© 2020

Solving Problems in Mathematical Analysis, Part I

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


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

Table of contents

  1. Front Matter
    Pages i-xii
  2. Tomasz Radożycki
    Pages 1-29
  3. Tomasz Radożycki
    Pages 31-49
  4. Tomasz Radożycki
    Pages 51-62
  5. Tomasz Radożycki
    Pages 63-87
  6. Tomasz Radożycki
    Pages 131-141
  7. Tomasz Radożycki
    Pages 143-158
  8. Tomasz Radożycki
    Pages 181-200
  9. Tomasz Radożycki
    Pages 253-270
  10. Tomasz Radożycki
    Pages 271-298
  11. Tomasz Radożycki
    Pages 299-340
  12. Back Matter
    Pages 367-369

About this book


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.


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

About the authors

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
  • Authors Tomasz Radożycki
  • Series Title Problem Books in Mathematics
  • Series Abbreviated Title Problem Books Mathematics
  • DOI
  • 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
  • Additional Information English translation of the original Polish edition published by FOSZE, Rzeszów, 2010
  • Topics Calculus
    Sequences, Series, Summability
    Mathematical Logic and Foundations
  • Buy this book on publisher's site


“The volume is intended for undergraduate students in mathematics, physics and engineering. This book is a good addition to other problem books dealing with elementary mathematical analysis.” (Vicenţiu D. Rădulescu, zbMATH 1452.26002, 2021)