* Exciting exposition integrates history, philosophy, and mathematics
* Combines a mathematical analysis of approximation theory with an engaging discussion of the differing philosophical underpinnings behind its development
* Appendices containing biographical data on numerous eminent mathematicians, explanations of Russian nomenclature and academic degrees, and an excellent index round out the presentation
* Exciting exposition integrates history, philosophy, and mathematics
* Combines a mathematical analysis of approximation theory with an eng...
This monograph examines in detail two aspects in the field of interpolation of functions -the Global Smoothness Preservation Property (GSPP) and the Shape Preservation Property (SPP). By considering well-known classical interpolation operators such as Lagrange, Grunwald, Hermite-Fejer and Shepard type, the study is mainly developed for the univariate and bivariate cases. One of the first books on the subject, it presents to the reader, recent work featuring many new interesting results in this field, including an excellent survey of past research. Accompanied by numerous open problems, an...
This monograph examines in detail two aspects in the field of interpolation of functions -the Global Smoothness Preservation Property (GSPP) and th...
Working computationally in applied mathematics is the very essence of dealing with real-world problems in science and engineering. Approximation theory-on the borderline between pure and applied mathematics- has always supplied some of the most innovative ideas, computational methods, and original approaches to many types of problems. The first of its kind, the Handbook on Analytic-Computational Methods in Applied Mathematics comprises 22 self-contained chapters focused on various aspects of analytic computational methods in approximation theory and other related fields. The articles...
Working computationally in applied mathematics is the very essence of dealing with real-world problems in science and engineering. Approximation theor...
Quantitative approximation methods apply in many diverse fields of research-neural networks, wavelets, partial differential equations, probability and statistics, functional analysis, and classical analysis to name just a few. For the first time in book form, Quantitative Approximations provides a thorough account of all of the significant developments in the area of contemporary quantitative mathematics. It offers readers the unique opportunity of approaching the field under the guidance of an expert. Among the book's outstanding features is the inclusion of the introductory chapter that...
Quantitative approximation methods apply in many diverse fields of research-neural networks, wavelets, partial differential equations, probability and...
In this book the author presents the Opial, Poincare, Sobolev, Hilbert, and Ostrowski fractional differentiation inequalities. Results for the above are derived using three different types of fractional derivatives, namely by Canavati, Riemann-Liouville and Caputo. The univariate and multivariate cases are both examined. Each chapter is self-contained. The theory is presented systematically along with the applications. The application to information theory is also examined.
This monograph is suitable for researchers and graduate students in pure mathematics. Applied mathematicians,...
In this book the author presents the Opial, Poincare, Sobolev, Hilbert, and Ostrowski fractional differentiation inequalities. Results for the abov...
Presents univariate and multivariate probabilistic inequalities with coverage on basic probabilistic entities like expectation, variance, moment generating function and covariance. This book deals with inequalities in information theory and the Csiszar's f-Divergence between probability measures.
Presents univariate and multivariate probabilistic inequalities with coverage on basic probabilistic entities like expectation, variance, moment gener...
Differential geometry, in the classical sense, is developed through the theory of smooth manifolds. Modern differential geometry from the author s perspective is used in this work to describe physical theories of a geometric character without using any notion of calculus (smoothness). Instead, an axiomatic treatment of differential geometry is presented via sheaf theory (geometry) and sheaf cohomology (analysis). Using vector sheaves, in place of bundles, based on arbitrary topological spaces, this unique approach in general furthers new perspectives and calculations that generate...
Differential geometry, in the classical sense, is developed through the theory of smooth manifolds. Modern differential geometry from the author s ...
This monograph belongs to the broader area of Fuzzy Mathematics and it is the first one in Fuzzy Approximation Theory. The chapters are self-contained with lots of applications to teach several advanced courses and the topics covered are very diverse. An extensive background of Fuzziness and Fuzzy Real Analysis is given. The author covers Fuzzy Differentiation and Integration Theory followed by Fuzzy Ostrowski inequalities. Then results on classical algebraic and trigonometric polynomial Fuzzy Approximation are presented. The author develops a complete theory of convergence with rates of...
This monograph belongs to the broader area of Fuzzy Mathematics and it is the first one in Fuzzy Approximation Theory. The chapters are self-contained...
"Intelligent Routines II: Solving Linear Algebra and Differential Geometry with Sage" contains numerous of examples and problems as well as many unsolved problems. This book extensively applies the successful software Sage, which can be found free online http: //www.sagemath.org/. Sage is a recent and popular software for mathematical computation, available freely and simple to use. This book is useful to all applied scientists in mathematics, statistics and engineering, as well for late undergraduate and graduate students of above subjects. It is the first such book in solving...
"Intelligent Routines II: Solving Linear Algebra and Differential Geometry with Sage" contains numerous of examples and problems as well as many un...
This monograph presents univariate and multivariate classical analyses of advanced inequalities. This treatise is a culmination of the author's last thirteen years of research work. The chapters are self-contained and several advanced courses can be taught out of this book. Extensive background and motivations are given in each chapter with a comprehensive list of references given at the end.The topics covered are wide-ranging and diverse. Recent advances on Ostrowski type inequalities, Opial type inequalities, Poincare and Sobolev type inequalities, and Hardy-Opial type inequalities...
This monograph presents univariate and multivariate classical analyses of advanced inequalities. This treatise is a culmination of the author's...
