Real Analysis
Series, Functions of Several Variables, and Applications
Buch in deiner Nähe kaufen
Beschreibung
This book develops the theory of multivariable analysis, building on the single variable foundations established in the companion volume, Real Analysis: Foundations and Functions of One Variable. Together, these volumes form the first English edition of the popular Hungarian original, Valós Analízis I & II, based on courses taught by the authors at Eötvös Loránd University, Hungary, for more than 30 years. Numerous exercises are included throughout, offering ample opportunities to master topics by progressing from routine to difficult problems. Hints or solutions to many of the more challenging exercises make this book ideal for independent study, or further reading.
Intended as a sequel to a course in single variable analysis, this book builds upon and expands these ideas into higher dimensions. The modular organization makes this text adaptable for either a semester or year-long introductory course. Topics include: differentiation and integration of functions of several variables; infinite numerical series; sequences and series of functions; and applications to other areas of mathematics. Many historical notes are given and there is an emphasis on conceptual understanding and context, be it within mathematics itself or more broadly in applications, such as physics. By developing the student’s intuition throughout, many definitions and results become motivated by insights from their context.
Corresponds to a second course in real analysis to follow the authors' book Real Analysis: Foundations and Functions of One Variable
Motivates ideas and results in analysis by exploring concepts and applications
Showcases a comprehensive collection of exercises, allowing students to develop proficiency over a broad range of problems
Corresponds to a second course in real analysis to follow the authors' book Real Analysis: Foundations and Functions of One Variable Motivates ideas and results in analysis by exploring concepts and applications Showcases a comprehensive collection of exercises, allowing students to develop proficiency over a broad range of problems Includes supplementary material: sn.pub/extras
Autor*in
Miklós Laczkovich
Themen in »Real Analysis«
Continuity of functions History of Fourier series History of infinite series Limit of functions Real analysis Multivariable real analysis Multivariable real analysis textbook adoption
Stimmen zu »Real Analysis«
“This book develops a thorough treatment of multivariate derivatives, viewing them both as linear transformations and as partial derivatives. … The book is consistent in addressing the classical analysis of real functions of several variables. This volume will appeal to students in pure and applied mathematics, as well as scientists looking to acquire a firm footing in mathematical analysis.” (Teodora-Liliana Rădulescu, zbMATH 1407.26001, 2019)
“The explicit intent of the authors is to present material gradually, and to develop precision based on intuition with the help of well-designed examples. The book contains 600 exercises. In my opinion this interesting book represents an alternative viewpoint in real analysis.” (Zbigniew Grande, Mathematical Reviews, August, 2018)
()