Discusses the theory from its very beginning Foundations have been laid very carefully and the treatment is rigorous, and on modern lines The Riemann integration is treated in full Large number of well graded examples have been given and some of these have been solved.
The International Conference on Modern Analysis and Applications, which was dedicated to the 100th anniversary of the birth of Mark Krein, one of the greatest mathematicians of the 20th century, was held in Odessa, Ukraine, on April 9-14, 2007. This title contains peer-reviewed research and survey papers based on invited talks at this conference.
Presents survey articles addressing topics surrounding positivity, with an emphasis on functional analysis. This book provides insight into the structure of classical spaces of continuous functions, f-algebras, and integral operators, and contains contributions to modern topics like vector measures, operator spaces, and ordered tensor products.
Intended for the students interested in the disciplines of mathematics, physics, engineering, and finance, at both the undergraduate and graduate levels, this third volume in a series of titles focuses on the development of measure and integration theory, differentiation and integration, Hilbert spaces, and Hausdorff measure and fractals.
The Henstock-Kurzweil integral, which is also known as the generalized Riemann integral, arose from a slight modification of the classical Riemann integral. This book presents an introduction of the multiple Henstock-Kurzweil integral. It covers the developments connected with measures, multiple integration by parts, and multiple Fourier series.
Inequalities based on Sobolev Representations deals exclusively with tight integral inequalities of Chebyshev-Gruss and Ostrowski types, and of integral means. Applications illustrate inequalities that engage in ordinary and weak partial derivatives of the involved functions.
Provides a foundation of real analysis concepts and principles presenting a range of topics. This book takes a progressive approach of skill building to help students learn to absorb the abstract. It includes real world applications, probability theory, harmonic analysis, and dynamical systems theory.
This book stresses applications of real analysis, detailing how its principles and theory can be applied in a variety of settings in subjects ranging from Fourier series and polynomial approximation to discrete dynamical systems and nonlinear optimization.
This book provides a comprehensive treatment of extrapolation theory. Starting from an extremely clear and simple proof of the classical result of Rubio de Francia, the authors show how the key ideas can be used to extend the theory to a variety of contexts.
Mathematics provides the tools and ideas to formulate real-life problems mathematically and then help in solving them. This book deals with several different problems arising from many disciplines and offers some modern mathematical approaches to handle them.
Contains peer-reviewed research and survey papers based on invited talks at the International Conference on Modern Analysis and Applications. The conference, which was dedicated to the 100th anniversary of the birth of Mark Krein, one of the greatest mathematicians of the 20th century, was held in Odessa, Ukraine, on April 9-14, 2007.
In what is a rigorous treatment of multivariable differential and integral calculus, this book explains key theorems including Stokes's as well as covering extrema such as Lagrange multipliers. It explores Riemann integration in n dimensions in detail.
Presents a course in analysis, leading from real numbers to such advanced topics as differential forms on manifolds, asymptotic methods, Fourier, Laplace, and Legendre transforms, elliptic functions and distributions. This book explores the essence and the roots of the basic concepts and theorems of calculus.
This textbook presents an array of topics in Calculus, and conceptually follows Mathematical Analysis I. The present material is partly found, in fact, in the syllabus of the typical second lecture course in Calculus as offered in most Italian universities.
This book illustrates interactions of pure mathematics with other sciences, such as hydrodynamics, thermodynamics, statistical physics and information theory. It includes problems, historical remarks and Zorich's article "Mathematics as Language and Method."
Ordinary differential equations have been extended to evolution equations in Banach spaces. This book generalizes ordinary differential equations beyond the borders of vector spaces with a focus on the well-posed Cauchy problem in finite time intervals.
Contains selected papers from the ISAAC conference 2007 and invited contributions. This book covers various topics that represent the main streams of research in hypercomplex analysis as well as the expository articles. It is suitable for researchers and postgraduate students in various areas of mathematical analysis.
Explores the theory of calculus and highlights the connections between calculus and real analysis, providing a mathematically sophisticated introduction to functional analytical concepts. This text provides coverage of exponential function, and the development of trigonometric functions from the integral.
The International Conference on Modern Analysis and Applications, which was dedicated to the 100th anniversary of the birth of Mark Krein, one of the greatest mathematicians of the 20th century, was held in Odessa, Ukraine, on April 9-14, 2007. This title contains peer-reviewed research and survey papers based on invited talks at this conference.
Sobolev spaces and inequalities are fundamental tools in the theory of partial differential equations, analysis, differential geometry, and mathematical physics. This book is dedicated to the centenary of S L Sobolev and includes biographical articles supplied with the bibliography of Sobolev's works in the 1930s and archive photos of Sobolev.
Outlines an elementary, one semester course, which exposes students to both the process of rigor, and the rewards inherent in taking an axiomatic approach to the study of functions of a real variable. This book focuses on questions which give analysis its inherent fascination.
Intended to follow the usual introductory physics courses, this book includes a feature of addressing the mathematical needs of sophomores and juniors in physics, engineering and other related fields. It includes examples from the physical sciences, problems at the ends of chapters, and boxes to emphasize important concepts.