Real Analysis: Series, Functions of Several Variables, and Applications

This book is a comprehensive introduction to multivariable analysis, building on the foundations of single variable analysis. It covers topics such as differentiation and integration of functions of several variables, infinite numerical series, sequences and series of functions, and applications to other areas of mathematics. With numerous exercises and hints, it is ideal for independent study or as a supplement to a course in single variable analysis.

Format: Hardback
Length: 392 pages
Publication date: 16 December 2017
Publisher: Springer-Verlag New York Inc.

This comprehensive textbook delves into the realm of multivariable analysis, building upon the solid foundations laid in the companion volume, Real Analysis: Foundations and Functions of One Variable. Together, these volumes constitute the inaugural English edition of the widely acclaimed Hungarian original, Valós Analízis I & II, which has been instrumental in shaping the mathematical education of students at Eötvös Loránd University, Hungary, for over three decades. Encompassing a wealth of knowledge and exercises, this book offers ample opportunities for students to master various topics, progressing from straightforward to challenging problems. Additionally, hints or solutions to many of the more intricate exercises are provided, making it an ideal resource for independent study or further exploration.

Designed as a sequel to a course in single variable analysis, this book takes these concepts to new heights, introducing students to the analysis of functions of multiple variables. The textbook adopts a modular structure, making it flexible for either a semester-long or year-long introductory course. Within its pages, students will explore a range of topics, including the differentiation and integration of functions of several variables, infinite numerical series, sequences and series of functions, and their applications in other branches of mathematics, such as physics.

To enhance the understanding of the subject matter, numerous historical notes are included, providing context and insights into the development of multivariable analysis. Moreover, a strong emphasis is placed on fostering conceptual understanding and intuition, helping students connect the dots between mathematical concepts and their real-world applications. By nurturing students' intuition throughout, many definitions and results acquire a deeper meaning and relevance, rooted in the broader realm of mathematics and its interdisciplinary connections.

In summary, this textbook serves as an essential guide for students seeking to delve into the world of multivariable analysis. With its comprehensive coverage, engaging exercises, and emphasis on intuition and context, it equips students with the tools they need to excel in this field and pursue their academic aspirations.

Weight: 716g
Dimension: 162 x 240 x 27 (mm)
ISBN-13: 9781493973675
Edition number: 1st ed. 2017