Sequences and Series

• Verfasst von: Alves de Sá, Ana [VerfasserIn]
• Verfasst von: Louro, Bento [VerfasserIn]
• Titel: Sequences and Series
• Titelzusatz: Theory and Practice
• Verf.angabe: by Ana Alves de Sá, Bento Louro
• Ausgabe: 1st ed. 2024.
• Verlagsort: Cham
• Verlagsort: Cham
• Verlag: Springer Nature Switzerland
• Verlag: Imprint: Springer
• E-Jahr: 2024
• Jahr: 2024.
• Jahr: 2024.
• Umfang: 1 Online-Ressource(XI, 342 p. 141 illus., 120 illus. in color.)
• ISBN: 978-3-031-67202-6
• DOI: doi:10.1007/978-3-031-67202-6
• Schlagwörter: (s)Folge <Mathematik> / (s)Reihe / (s)Zahlenreihe / (s)Gleichmäßige Konvergenz / (s)Taylor-Reihe / (s)Maclaurin-Reihe / (s)Fourier-Reihe
• Datenträger: Online-Ressource
• Sprache: eng
• Bibliogr. Hinweis: Erscheint auch als : Druck-Ausgabe
• Bibliogr. Hinweis: Erscheint auch als : Druck-Ausgabe
• Bibliogr. Hinweis: Erscheint auch als : Druck-Ausgabe
• Bibliogr. Hinweis: Erscheint auch als : Druck-Ausgabe: Alves de Sá, Ana: Sequences and series. - Cham, Switzerland : Springer Nature, 2024. - xi, 342 Seiten
• K10plus-PPN: 1908296364
• K10plus-PPN:
  Universitätsbibliothek
• Lokale URL UB: Zum Volltext

Abstract

Sequences -- Sequences of Real Numbers -- Solved Exercises -- Proposed Exercises -- Numerical Series -- Generalization of the Addition Operation -- Series Definition. Convergence. General Properties -- Alternating Series -- Absolute Convergence -- Series of Non-Negative Terms -- Multiplication of Series -- Solved Exercises -- Proposed Exercises -- Series of Functions -- Introduction. Sequences of Functions - Pointwise Convergence and Uniform Convergence of Series of Functions - Power Series - Taylor Series and Maclaurin Series - Introduction to Fourier Series - Solved Exercises - Proposed Exercises -- Additional Proofs -- Sequences of Real Numbers -- Solutions to Proposed Exercises -- Bibliography -- Index.

Abstract

This book investigates sequences and series with a clear and focused approach, presenting key theoretical concepts alongside a diverse range of examples and proposed problems, complete with solutions. It is designed to be largely self-contained, offering formal proofs when they enhance understanding. Solutions are provided separately, encouraging students to develop their problem-solving skills. Chapters 1 and 2 focus on sequences and numerical series, drawing primarily on knowledge acquired in high school. Calculus concepts become important from the end of Chapter 2, extending into Chapter 3, which is entirely dedicated to function series. This includes in-depth discussions of Taylor, Maclaurin, and Fourier series. Many of the exercises have been rigorously tested in actual classes and exams. The book is enriched by historical facts about mathematicians who have contributed to the subject, fostering students' motivation. It is valuable reading for undergraduates in mathematics, engineering, and other STEM-related fields, as well as for any student with a specific interest in the matter. The English translation of this book, originally in Portuguese, was facilitated by artificial intelligence. The content was later revised by the authors for accuracy.