Basic Analysis: Introduction to Real Analysis II by Jiri Lebl
Basic Analysis: Introduction to Real Analysis II - Table of Contents
8. Several Variables and Partial Derivatives
9. One Dimensional Integrals in Several Variables
10. Multivariable Integral
11. Functions as Limits
What You Will Learn in Basic Analysis: Introduction to Real Analysis II
"Basic Analysis: Introduction to Real Analysis II" by "Jirí Lebl" is a continuation of the first volume, designed for students who already understand the basics of limits, continuity, and elementary proofs. This book moves deeper into "real analysis", helping readers strengthen their logical thinking and gain confidence with more abstract mathematical ideas. The writing remains clear and approachable, making advanced topics easier to follow without sacrificing rigor.
The book focuses on key subjects such as "sequences and series of functions", uniform convergence, and deeper properties of continuity and integration. It also introduces "metric spaces", which allow readers to understand analysis beyond the real line. Throughout the chapters, Lebl emphasizes careful definitions and step-by-step proofs, supported by examples and exercises that reinforce understanding and develop strong proof-writing skills.
Like the first volume, this book is an "open access textbook", freely available online under a Creative Commons license. This makes it an excellent resource for university courses, independent learners, and educators seeking high-quality materials without cost barriers. Overall, "Basic Analysis II" provides a solid and well-structured path toward advanced topics in "proof-based mathematics", preparing readers for further study in analysis and related fields.
Book Details & Specifications
Title:
Basic Analysis: Introduction to Real Analysis II by Jiri Lebl
Publisher:
Jiri Lebl/Lulu.com
Year:
2009
Pages:
161
Type:
PDF
Language:
English
ISBN-10 #:
1505695910
ISBN-13 #:
979-8851945977
License:
CC BY-NC-SA 4.0
Amazon:
Amazon
About the Author: Jiri Lebl
The author
Jiri Lebl
is an Assistant Professor in the Department of Mathematics at the "Oklahoma State University". Jiri has taught mathematics at all levels for well over a decade at several other institutions as well: San Diego State University, University of California at San Diego, University of Illinois at Urbana-Champaign, and University of Wisconsin-Madison. He has published over 30 peer reviewed scientific papers, mostly focused on complex analysis in several variables. Before jumping fully into mathematics, he was involved in programming and free software, in particular the GNOME desktop project, and he wrote several programming tutorials. As the author of "Basic Analysis: Introduction to Real Analysis II", Lebl continues his mission of making rigorous mathematics accessible. The book reflects his commitment to "Mathematics Education" and is released as an "Open Educational Resource", allowing students worldwide to learn advanced analysis through structured explanations and proofs.
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