__Analytical derivatives (what you learned in calculus)__

- Interpreting a derivative (notes from Lamar University)
- Review example on calculating analytical derivatives. More information on formal method from UC Davis is here. Analytical derivatives shortcuts discussed here and here. Online analytical derivative calculator here.

__Numerical derivatives__

- Definition
- Numerical differentiation and an advection example
- Numerical derivatives by grid point dimensions (called stencils in numerical analysis nomenclature)
- Table of 1st, 2nd, 3rd, and 4th-order derivatives by stencil points, centered, forward, and backwards
- Richardson extrapolation
- Computing derivatives with unevenly spaced data
- Supplementary material - Additional material from Oregon State
- Supplementary material - Youtube lecture from Waterloo University

__Online calculator__

__Spreadsheet examples__

- Documentation on spreadsheet exercises
- Basic example, centered difference
- On titration data
- Using polynomial fit (for unevenly spaced data)
- VBA example, Part 1
- VBA example,Part 2

__Miscellaneous numerical derivative routines from computer languages__

- Matlab example, derivatives
- Matlab gradient example on vectors
- Mathematica language
- R language
- maple language
- Compute gradients from gridded meteorology data using ncl. a. gradsf b. grad_latlon_cfd c. gradsg
- FORTRAN -- derivatives on equally spaced data.
- FORTRAN -- derivative on three-point Lagranian.

__Recorded lectures__