The book deals with continuous piecewise linear differential systems in the plane with three pieces separated by a pair of parallel straight lines. Moreover, these differential systems are symmetric with respect to the origin of coordinates. This class of systems driven by concrete applications is of interest in engineering, in particular in control theory and the design of electric circuits. By studying these particular differential systems we will introduce the basic tools of the qualitative theory of ordinary differential equations, which allow us to describe the global dynamics of these...
The book deals with continuous piecewise linear differential systems in the plane with three pieces separated by a pair of parallel straight lines. Mo...
Intended as a self-contained introduction to measure theory, this textbook provides a comprehensive treatment of integration on locally compact Hausdorff spaces, the analytic and Borel subsets of Polish spaces, and Haar measures on locally compact groups. This second edition provides the reader with a broad perspective on measure theory through additional topics such as the Kurzweil-Henstock integral, the Banach-Tarski paradox, a proof of the existence of liftings, the Daniell integral. In addition, applications and introductions to other related areas such as measure-theoretic probability...
Intended as a self-contained introduction to measure theory, this textbook provides a comprehensive treatment of integration on locally compact Hau...
The second edition of this classic textbook presents a rigorous and self-contained introduction to real analysis with the goal of providing a solid foundation for future coursework and research in applied mathematics. Written in a clear and concise style, it covers all of the necessary subjects as well as those often absent from standard introductory texts. Each chapter features a Problems and Complements section that includes additional material that briefly expands on certain topics within the chapter and numerous exercises for practicing the key concepts.
The first eight chapters...
The second edition of this classic textbook presents a rigorous and self-contained introduction to real analysis with the goal of providing a solid...
..".The authors of this remarkable book are among the very few who have faced up to the challenge of explaining what an asymptotic expansion is, and of systematizing the handling of asymptotic series. The idea of using distributions is an original one, and we recommend that you read the book... it] should be on your bookshelf if you are at all interested in knowing what an asymptotic series is." -"The Bulletin of Mathematics Books" (Review of the 1st edition) ** ..".The book is a valuable one, one that many applied mathematicians may want to buy. The authors are undeniably experts in their...
..".The authors of this remarkable book are among the very few who have faced up to the challenge of explaining what an asymptotic expansion is, and o...
Key topics in the theory of real analytic functions are covered in this text, and are rather difficult to pry out of the mathematics literature.; This expanded and updated 2nd ed. will be published out of Boston in Birkhauser Adavaned Texts series.; Many historical remarks, examples, references and an excellent index should encourage the reader study this valuable and exciting theory.; Superior advanced textbook or monograph for a graduate course or seminars on real analytic functions.; New to the second edition a revised and comprehensive treatment of the Faa de Bruno formula, topologies on...
Key topics in the theory of real analytic functions are covered in this text, and are rather difficult to pry out of the mathematics literature.; This...
This book is a self-contained introduction to real analysis assuming only basic notions on limits of sequences in ]RN, manipulations of series, their convergence criteria, advanced differential calculus, and basic algebra of sets. The passage from the setting in ]RN to abstract spaces and their topologies is gradual. Continuous reference is made to the ]RN setting, where most of the basic concepts originated. The first seven chapters contain material forming the backbone of a basic training in real analysis. The remaining two chapters are more topical, relating to maximal functions, functions...
This book is a self-contained introduction to real analysis assuming only basic notions on limits of sequences in ]RN, manipulations of series, their ...
The analysis of Euclidean space is well-developed. The classical Lie groups that act naturally on Euclidean space-the rotations, dilations, and trans- lations-have both shaped and guided this development. In particular, the Fourier transform and the theory of translation invariant operators (convolution transforms) have played a central role in this analysis. Much modern work in analysis takes place on a domain in space. In this context the tools, perforce, must be different. No longer can we expect there to be symmetries. Correspondingly, there is no longer any natural way to apply the...
The analysis of Euclidean space is well-developed. The classical Lie groups that act naturally on Euclidean space-the rotations, dilations, and trans-...
This book provides proofs of the asymptotic behavior of solutions to various important cases of linear and nonlinear problems in the theory of elliptic and parabolic partial differential equations. It is a valuable resource for graduates and researchers in applied mathematics and for engineers. Many results presented here have not been published elsewhere. They will motivate and enable the reader to apply the theory to other problems in partial differential equations.
This book provides proofs of the asymptotic behavior of solutions to various important cases of linear and nonlinear problems in the theory of elli...
"This book covers some of the main aspects of nonlinear analysis. It concentrates on stressing the fundamental ideas instead of elaborating on the intricacies of the more esoteric ones...it encompass es] many methods of dynamical systems in quite simple and original settings. I recommend this book to anyone interested in the main and essential concepts of nonlinear analysis as well as the relevant methodologies and applications." --MATHEMATICAL REVIEWS
"This book covers some of the main aspects of nonlinear analysis. It concentrates on stressing the fundamental ideas instead of elaborating on the ...
These notes are based on lectures given at the University of Virginia over the past twenty years. They may be viewed as a course in function theory for nonspecialists. Chapters 1-6 give the function-theoretic background to Hardy Classes and Operator Theory, Oxford Mathematical Monographs, Oxford University Press, New York, 1985. These chapters were written first, and they were origi- nally intended to be a part of that book. Half-plane function theory continues to be useful for applications and is a focal point in our account (Chapters 5 and 6). The theory of Hardy and Nevanlinna classes is...
These notes are based on lectures given at the University of Virginia over the past twenty years. They may be viewed as a course in function theory fo...
