Riemann Integration and Series of Functions: A rigorous introduction to Riemann integration, convergence, and foundational concepts in real analysis - Couverture souple

Saha, Biswajit

 
9786209122897: Riemann Integration and Series of Functions: A rigorous introduction to Riemann integration, convergence, and foundational concepts in real analysis
Couverture souple
ISBN 10 : 6209122892 ISBN 13 : 9786209122897
Editeur : LAP LAMBERT Academic Publishing, 2025

Synopsis

The book Riemann Integration and Series of Functions presents a rigorous introduction to two central areas of real analysis — the Riemann integral and the convergence of functions. It begins with the definition of Riemann sums and integrability, explaining how the area under a curve can be approximated and formalized. The equivalence of Riemann and Darboux integrals, along with key results like the integrability of continuous and monotonic functions and the Fundamental Theorem of Calculus, are discussed in detail.The second part explores sequences and series of functions, focusing on pointwise and uniform convergence, their impact on continuity and differentiability, and criteria like the Weierstrass M-test. Applications to power and Fourier series illustrate practical significance. Overall, the book provides a solid foundation in rigorous analysis, bridging basic calculus with advanced mathematical theory through clear explanations and logical proofs.

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Éditeur
LAP LAMBERT Academic Publishing
Date d'édition
2025
Langue
anglais
ISBN 10 
6209122892
ISBN 13 
9786209122897
Reliure
Broché
Nombre de pages
148
Coordonnées du fabricant
non disponible
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