Introduction to Real Analysis | Buch

Cover: 9783030269012 | Introduction to Real Analysis | Christopher Heil | Buch | Englisch

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Sprache: Englisch

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Beschreibung

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.

Über den Autor

Christopher Heil is Professor of Mathematics at the Georgia Institute of Technology in Atlanta, Georgia. His research interests include harmonic analysis, time-frequency analysis, image processing, and more.

Zusammenfassung

Introduces real analysis to students with an emphasis on accessibility and clarity

Adapts the author's successful, classroom-tested lecture notes to motivate a thorough exploration of real analysis

Includes numerous exercises, definitions, and theorems, which are both easy to understand and rigorous

Reinforces the material with numerous additional online resources

Request lecturer material: [...]

Inhaltsverzeichnis

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 L^2(E).- 9. Convolution and the Fourier Transform.

Details

Erscheinungsjahr:	2019
Fachbereich:	Analysis
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
Reihe:	Graduate Texts in Mathematics
Inhalt:	xxxii 386 S. 1 s/w Illustr. 386 p. 1 illus.
ISBN-13:	9783030269012
ISBN-10:	3030269019
Sprache:	Englisch
Ausstattung / Beilage:	HC runder Rücken kaschiert
Einband:	Gebunden
Autor:	Heil, Christopher
Auflage:	1st ed. 2019
Hersteller:	Springer International Publishing Graduate Texts in Mathematics
Maße:	241 x 160 x 29 mm
Von/Mit:	Christopher Heil
Erscheinungsdatum:	30.07.2019
Gewicht:	0,793 kg

Artikel-ID: 116841464