apply tensor and tensor expression symmetries.
• Kronecker, generalized Kronecker and Levi-Civita routines.
• Partial, covariant, total, absolute and Lie derivative routines.
• Christoffel, Riemann, Ricci, Einstein, Weyl and scalar curvature routines.
• Conversions from coordinate basis to orthonormal basis.
• Dot mode routines to convert from index notation to Mathematica array form calculations.
• Blends naturally with the normal Mathematica notebook interface and kernel routines.
• Customizable
• Complete documented Help with individual pages and examples for each command.

Tensorial 4 and TContinuumMechanics 2 were written up to 2006.
    The package TContinuumMechanics is devoted to the manipulation of tensors in the context of Continuum Mechanics problems.  TContinuumMechanics needs Mathematica (version 4 or higher) and Tensorial 4, the files have been divided into two parts: the program TContinuumMechanics (version 2.1) itself, and specific applications.
       The various functions created for the present purpose are shown in the link Package.
The main example of application TContinuumMechanics_Fluegge is composed of the twelve chapters of  the well known book of Wilhelm Flügge "Tensorial Analysis and Continuum Mechanics", Wilhelm Flügge, Springer, 1972. It shows how TContinuumMechanics 2.1 can be used in continuum mechanics problems. In this application, I closely followed Flügge's book all along the chapters, as it is to my opinion one of the clearest presentation of Continuum Mechanics using tensors extensively. It demonstrates how the Mathematica packages Tensorial and TContinuumMechanics permit to express in a very clear manner the tensorial structure of the equations of Continuum Mechanics.

Two new version have been written up to 2014 :  Tensorial 5 for the manipulation of tensors, and TContinuum Mechanics 3 for Continuum Mechanics teatments.

This site is structured as follows:

=> The Tensorial4 version and the TContinuumMechanics2 version (2006 versions) are

presented explicitly in pdf presentation. This allows the reader to see all the possibilities

and understand how these programs work.

=> In a second part, all the software necessary for the implementation of Tensorial 5 and

TContinuumMechanics 3 (2014 versions) are provided with free access and download,

where only the reference to the authors is requested.

=> Access to the various parts can be found here in the left column