1 Summary

The MATH2 upper-level math package is a group of basic tools for standard numerical calculations that are frequently used in geophysical fluid dynamic studies. Regrettably, it is only partially complete at the present, and much more work is needed.

Many of the packages corresponding to MATH2 can be acquired as source codes from existing software, such as IMSL^1.1, NAG ^1.2, and Numerical Recipes^1.3. However, these source codes do not necessarily have the precision required by researchers in the geophysical fluid dynamic field. Furthermore, many of the above have the setback of not being a Public Domain Software (PDS), and so their source codes cannot be incorporated into and freely distributed as part of original software developed by researchers.

The goal of the MATH2 package is to independently develop or to extract from the PDS, the tools for the following calculations.

Basic scheme for differential calculation
Fourier transformation
Expansion and inversion of orthogonal spherical functions
Coordinate transformations
Basic statistical analysis package
Special functions
Eigenvalue problems
...