Luís Vieira holds a Ph.D. in Mathematics and is currently an assistant professor at the Faculty of Engineering, University of Porto, Portugal. His research focuses mainly on algebra and combinatorics. In addition to his numerous publications, Dr. Vieira is an active developer of pedagogical materials, having published several books on calculus and real analysis.
The author invites the reader to embark on a journey through the interesting and surprising subject of sequences and series of real numbers and functions in this clear and easy-to-read theoretical exposition. The book provides several examples and applications of sequences and series, as well as a list of proposed exercises to provide a full learning experience. From the secondary to the university level, this textbook provides a solid foundation in mathematics and a basis for further studies.
Go to the bookThis mathematics book presents the main definitions and properties of sequences, series of real numbers, sequences, and series of functions. We combine a rigorous exposition with a set of intuitive examples to achieve an easily readable final text that is approachable by intermediate and more advanced calculus students from the secondary to the university level. This book is divided into three sections: an introductory one where we present the basic mathematical concepts and notation we will follow; a section devoted to sequences of real numbers; and a section dedicated to series of real numbers, sequences, and functions. These two last sections end with exercises with solutions for the readers to test their learning and knowledge. Our objective was to provide students and curious minds on the subject of the book with a tool for autonomous learning.
Part of the book: Sequences and Series