Real Analysis via Sequences and Series

• Κύριοι συγγραφείς: Little, Charles H.C (Συγγραφέας), Teo, Kee L. (Συγγραφέας), van Brunt, Bruce (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: New York, NY : Springer New York : Imprint: Springer, 2015.
• Σειρά: Undergraduate Texts in Mathematics,
• Θέματα: Mathematics.; Functions of real variables.; Sequences (Mathematics).; Real Functions.; Sequences, Series, Summability.

 This text gives a rigorous treatment of the foundations of calculus. In contrast to more traditional approaches, infinite sequences and series are placed at the forefront. The approach taken has not only the merit of simplicity, but students are well placed to understand and appreciate more sophisticated concepts in advanced mathematics. The authors mitigate potential difficulties in mastering the material by motivating  definitions, results, and proofs. Simple examples  are provided to  illustrate new material and exercises are included at the end of most sections. Noteworthy topics include: an extensive discussion of convergence tests for infinite series, Wallis’s formula and Stirling’s formula, proofs of the irrationality of π and e, and a treatment of Newton’s method as a special instance of finding fixed points of iterated functions. 

 Preface -- 1. Introduction -- 2. Sequences -- 3. Series -- 4. Limits of Functions -- 5. Continuity -- 6. Differentiability -- 7. The Riemann Integral -- 8. Taylor Polynomials and Taylor Series -- 9. The Fixed Point Problem -- 10. Sequences of Functions -- Bibliography -- Index.