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Sequences and series = theory and practice /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Sequences and series/ by Ana Alves de Sá, Bento Louro.
其他題名:	theory and practice /
作者:	Alves de Sá, Ana.
其他作者:	Louro, Bento.
出版者:	Cham :Springer Nature Switzerland : : 2024.,
面頁冊數:	xi, 342 p. :ill. (some col.), digital ;24 cm.
內容註:	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.
Contained By:	Springer Nature eBook
標題:	Sequences (Mathematics) -
電子資源:	https://doi.org/10.1007/978-3-031-67202-6
ISBN:	9783031672026

Sequences and series = theory and practice /
Alves de Sá, Ana.

Sequences and seriestheory and practice /[electronic resource] :by Ana Alves de Sá, Bento Louro. - Cham :Springer Nature Switzerland :2024. - xi, 342 p. :ill. (some col.), digital ;24 cm.

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.

ISBN: 9783031672026

Standard No.: 10.1007/978-3-031-67202-6doiSubjects--Topical Terms:

555869
Sequences (Mathematics)

LC Class. No.: QA292

Dewey Class. No.: 515.24

Sequences and series = theory and practice /
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520 $a 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.
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