Elementary Functions and Equations. Fermat Last Theorem and Transformation of Geometrical Forms

The third revised version of the book introduces properties of elementary functions and equations with regard to their geometrical, physical and, in some instances, philosophical interpretation. The material shows when and how these functions can be used for developing adequate models of natural phenomena, systems and processes. The importance of relationships of mathematical concepts and constructs with geometry and physical reality is often underestimated, while we live in an inherently geometrical world. All our knowledge came from a 3-D space. Both fundamental concepts and examples of particular applications are presented, which can be used for modeling of different phenomena in diverse areas - physics, biology and others. The study of relationships of Fermat Last Theorem (FLT) with certain geometrical transformations, and an elementary proof of FLT, considered in the previous edition, received further development. The introduced geometrical concepts and methods can be used for other problems in number theory. The prerequisite for the material is a familiarity with the first year algebra and calculus.