Bøger af Svetlin Georgiev

The main purpose in this book is to represent some recent researches of Santilli iso-mathematics in the area of the plane geometry. This book is devoted to the iso-plane geometry. It summarizes the most recent contributions in this area. The book is intended for senior undergraduate students and beginning graduate students of engineering and science courses. The book contains five chapters. The chapters in the book are pedagogically organized. Each chapter concludes with a section with practical problems. In Chapter 1 we introduce iso-real numbers with one and several iso-units. They are defined the basic operations with them and they are deducted some of their basic properties. In the chapter they are defined iso-matrices, iso-determinants and iso-trigonometric functions. Chapter 2 deals with straight iso-lines. It is defined iso-angle between two iso-vectors. They are introduced iso-lines and they are deducted the main equations of iso-lines. They are given criteria for iso-perpendicularity and iso-parallel of iso-lines. In Chapter 3 we introduce iso-motions: iso-reflections, iso-rotations, iso-translations and iso-glide iso-reflections. Chapter 4 is devoted on iso-circles. They are given the iso- parametric iso-representations of the iso-circles. In Chapter 5 they are introduced iso-parabolas, iso-ellipses and iso-hyperbolas. The aim of this book is to present a clear and well-organized treatment of the concept behind the development of iso-mathematics as well as solution techniques. The text material of this book is presented in a readable and mathematically solid format.

This book encompasses recent developments of variational calculus on time scales. It is intended for use in the field of variational calculus on time scales. It is also suitable for graduate courses in the above fields. The book contains 8 chapters. The chapters in the book are pedagogically organized. This book is especially designed for those who wish to understand variational calculus on time scales without having extensive mathematical background.

The aim of this book is to present a clear and well-organized treatment of the concept behind the development of mathematics and solution techniques.

Real quaternion analysis is a multi-faceted subject. Created to describe phenomena in special relativity, electrodynamics, spin etc., it has developed into a body of material that interacts with many branches of mathematics, such as complex analysis, harmonic analysis, differential geometry, and differential equations. It is also a ubiquitous factor in the description and elucidation of problems in mathematical physics. In the meantime real quaternion analysis has become a well established branch in mathematics and has been greatly successful in many different directions. This book is based on concrete examples and exercises rather than general theorems, thus making it suitable for an introductory one- or two-semester undergraduate course on some of the major aspects of real quaternion analysis in exercises. Alternatively, it may be used for beginning graduate level courses and as a reference work. With exercises at the end of each chapter and its straightforward writing style the book addresses readers who have no prior knowledge on this subject but have a basic background in graduate mathematics courses, such as real and complex analysis, ordinary differential equations, partial differential equations, and theory of distributions.