Real Analysis and Applications

Fabio Silva Botelho (Autor)

Buch | Softcover

XIII, 567 Seiten

2018 | 1. Softcover reprint of the original 1st ed. 2018
Springer International Publishing (Verlag)
978-3-030-08750-0 (ISBN)

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This textbook introduces readers to real analysis in one and n dimensions. It is divided into two parts: Part I explores real analysis in one variable, starting with key concepts such as the construction of the real number system, metric spaces, and real sequences and series. In turn, Part II addresses the multi-variable aspects of real analysis. Further, the book presents detailed, rigorous proofs of the implicit theorem for the vectorial case by applying the Banach fixed-point theorem and the differential forms concept to surfaces in Rn. It also provides a brief introduction to Riemannian geometry.
With its rigorous, elegant proofs, this self-contained work is easy to read, making it suitable for undergraduate and beginning graduate students seeking a deeper understanding of real analysis and applications, and for all those looking for a well-founded, detailed approach to real analysis.

Fabio Botelho holds a PhD in Mathematics from Virginia Tech, USA, and a Master in Aeronautics and Mechanics Engineering from the Aeronautics Institute of Technology, Brazil. He is the author of the book "Functional Analysis and Applied Optimization in Banach Spaces," also published with Springer. His main research fields are calculus of variations, convex analysis and duality applied to problems in physics and engineering.

Chapter 01- Real Numbers.- Chapter 02- Metric Spaces.- Chapter 03- Real Sequences and Series.- Chapter 04- Real Function Limits.- Chapter 05- Continuous Functions.- Chapter 06- Derivatives.- Chapter 07- The Riemann Integral.- Chapter 08- Differential Analysis in Rn.- Chapter 09- Integration in Rn.- Chapter 10- Topics on Vector Calculus and Vector Analysis.

Erscheinungsdatum	21.01.2019
Zusatzinfo	XIII, 567 p.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	884 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Schlagworte	Arzela-Ascoli theorem • Banach's fixed point theorem • implicit function theorem • Metric Spaces • Real analysis • Riemannian Geometry
ISBN-10	3-030-08750-6 / 3030087506
ISBN-13	978-3-030-08750-0 / 9783030087500
Zustand	Neuware