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Birkhäuser

Methods of Mathematical Physics

Classical and Modern

  • Textbook
  • © 2022

Overview

Authors:
  1. Alexey N. Karapetyants

    1. Institute of Mathematics, Mechanics and Computer Sciences and Regional Mathematical Center, Southern Federal University, Rostov-on-Don, Russia

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  2. Vladislav V. Kravchenko

    1. Department of Mathematics, Cinvestav-IPN, Campus Queretaro, Santiago de Querétaro, Mexico

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    You can also search for this author in PubMed   Google Scholar

  • Provides a thorough overview of mathematical physics, highlighting classical topics as well as recent developments
  • Introduces readers to a variety of methods that reflect current trends in research not often found in textbooks
  • Suits both an introductory course on mathematical physics as well as more advanced

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Table of contents (16 chapters)

  1. Front Matter

    Pages i-xi
    Download chapter PDF

  2. Introduction

    • Alexey N. Karapetyants, Vladislav V. Kravchenko
    Pages 1-3

  3. Classification of Partial Differential Equations

    • Alexey N. Karapetyants, Vladislav V. Kravchenko
    Pages 5-17

  4. Some Models of Mathematical Physics Reduced to Partial Differential Equations

    • Alexey N. Karapetyants, Vladislav V. Kravchenko
    Pages 19-43

  5. Boundary Value Problem Statements for Partial Differential Equations

    • Alexey N. Karapetyants, Vladislav V. Kravchenko
    Pages 45-61

  6. Cauchy Problem for Hyperbolic Equations

    • Alexey N. Karapetyants, Vladislav V. Kravchenko
    Pages 63-85

  7. Fourier Method for the Wave Equation

    • Alexey N. Karapetyants, Vladislav V. Kravchenko
    Pages 87-129

  8. Methods of Solution of Sturm-Liouville Equations, Direct and Inverse Problems

    • Alexey N. Karapetyants, Vladislav V. Kravchenko
    Pages 131-183

  9. Boundary Value Problems for the Heat Equation

    • Alexey N. Karapetyants, Vladislav V. Kravchenko
    Pages 185-208

  10. Harmonic Functions and Their Properties

    • Alexey N. Karapetyants, Vladislav V. Kravchenko
    Pages 209-224

  11. Boundary Value Problems for the Laplace Equation

    • Alexey N. Karapetyants, Vladislav V. Kravchenko
    Pages 225-242

  12. Potential Theory

    • Alexey N. Karapetyants, Vladislav V. Kravchenko
    Pages 243-279

  13. Elements of Theory of Integral Equations

    • Alexey N. Karapetyants, Vladislav V. Kravchenko
    Pages 281-344

  14. Solution of Boundary Value Problems for the Laplace Equation

    • Alexey N. Karapetyants, Vladislav V. Kravchenko
    Pages 345-352

  15. Helmholtz Equation

    • Alexey N. Karapetyants, Vladislav V. Kravchenko
    Pages 353-375

  16. Method of Non-orthogonal Series

    • Alexey N. Karapetyants, Vladislav V. Kravchenko
    Pages 377-384

  17. Bergman Kernel Approach

    • Alexey N. Karapetyants, Vladislav V. Kravchenko
    Pages 385-398

  18. Back Matter

    Pages 399-405
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Keywords

About this book

This textbook provides a thorough overview of mathematical physics, highlighting classical topics as well as recent developments. Readers will be introduced to a variety of methods that reflect current trends in research, including the Bergman kernel approach for solving boundary value and spectral problems for PDEs with variable coefficients. With its careful treatment of the fundamentals as well as coverage of topics not often encountered in textbooks, this will be an ideal text for both introductory and more specialized courses.


The first five chapters present standard material, including the classification of PDEs, an introduction to boundary value and initial value problems, and an introduction to the Fourier method of separation of variables. More advanced material and specialized treatments follow, including practical methods for solving direct and inverse Sturm-Liouville problems; the theory of parabolic equations, harmonic functions, potential theory, integral equations and the method of non-orthogonal series.


Methods of Mathematical Physics is ideal for undergraduate students and can serve as a textbook for a regular course in equations of mathematical physics as well as for more advanced courses on selected topics.

Authors and Affiliations

  • Institute of Mathematics, Mechanics and Computer Sciences and Regional Mathematical Center, Southern Federal University, Rostov-on-Don, Russia

    Alexey N. Karapetyants

  • Department of Mathematics, Cinvestav-IPN, Campus Queretaro, Santiago de QuerĂ©taro, Mexico

    Vladislav V. Kravchenko

About the authors

Alexey N. Karapetyants is professor of the Institute of Mathematics, Mechanics and Computer Sciences and director of Regional Mathematical Center at the Southern Federal University, Rostov-on-Don, Russia. His research interests include operator theory, mathematical physics, harmonic analysis: real and complex variable methods, and functional analysis.

Vladislav V. Kravchenko is a researcher in the Department of Mathematics of Center for Research and Advanced Studies of the National Polytechnic Institute, Campus Queretaro, Mexico. His research interests include mathematical physics, differential equations, complex and hypercomplex analysis, spectral theory, and inverse problems. 


Bibliographic Information

  • Book Title: Methods of Mathematical Physics

  • Book Subtitle: Classical and Modern

  • Authors: Alexey N. Karapetyants, Vladislav V. Kravchenko

  • DOI: https://doi.org/10.1007/978-3-031-17845-0

  • Publisher: Birkhäuser 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: 978-3-031-17844-3Published: 18 November 2022

  • Softcover ISBN: 978-3-031-17847-4Published: 18 November 2023

  • eBook ISBN: 978-3-031-17845-0Published: 17 November 2022

  • Edition Number: 1

  • Number of Pages: XI, 405

  • Number of Illustrations: 34 b/w illustrations, 17 illustrations in colour

  • Topics: Mathematical Physics

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