Sequences and Series
Theory and Practice
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Beschreibung
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.
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.
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
Autor*in
Ana Alves de Sá
Themen in »Sequences and Series«
Numerical series Power series Taylor series Solved exercises Fourier series Sequences of real numbers Maclaurin series Absolute convergence