Introduction to Real Analysis by Christopher Heil
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About this book :-
Introduction to Real Analysis written by
Christopher Heil
This text grew out of lecture notes that I developed over the years for the “Real Analysis” graduate sequence here at Georgia Tech. This two-semester sequence is taken by first-year mathematics graduate students, well-prepared undergraduate mathematics majors, and graduate students from a wide variety of engineering and scientific disciplines. Covered in this book are the topics that are taught in the first semester: Lebesgue measure, the Lebesgue integral, differentiation and absolute continuity, the Lebesgue spaces Lp(E), and Hilbert spaces and L2(E). This material not only forms the basis of a core subject in pure mathematics, but also has wide applicability in science and engineering. A text covering the second semester topics in analysis, including abstract measure theory, signed and complex measures, operator theory, and functional analysis, is in development.
This text is an introduction to real analysis. There are several classic anal ysis texts that I keep close by on my bookshelf and refer to often. However, I find it difficult to use any of these as the textbook for teaching a first course on analysis. They tend to be dense and, in the classic style of mathematical elegance and conciseness, they develop the theory in the most general setting, with few examples and limited motivation. These texts are valuable resources, but I suggest that they should be the second set of books on analysis that you pick up.
(Christopher Heil)
Book Detail :-
Title: Real Analysis
Edition:
Author(s): Christopher Heil
Publisher: Springer International Publishing
Series: Graduate Texts in Mathematics
Year: 2019
Pages: 416
Type: PDF
Language: English
ISBN: 978-3-030-26901-2, 978-3-030-26903-6
Country: US
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About Author :-
Author Christopher Heil is from Georgia Institute of Technology. Heil has been involved in teaching calculus, linear algebra, analysis, and abstract algebra at Georgia Tech since 1993. He is an experienced author and served as a consultant on the previous edition of this text. His research is in harmonic analysis, including time-frequency analysis, wavelets, and operator theory.
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Book Contents :-
Introduction to Real Analysis written by
Christopher Heil
cover the following topics.
Preliminaries
1. Metric and Normed Spaces
2. Lebesgue Measure
3. Measurable Functions
4. The Lebesgue Integral
5. Differentiation
6. Absolute Continuity and the Fundamental Theorem of Calculus
7. The Lp Spaces
8. Hilbert Spaces and L2(E)
9. Convolution and the Fourier Transform
Hints for Selected Exercises and Problems
Index of Symbols
References
Index
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