Introduction to Real Analysis – eBook PDF
Developed over years of classroom use, Introduction to Real Analysis (PDF) offers a clear and accessible approach to real analysis. This modern version is based on the author’s lecture notes and has been carefully tailored to motivate students and motivate readers to explore the material, and to continue studying even after they have finished the ebook. The definitions, theorems, and proofs included within are presented with mathematical rigor, but communicated in an accessible manner and with motivation and language meant for students who have not taken a prior course on this subject.
The text includes all of the topics essential for an introductory course, including Lebesgue measure, Lebesgue integrals, differentiation, measurable functions, absolute continuity, Banach and Hilbert spaces, and more. Throughout every chapter, challenging exercises are presented, and the end of every section includes additional problems. Such an inclusive approach creates a wealth of opportunities for readers to develop their understanding, and helps instructors as they plan their coursework. Added resources are available online, including expanded chapters, a detailed course outline, and enrichment exercises and much more.
Introduction to Real Analysis is intended for first-year graduate students taking a first course in real analysis, along with instructors seeking detailed lecture material with accessibility and structure in mind. Moreover, its content is appropriate for Ph.D. students in any engineering or scientific discipline who have taken a standard upper-level undergraduate real analysis course.
“This ebook is intended primarily for students beginning their graduate studies in mathematics but it will also be appropriate for well-prepared undergraduates.” — Frédéric Morneau-Guérin, MAA Reviews, February 2020
“The ebook is really a textbook full of intermediate motivated questions addressed to the audience and step-divided discussions. It can be appropriate 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 ebook is written in a clear style that is suitable for students reading on their own or as part of a guided class. … this ebook gives an accessible introduction to real analysis with focus on Lebesgue measure and Lebesgue integration in Euclidean spaces. This ebook could be suitable as a primary text for a first course stressed on measure theory in Euclidean spaces or, due to the various exercises throughout, as a supplemental text for instructors giving other introductory measure theory courses.” — Gareth Speight, Mathematical Reviews, June 2020
NOTE: The product only includes the ebook, Introduction to Real Analysis in PDF. No access codes are included.