Sequences and Series: Theory and Practice
Autor Ana Alves de Sá, Bento Louroen Limba Engleză Hardback – 14 oct 2024
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.
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Specificații
ISBN-13: 9783031672019
ISBN-10: 3031672011
Ilustrații: XX, 330 p.
Dimensiuni: 155 x 235 mm
Greutate: 1.07 kg
Ediția:2024
Editura: Springer Nature Switzerland
Colecția Springer
Locul publicării:Cham, Switzerland
ISBN-10: 3031672011
Ilustrații: XX, 330 p.
Dimensiuni: 155 x 235 mm
Greutate: 1.07 kg
Ediția:2024
Editura: Springer Nature Switzerland
Colecția Springer
Locul publicării:Cham, Switzerland
Cuprins
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.
Notă biografică
Ana Alves de Sá is an Assistant Professor at the NOVA School of Science and Technology, Portugal. She earned her Ph.D. in Mathematics (1994) from NOVA University Lisbon, with visiting periods at the Center for Mathematical Research of the Autonomous University of Barcelona, Spain. Her research interests lie in Differential Equations.
Bento Louro is an Associate Professor (retired) at the NOVA School of Science and Technology, Portugal. His research focuses on mathematical analysis, with an emphasis on Partial Differential Equations.
Bento Louro is an Associate Professor (retired) at the NOVA School of Science and Technology, Portugal. His research focuses on mathematical analysis, with an emphasis on Partial Differential Equations.
Textul de pe ultima copertă
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.
This book is a translation of an original Portuguese edition. The translation was done with the help of artificial intelligence (machine translation by the service DeepL.com). A subsequent human revision was done primarily in terms of content, so that the book will read stylistically differently from a conventional translation.
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.
This book is a translation of an original Portuguese edition. The translation was done with the help of artificial intelligence (machine translation by the service DeepL.com). A subsequent human revision was done primarily in terms of content, so that the book will read stylistically differently from a conventional translation.
Caracteristici
Explores sequences and series with a clear and focused approach Covers numerical and function series, including Taylor, MacLaurin, and Fourier series Includes an extensive list of proposed exercises with solutions