Introduction to real analysis / Christopher Heil.

Format:

Book

Author/Creator:

Heil, Christopher, 1960- author.

Series:

Graduate texts in mathematics ; 280.

Graduate texts in mathematics ; 280

Language:

English

Subjects (All):

Mathematical analysis.

Physical Description:

xvii, 400 pages : illustrations ; 24 cm.

Place of Publication:

Cham, Switzerland : Springer Science+Business LLC/Spring Nature Switzerland AG, [2019]

Summary:

"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."--Provided by publisher.

Contents:

Metric and Normed Spaces

Lebesgue Measure

Measurable Functions

The Lebesgue Integral

Differentiation

Absolute Continuity and the Fundamental Theorem of Calculus

The Lp Spaces

Hilbert Spaces and L²(E)

Convolution and the Fourier Transform.

Notes:

Includes bibliographical references (pages 393-394) and indexes.

Other Format:

Online version: Heil, Christopher, 1960- Introduction to real analysis.

ISBN:

9783030269012

3030269019

OCLC:

1107364855