Some Applications of Nonstandard Analysis to Advanced Undergraduate Mathematics -- Infinitesimal Modeling, Elementary Physics, Generalized Functions
|Author||Robert A Herrmann|
This 217 page book is constructed in a somewhat unusual manner. It is composed of three "manuals". In the first manual, the rigorous rules and procedures are presented and examples are given as to their use. With the exception of chapter 9, the actual proofs of the mathematical theorems that are so applied appear in a series of appendices. The second much smaller manual applies these rigorous methods to some areas in physics not covered in the first manual. Such things as an actual formal derivation of Newton's Second Law of motion from more fundamental observations is given. Certain methods used in physics that deal with the concept of point masses are shown to be incorrectly expressed in the language that appears in elementary texts and the proper concept is presented.
As an added feature, the third manual deals with a very significant concept within nonstandard analysis, not specifically identified previously, the enlargement and the saturation properties for a model. In order to give appropriate instruction in the use of such concepts, they are applied to the important scientific and mathematical subject known as generalized functions or distributions.