(正版) Introduction to Real Analysis by Christopher Heil 实分析导论（数学研究生课本） (需预定或E版)
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作者Christopher Heil
出版社Springer International Publishing A&G
ISBN9783030269012
出版时间2019
装帧精装
上书时间2024-06-12
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Developed over years of classroom use, this textbook provides a clear and accessible approach to real analysis. This modern interpretation is based on the author's lecture notes and has been meticulously tailored to motivate students and inspire readers to explore the material, and to continue exploring even after they have finished the book. The definitions, theorems, and proofs contained within are presented with mathematical rigor, but conveyed in an accessible manner and with language and motivation meant for students who have not taken a previous course on this subject. The text covers all of the topics essential for an introductory course, including Lebesgue measure, measurable functions, Lebesgue integrals, differentiation, absolute continuity, Banach and Hilbert spaces, and more. Throughout each chapter, challenging exercises are presented, and the end of each section includes additional problems. Such an inclusive approach creates an abundance of opportunities for readers to develop their understanding, and aids instructors as they plan their coursework. Additional resources are available online, including expanded chapters, enrichment exercises, a detailed course outline, and much more. Introduction to Real Analysis is intended for first-year graduate students taking a first course in real analysis, as well as for instructors seeking detailed lecture material with structure and accessibility in mind. Additionally, its content is appropriate for Ph.D. students in any scientific or engineering discipline who have taken a standard upper-level undergraduate real analysis course.
"The book is really a textbook full of intermediate motivated questions addressed to the audience and step-divided discussions. It can be suitable for first-year students in mathematics, for well-prepared undergraduate mathematical majors, and for graduate students from a variety of engineering and scientific applications." (Sergei V. Rogosin, zbMATH 1426.26001, 2020), "This book is intended primarily for students beginning their graduate studies in mathematics but it will also be suitable for well-prepared undergraduates." (Frédéric Morneau-Guérin, MAA Reviews, February 16, 2020) "The book is really a textbook full of intermediate motivated questions addressed to the audience and step-divided discussions. It can be suitable for first-year students in mathematics, for well-prepared undergraduate mathematical majors, and for graduate students from a variety of engineering and scientific applications." (Sergei V. Rogosin, zbMATH 1426.26001, 2020)
Table of Content
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 L p Spaces.- 8. Hilbert Spaces and L^2( E).- 9. Convolution and the Fourier Transform.
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