Differentiability has a very strange and counterintuitive definition, until you think about it with linear approximations in mind. Even better (and not covered in this comic), this definition of differentiability allows us to keep the beloved "differentiability implies continuity" result from single-variable calculus.

This definition of differentiability is known as Fréchet differentiability and is easily extended to vector spaces that are more generic than \(\mathbb{R}^n\) such as Banach spaces and Hilbert spaces.

The first two posts have been back-to-back since the comics were already completed. Our posting schedule is about to get more erratic since we'll publish as we go. Hopefully we can manage to post every two weeks or so!