Georgiev S.G. Foundations of Iso-Differential Calculus (vol. 2)

Nova Science Publishers, 2014. — 215 p.This book introduces the main ideas and the fundamental methods of the iso-differential calculus for the iso-functions of several variables.
In Chapter 1 are discussed the structure of the iso-Euclidean spaces, the main conceptions for the iso-functions of the first, the second, the third, the fourth and the fifth kind of n - variables, limits of the iso-real iso-valued iso-functions of several variables, the continuous iso-functions, the main ideas for the iso-partial derivatives of the first, the second, the third, the fourth, the fifth, the sixth and the seventh kind of the iso-functions of several variables, they are introduced the main approaches for the finding of the minima and the maxima of the iso-functions of n variables.
In Chapter 2 are represented some of the most relevant results of the iso-integration theory. The aim is to provide the reader with all that is needed to use the power of the iso-integration.
In Chapter 3 we deal with the line and the surface iso-integrals.
Chapter 4 provides a sufficiently wide introduction to the theory of the iso-Fourier integral.
Chapter 5 is dedicated to some conceptions connected with the iso-Hilbert spaces. They are defined some classes of iso-operators in the iso-Hilbert spaces and given some of their properties.
In Chapter 6 is given a definition for the Santilli-Lie-isotopic power series and they are deducted some of its properties.
I think, in fact, that it is useful for the reader to have a wide spectrum of context in which these ideas play an important role and wherein even the technical and formal aspects play a role. However, I have tried to keep the same spirit, always providing examples and exercises to clarify the main presentation.