# Course lectures

These are the notebooks used during a xAct course at the Institute of Theoretical Physics, Charles University in Prague during the first term of 2018:

- Lecture 1. General description of xAct and some selected examples.
- Lecture 2. Introduction to the Wolfram Language.
- Lecture 3. xTensor and its data types: working with tensors and covariant derivatives. Canonicalization of tensorial expressions.
- Lecture 4. Working with a single and multiple metric tensors. Canonicalization of expressions with a metric tensor.
- Lecture 5. Canonicalization of expressions with covariant derivatives. Pattern indices.
- Lecture 6. Implementation of general tensorial rules.
- Lecture 7. Constant symbols, inert heads, parameters and scalar functions. Lie brackets and vector contraction of tensor slots.
- Lecture 8. The variational derivative. Working examples with the Einstein-Hilbert action (Palatini formalism), f(R) theory and Lovelock gravity.
- Lecture 9. The 1+3 decomposition. ADM formalism.
- Lecture 10. Main differential identities of a Killing vector. The Mars-Simon tensor in vacuum.
- Lecture 11. The conformal equations.
- Lecture 12. Component computations with xCoba. Storage of components: the tensor values framework and the CTensor container.
- Lecture 13. The containers CTensor and CCovD and their converters. The xCoba cache system.
- Lecture 14. Curvature computations with xCoba.

See also the file MetricConventions.pdf and the
slide show notebook on *xTerior*: xTeriorSlideShow.nb.