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020 _a9783031672026
_9978-3-031-67202-6
024 7 _a10.1007/978-3-031-67202-6
_2doi
050 4 _aQA292
050 4 _aQA295
072 7 _aPBK
_2bicssc
072 7 _aMAT034000
_2bisacsh
072 7 _aPBK
_2thema
100 1 _aAlves de Sá, Ana.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_987015
245 1 0 _aSequences and Series
_h[electronic resource] :
_bTheory and Practice /
_cby Ana Alves de Sá, Bento Louro.
250 _a1st ed. 2024.
264 1 _aCham :
_bSpringer Nature Switzerland :
_bImprint: Springer,
_c2024.
300 _aXI, 342 p. 141 illus., 120 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
505 0 _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.
520 _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.
650 0 _aSequences (Mathematics).
_987016
650 0 _aFunctions of real variables.
_983964
650 0 _aMathematical analysis.
_964178
650 1 4 _aSequences, Series, Summability.
_987017
650 2 4 _aReal Functions.
_983965
650 2 4 _aAnalysis.
700 1 _aLouro, Bento.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_987018
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783031672019
776 0 8 _iPrinted edition:
_z9783031672033
776 0 8 _iPrinted edition:
_z9783031672040
856 4 0 _uhttps://doi.org/10.1007/978-3-031-67202-6
912 _aZDB-2-SMA
912 _aZDB-2-SXMS
999 _c64713
_d64713