## Video clips

This page provides video clips that are used in our courses to provide explanations and examples on using and installing Grind, performing algebra with free parameters, sketching functions and nullclines, and interpreting Tilman diagrams. Several videos come with an accompaning pdf (the script) providing background information. Do read these scripts (they are better than the videos).

## Grind

For using and installing Grind we provide 3 videos:

- The video grind.mp4 shows how one can open grind.R into RStudio and use RStudio to open and analyze a model.
- The video installGrind.mp4 shows how one can install grind.R and the 3 required libraries into RStudio.
- Finally, the video with.mp4 explains the "with" statement that is used in Grind models. This video on "with" comes with a short script.pdf.

## Algebra

We provide a set of videos explaining how one can solve equations composed of free parameters (i.e., equations using letters rather than numbers). The videos are backed up by the following script.pdf:

- The video algebra1.mp4 provides an introduction and a simple example.
- The video algebra2.mp4 shows how to solve a system of linear equations.
- The video algebra3.mp4 provides an simple example for solving a system of quadratic equations.
- The video algebra4.mp4 shows how to solve a general system of quadratic equations.
- The video algebra5.mp4 shows how to work with ratios.
- The video algebra6.mp4 illustrates basic rules for powers, radicals, and logarithms.

## Sketching functions

We provide a set of video how to sketch non-linear functions composed of free parameters (i.e., equations using letters rather than numbers). The videos are backed up by the following script.pdf:

- The video sketch1.mp4 provides an introduction and a simple example.
- The video sketch2.mp4 shows how to sketch exponential functions.
- The video sketch3.mp4 shows how to sketch third order functions.
- The video sketch4.mp4 shows how to sketch rational functions (i.e., a Hill function)
- The video sketch5.mp4 is the next episode of sketch4.mp4
- The video sketch6.mp4 shows how to sketch a function with a slanted asymptote.
- The video sketch7.mp4 shows some examples of optimum functions.

## Nullclines and phase plane analysis

We provide two examples where we sketch the nullclines and the vector field of 2-dimensional ODE models. The videos are backed up by the following script.pdf:

- The video null1.mp4 shows how to sketch the phase space of the Lotka-Volterra model.
- The video null2.mp4 shows how to sketch the phase space of a model with non-linear nullclines.

## Tilman diagrams

Intersection points of nullclines in a Tilman diagram need not correspond to steady states. These videos explain how to establish whether or not such an intersection point is a steady state, and whether or not it is expected to be stable. The videos are backed up by the following script.pdf:

- The video tilman1.mp4 shows how one sketches consumer nullclines in a phase space of resources.
- The video tilman2.mp4 shows how one sketches impact vectors around the intersection points of the nullclines.
- The video tilman3.mp4 computes Routh Horwitz criteria to show that the dominant eigenvalue is negative.
- The video tilman4.mp4 adds conversion parameters to show that the steady state can also be unstable.