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Applying Power Series to Differential Equations

An Exploration through Questions and Projects

  • Textbook
  • © 2022

Overview

Authors:
  1. James Sochacki

    1. Mathematics and Statistics, James Madison University, Harrisonburg, USA

    View author publications

    You can also search for this author in PubMed   Google Scholar

  2. Anthony Tongen

    1. Mathematics and Statistics, James Madison University, Harrisonburg, USA

    View author publications

    You can also search for this author in PubMed   Google Scholar

  • Explores ordinary differential equations through a computational approach
  • Brings 12 selected applications specially crafted for STEM students
  • Applies to undergraduate and graduate-level research as well as for independent study

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

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Table of contents (14 chapters)

  1. Front Matter

    Pages i-xii
    Download chapter PDF

  2. Introduction

    • James Sochacki, Anthony Tongen
    Pages 1-23

  3. Egg 1: The Quadratic Ordinary Differential Equation

    • James Sochacki, Anthony Tongen
    Pages 25-41

  4. Egg 2: A First Order Differential Equation with Exponent

    • James Sochacki, Anthony Tongen
    Pages 43-50

  5. Egg 3: The First Order Sine Differential Equation

    • James Sochacki, Anthony Tongen
    Pages 51-56

  6. Egg 4: A Second Order ODE with Exponent

    • James Sochacki, Anthony Tongen
    Pages 57-63

  7. Egg 5: The Second Order Sine ODE—The Single Pendulum

    • James Sochacki, Anthony Tongen
    Pages 65-78

  8. Egg 6: Newton’s Method and the Steepest Descent Method

    • James Sochacki, Anthony Tongen
    Pages 79-90

  9. Egg 7: Determining Power Series for Functions Through ODEs

    • James Sochacki, Anthony Tongen
    Pages 91-105

  10. Egg 8: The Periodic Planar ODE

    • James Sochacki, Anthony Tongen
    Pages 107-116

  11. Egg 9: The Complex Planar Quadratic ODE

    • James Sochacki, Anthony Tongen
    Pages 117-127

  12. Egg 10: Newton’s N-Body Problem

    • James Sochacki, Anthony Tongen
    Pages 129-136

  13. Egg 11: ODEs and Conservation Laws

    • James Sochacki, Anthony Tongen
    Pages 137-148

  14. Egg 12: Delay Differential Equations

    • James Sochacki, Anthony Tongen
    Pages 149-167

  15. An Overview of Polynomial ODEs

    • James Sochacki, Anthony Tongen
    Pages 169-185

  16. Back Matter

    Pages 187-217
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Keywords

About this book

This book is aimed to undergraduate STEM majors and to researchers using ordinary differential equations. It covers a wide range of STEM-oriented differential equation problems that can be solved using computational power series methods. Many examples are illustrated with figures and each chapter ends with discovery/research questions most of which are accessible to undergraduate students, and almost all of which may be extended to graduate level research. Methodologies implemented may also be useful for researchers to solve their differential equations analytically or numerically. The textbook can be used as supplementary for undergraduate coursework, graduate research, and for independent study.


Authors and Affiliations

  • Mathematics and Statistics, James Madison University, Harrisonburg, USA

    James Sochacki, Anthony Tongen

About the authors

​James Sochacki is a Professor Emeritus and Director of the Center for Computational Mathematics and Modeling at James Madison University, USA. Dr. Sochacki holds a PhD in Applied Mathematics (1985) and a Master´s degree (1981) from the University of Wyoming, USA. His research interests lie in initial value ordinary and partial differential equations.

Anthony Tongen is a Professor and Vice Provost, Office of Research and Scholarship, at James Madison University, USA. Dr. Tongen holds a PhD in Applied Mathematics (2002) from Northwestern University, USA. His research focuses on mathematical biology, numerical analysis, dynamical systems, and game theory.

Bibliographic Information

  • Book Title: Applying Power Series to Differential Equations

  • Book Subtitle: An Exploration through Questions and Projects

  • Authors: James Sochacki, Anthony Tongen

  • Series Title: Problem Books in Mathematics

  • DOI: https://doi.org/10.1007/978-3-031-24587-9

  • Publisher: Springer Cham

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

  • Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2022

  • Hardcover ISBN: 978-3-031-24586-2Published: 16 March 2023

  • Softcover ISBN: 978-3-031-24589-3Published: 17 March 2024

  • eBook ISBN: 978-3-031-24587-9Published: 15 March 2023

  • Series ISSN: 0941-3502

  • Series E-ISSN: 2197-8506

  • Edition Number: 1

  • Number of Pages: XII, 217

  • Number of Illustrations: 9 b/w illustrations, 36 illustrations in colour

  • Topics: Analysis, Sequences, Series, Summability, Complexity, Field Theory and Polynomials

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