Real Analysis and Applications

• Κύριος συγγραφέας: Botelho, Fabio Silva (Συγγραφέας, http://id.loc.gov/vocabulary/relators/aut)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Cham : Springer International Publishing : Imprint: Springer, 2018.
• Έκδοση: 1st ed. 2018.
• Θέματα: Functions of real variables.; Measure theory.; Sequences (Mathematics).; Real Functions.; Measure and Integration.; Sequences, Series, Summability.

 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. 

 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.