Real Analysis: Series, Functions of Several Variables, and Applications (Undergraduate Texts in Mathematics) - Hardcover

Laczkovich, Miklos; T. Sós, Vera

Hardcover

ISBN 10: 1493973673 ISBN 13: 9781493973675

Verlag: Springer-Verlag New York Inc., 2017

Inhaltsangabe

<P>THIS BOOK DEVELOPS THE THEORY OF MULTIVARIABLE ANALYSIS, BUILDING ON THE SINGLE VARIABLE FOUNDATIONS ESTABLISHED IN THE COMPANION VOLUME, <I>REAL ANALYSIS: FOUNDATIONS AND FUNCTIONS OF ONE VARIABLE</I>. TOGETHER, THESE VOLUMES FORM THE FIRST ENGLISH EDITION OF THE POPULAR HUNGARIAN ORIGINAL, <I>VALÓS ANALÍZIS I & II</I>, 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.</P><P>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.</P><P></P>

Über diesen Titel

Críticas

“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)

Reseña del editor

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.

Details zur Ausgabe

• Verlag: Springer-Verlag New York Inc.
• Erscheinungsdatum: 2017
• ISBN 10: 1493973673
• ISBN 13: 9781493973675
• Einband: Tapa dura
• Sprache: Englisch
• Auflage: 1
• Anzahl der Seiten: 392