Sequences and Series

Theory and Practice

verfasst von: Ana Alves de Sá, Bento Louro

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

Inhaltsverzeichnis

Über dieses Buch

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.

Inhaltsverzeichnis

Frontmatter

Chapter 1. Sequences of Real Numbers

Abstract

In everyday language, the word “sequence” refers to a collection of objects or events arranged in a specific order. For instance, the daily stock quotes of a particular company on the stock exchange market can be considered a sequence. In this chapter, we shall explore sequences of real numbers and establish precise definitions for the terms “sequence” and “convergence.”

Ana Alves de Sá, Bento Louro

Chapter 2. Numerical Series

Abstract

The operation of adding two numbers extends without any difficulty to a finite number of terms, even if this number is very large. However, considering an infinite number of terms raises more delicate issues addressed in this chapter.

Ana Alves de Sá, Bento Louro

Chapter 3. Series of Functions

It is possible to express various functions as a combination of “simpler” functions, such as a series of monomials (known as Taylor series) or trigonometric functions (known as Fourier series). These function series are useful not only in approximating other functions but also in other areas of mathematics, such as differential equations.

Ana Alves de Sá, Bento Louro

Backmatter

Titel: Sequences and Series
verfasst von: Ana Alves de Sá
Bento Louro
Verlag: Springer Nature Switzerland
Electronic ISBN: 978-3-031-67202-6
Print ISBN: 978-3-031-67201-9
DOI: https://doi.org/10.1007/978-3-031-67202-6