09 Differentiation

04 Mar 2021

Taking numerical derivatives is based on the elementary definition

\[\frac{dy(t)}{dt} := \lim_{h\rightarrow 0} \frac{y(t+h) - y(t)}{h}\]

We will then derive different finite difference approximations to the derivative and assess their error.

Class material

You can follow the lecture in the slides 09-differentiation-theory.ipynb.

For the problem that you should solve during the class, accept the GitHub Classroom Activity 11 via Canvas (or clone the repository ASU-CompMethodsPhysics-PHY494/Activity_11_differential_operators). The instructions are in the notebook differentiation.ipynb.

Additional resources

• Computational Physics: Ch 5.1 – 5.6
• If you are interested in integration then see the lectures on integration in 2016; this year we are skipping this part in favor of more in-depth programming exercises.