Introduction to Real Analysis
by Lee Larson
Publisher: University of Louisville 2014
Number of pages: 184
From the table of contents: Basic Ideas (Sets, Functions and Relations, Cardinality); The Real Numbers; Sequences; Series; The Topology of R; Limits of Functions; Differentiation; Integration; Sequences of Functions; Fourier Series.
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by Krzysztof Ciesielski - Heldermann Verlag
This text surveys the recent results that concern real functions whose statements involve the use of set theory. The choice of the topics follows the author's personal interest in the subject. Most of the results are left without the proofs.
by Juha Heinonen
In these lectures, we concentrate on the theory of Lipschitz functions in Euclidean spaces. From the table of contents: Introduction; Extension; Differentiability; Sobolev spaces; Whitney flat forms; Locally standard Lipschitz structures.
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This book provides an introductory chapter containing background material as well as a mini-overview of much of the course, making the book accessible to readers with varied backgrounds. It uses a wealth of examples to illustrate important concepts.
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The book is written in a rigorous, yet reader friendly style with motivational and historical material that emphasizes the big picture and makes proofs seem natural rather than mysterious. Introduces key concepts such as point set theory and other.