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Solving Problems in Mathematical Analysis, Part II

Definite, Improper and Multidimensional Integrals, Functions of Several Variables and Differential Equations

  • Textbook
  • © 2020

Overview

Authors:
  1. Tomasz Radożycki

    1. Faculty of Mathematics and Natural Sciences, College of Sciences, Cardinal Stefan Wyszyński University, Warsaw, Poland

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  • Offers an extensive list of completely solved problems in mathematical analysis
  • Covers definite, improper and multidimensional integrals, functions of several variables, differential equations, and more
  • Additional exercises at the end of each chapter provide rich material for independent study

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

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Table of contents (13 chapters)

  1. Front Matter

    Pages i-xi
    Download chapter PDF

  2. Exploring the Riemann and Definite Integral

    • Tomasz Radożycki
    Pages 1-51

  3. Examining Improper Integrals

    • Tomasz Radożycki
    Pages 53-74

  4. Applying One-Dimensional Integrals to Geometry and Physics

    • Tomasz Radożycki
    Pages 75-109

  5. Dealing with Functions of Several Variables

    • Tomasz Radożycki
    Pages 111-124

  6. Investigating Derivatives of Multivariable Functions

    • Tomasz Radożycki
    Pages 125-140

  7. Examining Higher Derivatives, Differential Expressions, and Taylor’s Formula

    • Tomasz Radożycki
    Pages 141-166

  8. Examining Extremes and Other Important Points

    • Tomasz Radożycki
    Pages 167-186

  9. Examining Implicit and Inverse Functions

    • Tomasz Radożycki
    Pages 187-205

  10. Solving Differential Equations of the First Order

    • Tomasz Radożycki
    Pages 207-250

  11. Solving Differential Equations of Higher Orders

    • Tomasz Radożycki
    Pages 251-278

  12. Solving Systems of First-Order Differential Equations

    • Tomasz Radożycki
    Pages 279-312

  13. Integrating in Many Dimensions

    • Tomasz Radożycki
    Pages 313-335

  14. Applying Multidimensional Integrals to Geometry and Physics

    • Tomasz Radożycki
    Pages 337-379

  15. Back Matter

    Pages 381-384
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Keywords

About this book

This textbook offers an extensive list of completely solved problems in mathematical analysis. This second of three volumes covers definite, improper and multidimensional integrals, functions of several variables, differential equations, and more. 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.

Authors and Affiliations

  • Faculty of Mathematics and Natural Sciences, College of Sciences, Cardinal Stefan Wyszyński University, Warsaw, Poland

    Tomasz Radożycki

About the author

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 II

  • Book Subtitle: Definite, Improper and Multidimensional Integrals, Functions of Several Variables and Differential Equations

  • Authors: Tomasz Radożycki

  • Series Title: Problem Books in Mathematics

  • DOI: https://doi.org/10.1007/978-3-030-36848-7

  • Publisher: Springer Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer Nature Switzerland AG 2020

  • Hardcover ISBN: 978-3-030-36847-0Published: 23 February 2020

  • eBook ISBN: 978-3-030-36848-7Published: 22 February 2020

  • Series ISSN: 0941-3502

  • Series E-ISSN: 2197-8506

  • Edition Number: 1

  • Number of Pages: XI, 384

  • Number of Illustrations: 54 b/w illustrations

  • Additional Information: English translation of the original Polish edition published by FOSZE, Rzeszów, 2013

  • Topics: Calculus, Ordinary Differential Equations, Difference and Functional Equations, Real Functions

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