# Videos: summary and additional material

The story of the derivation of the finite element method is told once more in this section with a series of videos. 

## Derivation of the finite element formulation in 1D

Recap of the derivation of the finite element formulation for the 1D Poisson equation. 

```{eval-rst}
.. raw:: html

    <iframe width="560" height="315" src="https://www.youtube.com/embed/VNfRdJdcSKM" title="YouTube video player" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe>
```

## Elements and shape functions

Recap of the role of elements and shape functions in the finite element method. 

```{eval-rst}
.. raw:: html

    <iframe width="560" height="315" src="https://www.youtube.com/embed/pywJkVwAZJA" title="YouTube video player" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe>
```

## 2D derivation and boundary conditions

Derivation of the finite element method for the 2D Poisson equation. In the Friday project you will work with a 2D finite element implementation. 

```{eval-rst}
.. raw:: html

    <iframe width="560" height="315" src="https://www.youtube.com/embed/LO26k4ep8pg" title="YouTube video player" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe>
```

## Numerical integration

In the notebooks of this week, numerical integration is implemented in a rather direct way. This video presents a more general discussion of numerical integration for different elements. 

```{eval-rst}
.. raw:: html

    <iframe width="560" height="315" src="https://www.youtube.com/embed/XQY8i0e-jUA" title="YouTube video player" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe>
```

## Isoparametric mapping

To complete the story of how shape functions and numerical integration are usually implemented in notebooks, here is a video with additional material on isoparametric mapping.


```{eval-rst}
.. raw:: html

    <iframe width="560" height="315" src="https://www.youtube.com/embed/C_DtidjOPB4" title="YouTube video player" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe>
```

