ENGLISH

Introduction to Analysis: Theorems and Examples

By Hidefumi Katsuura

Book information

Publisher
Springer
Year
2024
ISBN
3031679539, 9783031679537, 9783031679544, 9783031679568
DOI
10.1007/978-3-031-67954-4
ISSN
1938-1743
ASIN
B0DJ1VT8CP
LCC
QA300
Language
english
Format
EPUB
Filesize
26 MB (27190973 bytes)
Series
Synthesis Lectures on Mathematics & Statistics
Edition
1
Pages
xiv, 214\0
Orientation
yes
Scanned
no
Time added
2025-01-02 14:54:12
Set Theory; Real Numbers; Sequences and Series; Co

Description

This book focuses on the theoretical aspects of calculus. The book begins with a chapter on set theory before thoroughly discussing real numbers, then moves onto sequences, series, and their convergence. The author explains why an understanding of real numbers is essential in order to create a foundation for studying analysis. Since the Cantor set is elusive to many, a section is devoted to binary/ternary numbers and the Cantor set. The book then moves on to continuous functions, differentiations, integrations, and uniform convergence of sequences of functions. An example of a nontrivial uniformly Cauchy sequence of functions is given. The author defines each topic, identifies important theorems, and includes many examples throughout each chapter. The book also provides introductory instruction on proof writing, with an emphasis on how to execute a precise writing style.

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