6 Application and Educational Modules

The DLMF is envisioned not only as a basic resource for scientific professionals but also as a foundation for innovative, discipline-specific ``application modules'' that can, for example, eliminate some of the vexing variations that occur in the use of mathematical functions in different application areas. Some of these variations are merely notational but most are related to the fact that real-world applications involve physical constants, normalization conventions, and special conditions that have no place in a purely mathematical treatment. Since mathematical functions are intrinsic in so many different fields, no attempt can be made to cover all fields within the DLMF project. Thus the DLMF will contain only a very restricted set of illustrative examples that have a connection to an application area in chapters where it is appropriate. However, one of the outstanding benefits of a richly interactive and interlinked Web site is the opportunity it presents to construct associated Web sites that are tailored to specific application areas and discuss them in substantial detail. We expect that the DLMF will serve as the repository of core mathematical information for such Web sites. The DLMF project intends to provide two such application modules, in quantum mechanics and electomagnetic theory, as prototypes for others to consider.

The DLMF provides an opportunity to construct educational modules in exactly the same way, and a prototype in this field is being developed also. It will focus on mathematical functions that are introduced in high school, elaborated in university, and used in virtually all engineering and scientific applications. We expect that it will quickly become popular as an innovative learning resource for well-motivated high-school students, university students and technological professionals. It will provide an on-line tutorial with the ability to (i) search for and retrieve formulas and other information from the DLMF, (ii) generate computational results on demand, (iii) generate user-controlled graphics and visualizations on demand, (iv) check the correctness of exercises completed by the student, and (v) follow links to related Web sites.