Some comments

[hherlyng]

1. Add function expressions for the Lagrange element basis functions shown in "An introduction to the unified form language"? Would make it clearer that the planes in the figure "First order Lagrange basis functions" are spanned by the basis functions
2. When printing the basix tabulations, specify what the array values printed are? (if I understood correctly they are the function values of the basis functions in the tabulated points?)
3. In the introduction under "The computational domain" it says "For now, we don’t know if we are solving the Poisson equation on..." but the impression from the start is that we are to solve a projection problem?
4. The "Code generation" chapter begins with "All the code in the previous section is Python code symbolically describing the variational form of the projection. This is why we in FEniCS rely on code generation." It's not entirely clear why we need code generation, is it because the code is symbolic and we need to convert the code to something we can evaluate?
5. Transition from "Code generation" chapter to "Mesh generation" is somewhat abrupt, but you might be planning to add something? Would suffice to e.g. just add a comment to what is being printed when you're inspecting the introduction.c code.

[jorgensd]

1. Add function expressions for the Lagrange element basis functions shown in "An introduction to the unified form language"? Would make it clearer that the planes in the figure "First order Lagrange basis functions" are spanned by the basis functions

Will fix

2. When printing the basix tabulations, specify what the array values printed are? (if I understood correctly they are the function values of the basis functions in the tabulated points?)

Will add a slightly more verbose print

3. In the introduction under "The computational domain" it says "For now, we don’t know if we are solving the Poisson equation on..." but the impression from the start is that we are to solve a projection problem?

Remainder from when I was thinking about using Poisson as an example, will fix.

[jorgensd]

4. The "Code generation" chapter begins with "All the code in the previous section is Python code symbolically
   describing the variational form of the projection. This is why we in FEniCS rely on code generation." It's not entirely
   clear why we need code generation, is it because the code is symbolic and we need to convert the code to something > we can evaluate?

Will make a better justification/explaination

5. Transition from "Code generation" chapter to "Mesh generation" is somewhat abrupt, but you might be planning
   to add something? Would suffice to e.g. just add a comment to what is being printed when you're inspecting the
   introduction.c code.

Will think of a way of bridging the gap

[jorgensd]

@hherlyng do you mind revisiting these points?

1. Major refactoring of the tutorial has happened, introduction is way more basi(x)c now: http://jsdokken.com/FEniCS23-tutorial/src/introduction.html

2. Should be dealt with in the refactoring

3. Fixed

4. Tried to add some comments on why we need this.

5. This year the lecture is split in 2, this is where the second lecture will start.