## Chapter 4

Summary

You should be now familiar with the following topics:

- Define an
`Array`

, a `NekMatrix`

and a `PointsKey`

in *Nektar++*.
- Use the
`PointsManager`

with a `PointsKey`

to get hold of quadrature zeros and
differentiation matrices.
- Differentiate a polynomial function in the standard region ξ ∈ [-1,1] using
Gauss-Gauss-Legendre and Gauss-Lobatto-Legendre quadrature.
- Extend the standard region to a standard quadrilateral region.
- Introduce a linear mapping from a general quadrilateral region to the standard
quadrilateral region. Evaluate the Jacobian of this mapping and evaluate
derivatives in a general straight sided quadrilateral region.