03949nam a22005415i 4500 978-3-031-67202-6 DE-He213 20251030113258.0 cr nn 008mamaa 241105s2024 sz | s |||| 0|eng d 9783031672026 978-3-031-67202-6 10.1007/978-3-031-67202-6 doi QA292 QA295 PBK bicssc MAT034000 bisacsh PBK thema Alves de Sá, Ana. author. aut http://id.loc.gov/vocabulary/relators/aut 87015 Sequences and Series [electronic resource] : Theory and Practice / by Ana Alves de Sá, Bento Louro. 1st ed. 2024. Cham : Springer Nature Switzerland : Imprint: Springer, 2024. XI, 342 p. 141 illus., 120 illus. in color. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda 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. 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. Sequences (Mathematics). 87016 Functions of real variables. 83964 Mathematical analysis. 64178 Sequences, Series, Summability. 87017 Real Functions. 83965 Analysis. Louro, Bento. author. aut http://id.loc.gov/vocabulary/relators/aut 87018 SpringerLink (Online service) Springer Nature eBook Printed edition: 9783031672019 Printed edition: 9783031672033 Printed edition: 9783031672040 https://doi.org/10.1007/978-3-031-67202-6 ZDB-2-SMA ZDB-2-SXMS 64713 64713