03585nam a22004575i 4500001001800000003000900018005001700027007001500044008004100059020001800100024003500118050001000153050001000163072001600173072002300189072001500212100008100227245010900308250001800417264006900435300006600504336002600570337002600596338003600622347002400658505072100682520127601403650002902679650003302708650002702741650003602768650002002804650001402824700007502838710003402913773002602947776003602973776003603009776003603045856004603081978-3-031-67202-6DE-He21320251030113258.0cr nn 008mamaa241105s2024    sz |    s    |||| 0|eng d  a97830316720267 a10.1007/978-3-031-67202-62doi 4aQA292 4aQA295 7aPBK2bicssc 7aMAT0340002bisacsh 7aPBK2thema1 aAlves de Sá, Ana.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut10aSequences and Seriesh[electronic resource] :bTheory and Practice /cby Ana Alves de Sá, Bento Louro.  a1st ed. 2024. 1aCham :bSpringer Nature Switzerland :bImprint: Springer,c2024.  aXI, 342 p. 141 illus., 120 illus. in color.bonline resource.  atextbtxt2rdacontent  acomputerbc2rdamedia  aonline resourcebcr2rdacarrier  atext filebPDF2rda0 aSequences -- 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.  aThis 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. 0aSequences (Mathematics). 0aFunctions of real variables. 0aMathematical analysis.14aSequences, Series, Summability.24aReal Functions.24aAnalysis.1 aLouro, Bento.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut2 aSpringerLink (Online service)0 tSpringer Nature eBook08iPrinted edition:z978303167201908iPrinted edition:z978303167203308iPrinted edition:z978303167204040uhttps://doi.org/10.1007/978-3-031-67202-6