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Basic Concepts of Mathematical Analysis
This book introduces and explains basic concepts of mathematical analysis, which include: the concept of a function and functions’ properties, such as symmetry and periodicity (which gives some conditions under which we can determine the periodicity of functions). These concepts are applied to real numbers. The book also covers the concept of numerical sequences, their properties, the convergence of sequences and their limits. The concept of the limit of functions and their continuity, as well as the differentially of functions, are also discussed, including basic theorems of differentially and their applications. Lastly, the book explores parametric functions and their graphic representation.
Approximation Theory, Sequence Spaces and Applications
This book publishes original research chapters on the theory of approximation by positive linear operators as well as theory of sequence spaces and illustrates their applications. Chapters are original and contributed by active researchers in the field of approximation theory and sequence spaces. Each chapter describes the problem of current importance and summarizes ways of their solution and possible applications which improve the current understanding pertaining to sequence spaces and approximation theory. The presentation of the articles is clear and self-contained throughout the book.
Classical and Modern Methods in Summability
Summability is a mathematical topic with a long tradition and many applications in, for example, function theory, number theory, and stochastics. It was originally based on classical analytical methods, but was strongly influenced by modern functional analytical methods during the last seven decades. The present book aims to introduce the reader to the wide field of summability and its applications, and provides an overview of the most important classical and modern methods used. Part I contains a short general introduction to summability, the basic classical theory concerning mainly inclusion theorems and theorems of the Silverman-Toeplitz type, a presentation of the most important classes ...
Innovations, Technologies and Research in Education
The book includes studies presented at the ATEE Spring Conference 2017 on emerging trends in the use of technology in educational processes, the use of robotics to facilitate the construction of knowledge, how to facilitate learning motivation, transformative learning, and innovative educational solutions. Chapters here are devoted to studies on the didactic aspects of technology usage, how to facilitate learning, and the social aspects affecting acquisition of education, among others. This volume serves as a basis for further discussions on the development of educational science, on topical research fields and practical challenges. It will be useful to scientists in the educational field who wish to get acquainted with the results of studies conducted in countries around the world on emerging educational issues. Moreover, teachers who need to implement into practice the newest scientific findings and opinions and future teachers who need to acquire new knowledge will also find this book useful.
Sequence Spaces and Series
Topological vector spaces; Sequences spaces; Conservence of series; Further developments in sequences spaces.
Summability Theory And Its Applications
The theory of summability has many uses throughout analysis and applied mathematics. Engineers and physicists working with Fourier series or analytic continuation will also find the concepts of summability theory valuable to their research. The concepts of summability have been extended to the sequences of fuzzy numbers and also to the theorems of ergodic theory. This ebook explains various aspects of summability and demonstrates applications in a coherent manner. The content can readily serve as a useful series of lecture notes on the subject. This ebook comprises of 8 chapters starting from classical sequence spaces and covering matrix transformations and fuzzy numbers. An accompanying bibliography with extensive references makes this a valuable source of information for readers interested in summability theory as well as other branches of science.
Sensitive Chaos
Why does water always take a winding course in streams and rivers? Do common principles and rhythms underlie its movement - whether it be in the sea, in a plant, or even in the blood of a human being? In this seminal and thought-provoking work, the laws apparent in the subtle patterns of water in movement are shown to be the same as those perceptible in the shaping of bones, muscles and a myriad of other forms in nature. Fully illustrated, Sensitive Chaos reveals the unifying forces that underlie all living things. The author observes and explains such phenomena as the flight of birds, the formation of internal organs such as the heart, eye and ear, as well as mountain ranges and river deltas, weather and space patterns, and even the formation of the human embryo.
A Tauberian Theorem
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Quasi-Interpolation
Delve into an in-depth description and analysis of quasi-interpolation, starting from various areas of approximation theory.
Sequence Spaces
This book is aimed at both experts and non-experts with an interest in getting acquainted with sequence spaces, matrix transformations and their applications. It consists of several new results which are part of the recent research on these topics. It provides different points of view in one volume, e.g. their topological properties, geometry and summability, fuzzy valued study and more. This book presents the important role sequences and series play in everyday life, it covers geometry of Banach Sequence Spaces, it discusses the importance of generalized limit, it offers spectrum and fine spectrum of several linear operators and includes fuzzy valued sequences which exhibits the study of sequence spaces in fuzzy settings. This book is the main attraction for those who work in Sequence Spaces, Summability Theory and would also serve as a good source of reference for those involved with any topic of Real or Functional Analysis.
