Bøger af Svetlin G. Georgiev

This book is focused on the qualitative theory of general quantum calculus, the modern name for the investigation of calculus without limits. It centers on designing, analysing and applying computational techniques for general quantum differential equations.

Curve fitting is the process of constructing a curve that has the best fit to a series of data points, possibly subject to constraints. Curve fitting can involve either interpolation, where an exact fit to the data is required, or smoothing, in which a "smooth" function is constructed that approximately fits the data. Fitted curves can be used as an aid for data visualization, to infer values of a function where no data are available, and to summarize the relationships among two or more variables. Extrapolation refers to the use of a fitted curve beyond the range of the observed data, and is subject to a degree of uncertainty since it may reflect the method used to construct the curve as much as it reflects the observed data.This book is devoted on the qualitative theory of quantum curve fittings. The book is intended for senior undergraduate students and beginning graduate students of engineering and science courses. There are four chapters in this book. The chapters in the book are pedagogically organized. Each chapter concludes with a section with practical problems.

Presenting a rich collection of exercises on partial differential equations, this textbook equips readers with 96 examples, 222 exercises, and 289 problems complete with detailed solutions or hints. It explores a broad spectrum of partial differential equations, fundamental to mathematically oriented scientific fields, from physics and engineering to differential geometry and variational calculus.Organized thoughtfully into seven chapters, the journey begins with fundamental problems in the realm of PDEs. Readers progress through first and second-order equations, wave and heat equations, and finally, the Laplace equation. The text adopts a highly readable and mathematically solid format, ensuring concepts are introduced with clarity and organization.Designed to cater to upper undergraduate and graduate students, this book offers a comprehensive understanding of partial differential equations. Researchers and practitioners seeking to strengthen their problem-solving skills will also find this exercise collection both challenging and beneficial.

Mathematical models cannot be solved using the traditional analytical methods for dynamic equations on time scales. These models must be dealt with using computational methods. This textbook introduces numerical methods for initial value problems for dynamic equations on time scales. Hands-on examples utilizing MATLAB and practical problems illustrate a wide variety of solution techniques.

The main purpose of this book is to explain the basic ideas of iso-mathematics and to help to the readers to operate with them in their researchers. This book contains six chapters, and each chapter consists of results with their proofs, numerous examples, and exercises with solutions. Each chapter concludes with a section featuring advanced practical problems with solutions. The text material of this book is presented in a readable and mathematically solid format.

The theory of dynamic equations has many interesting applications in control theory, mathematical economics, mathematical biology, engineering and technology. show the essential unity achieved in the theory fuzzy dynamic equations, dynamic inclusions and optimal control problems on time scales;

The author introduces the main conceptions for multiplicative surfaces: multiplicative first fundamental form, the main multiplicative rules for differentiations on multiplicative surfaces, and the main multiplicative regularity conditions for multiplicative surfaces. Many examples and problems are included.

This book is devoted to recent developments of linear and nonlinear integral inequalities on time scales. The book is intended for the use in the field of dynamic calculus on time scales, dynamic equation and integral equations on time scales. It is also suitable for graduate courses in the above fields. The book is designed for those who have mathematical background on time scales calculus.

This book on functional analysis covers all the basics of the subject (normed, Banach and Hilbert spaces, Lebesgue integration and spaces, linear operators and functionals, compact and self-adjoint operators, small parameters, fixed point theory) with a strong focus on examples, exercises and practical problems, thus making it ideal as course material but also as a reference for self-study.

This book explains many fundamental ideas on the theory of distributions. The theory of partial differential equations is one of the synthetic branches of analysis that combines ideas and methods from different fields of mathematics, ranging from functional analysis and harmonic analysis to differential geometry and topology.

This book provides the first and second fundamental forms of surfaces on time scales. They are introduced minimal surfaces and geodesics on time scales. In the book are studied the covaraint derivatives on time scales, pseudo-spherical surfaces and \sigma_1, \sigma_2 manifolds on time scales.

This book offers the reader an overview of recent developments of multivariable dynamic calculus on time scales, taking readers beyond the traditional calculus texts.

This book is devoted to some recent aspects of calculus. The book contains seven chapters. Chapter 1 introduces the conception for conformable delta (Hilger) derivative and some of its properties. Results in this chapter include basic conformable delta derivative, the conformable exponential function, conformable trigonometric and hyperbolic functions, conformable delta integral and integral rules and Taylor''s formula. They are considered first order conformable dynamic equations on time scales. Chapter 2 is devoted to some classes second order quadratic difference equations. They are given criteria for existence of a unique equilibrium point that is stable and unstable, existence of prime period-two solutions. Chapter 3 is aimed to develop two calculi over the specific algebraic operations, preserving the preceding relativistic addition formula and having all ordinary properties. Chapter 4 is devoted to principles of hypercomplex random function calculus. Generalized Gaussian-type hypercomplex valued measures are studied. Random functions controlled by these measures are investigated. Solutions of hyperbolic PDEs over hypercomplex numbers such as the octonion algebra and Cayley-Dickson algebras are scrutinized. Chapter 5 covers the interesting historical aspects of the spreadsheets and their distinct advantages. It is described how the ubiquitous Microsoft Excel spreadsheets can be used to implement well-known numerical methods such as Simpson''s Rule and Trapezoidal Rules. Appropriate examples are presented in substantial detail. The aim of Chapter 6 is to show some didactic tools that can be suggested by professors so that students can recall those issues saved in the deepest part of their minds. In Chapter 7, based on fractional differences, a fractional calculus is developed which complies with most of the properties that is to say non-differentiability, non-commutativity of derivative and long-range memory. The book is addressed to a wide audience of specialists such as mathematicians, physicists, engineers and biologists.

Pedagogically organized, this monograph introduces fractional calculus and fractional dynamic equations on time scales in relation to mathematical physics applications and problems. Much discussion is devoted to Riemann-Liouville fractional dynamic equations and Caputo fractional dynamic equations.

This book is devoted to the qualitative theory of functional dynamic equations on time scales, providing an overview of recent developments in the field as well as a foundation to time scales, dynamic systems, and functional dynamic equations.

Pedagogically organized, this monograph introduces fractional calculus and fractional dynamic equations on time scales in relation to mathematical physics applications and problems. Much discussion is devoted to Riemann-Liouville fractional dynamic equations and Caputo fractional dynamic equations.

This book offers the reader an overview of recent developments of integral equations on time scales. This book is primarily intended for senior undergraduate students and beginning graduate students of engineering and science courses.