# Solving Problems in Mathematical Analysis, Part I

## Sets, Functions, Limits, Derivatives, Integrals, Sequences and Series

Textbook

Part of the Problem Books in Mathematics book series (PBM)

1. Front Matter
Pages i-xii
Pages 1-29
Pages 31-49
Pages 51-62
Pages 63-87
Pages 89-130
Pages 131-141
Pages 143-158
Pages 159-180
Pages 181-200
Pages 201-231
Pages 233-252
Pages 253-270
Pages 271-298
Pages 299-340
Pages 341-365
17. Back Matter
Pages 367-369

### Introduction

This textbook offers an extensive list of completely solved problems in mathematical analysis. This first of three volumes covers sets, functions, limits, derivatives, integrals, sequences and series, to name a few. The series contains the material corresponding to the first three or four semesters of a course in Mathematical Analysis.

Based on the author’s years of teaching experience, this work stands out by providing detailed solutions (often several pages long) to the problems. The basic premise of the book is that no topic should be left unexplained, and no question that could realistically arise while studying the solutions should remain unanswered. The style and format are straightforward and accessible. In addition, each chapter includes exercises for students to work on independently. Answers are provided to all problems, allowing students to check their work.

Though chiefly intended for early undergraduate students of Mathematics, Physics and Engineering, the book will also appeal to students from other areas with an interest in Mathematical Analysis, either as supplementary reading or for independent study.

### Keywords

calculus set theory relations metric spaces functions sequences series differentiable functions indefinite integrals functional sequences functional series

#### Authors and affiliations

1. 1.Faculty of Mathematics and Natural Sciences, College of SciencesCardinal Stefan Wyszyński UniversityWarsawPoland

Tomasz Radożycki is a Professor at the Faculty of Mathematics and Natural Sciences, Cardinal Stefan Wyszyński University in Warsaw, Poland. He is also a former lecturer at both the University of Warsaw and the Warsaw University of Technology. His primary research interest is in Theoretical and Mathematical Physics.

### Bibliographic information

• Book Title Solving Problems in Mathematical Analysis, Part I
• Book Subtitle Sets, Functions, Limits, Derivatives, Integrals, Sequences and Series
• Series Title Problem Books in Mathematics
• Series Abbreviated Title Problem Books Mathematics
• DOI https://doi.org/10.1007/978-3-030-35844-0
• Copyright Information Springer Nature Switzerland AG 2020
• Publisher Name Springer, Cham
• eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
• Hardcover ISBN 978-3-030-35843-3
• eBook ISBN 978-3-030-35844-0
• Series ISSN 0941-3502
• Series E-ISSN 2197-8506
• Edition Number 1
• Number of Pages XII, 369
• Number of Illustrations 33 b/w illustrations, 0 illustrations in colour