Essentials of Partial Differential Equations

With Applications

  • Marin Marin
  • Andreas Öchsner

Table of contents

  1. Front Matter
    Pages i-xi
  2. Classical Solutions

    1. Front Matter
      Pages 1-1
    2. Marin Marin, Andreas Öchsner
      Pages 3-15
    3. Marin Marin, Andreas Öchsner
      Pages 17-59
    4. Marin Marin, Andreas Öchsner
      Pages 61-109
    5. Marin Marin, Andreas Öchsner
      Pages 111-136
    6. Marin Marin, Andreas Öchsner
      Pages 137-168
    7. Marin Marin, Andreas Öchsner
      Pages 169-199
    8. Marin Marin, Andreas Öchsner
      Pages 201-224
  3. Solutions in Distributions

    1. Front Matter
      Pages 225-225
    2. Marin Marin, Andreas Öchsner
      Pages 227-260
    3. Marin Marin, Andreas Öchsner
      Pages 261-266
    4. Marin Marin, Andreas Öchsner
      Pages 267-276
    5. Marin Marin, Andreas Öchsner
      Pages 277-288
    6. Marin Marin, Andreas Öchsner
      Pages 289-308
    7. Marin Marin, Andreas Öchsner
      Pages 309-326
    8. Marin Marin, Andreas Öchsner
      Pages 327-342
    9. Marin Marin, Andreas Öchsner
      Pages 343-364
    10. Marin Marin, Andreas Öchsner
      Pages 365-377
  4. Back Matter
    Pages 379-380

About this book

Introduction

This book offers engineering students an introduction to the theory of partial differential equations and then guiding them through the modern problems in this subject.

Divided into two parts, in the first part readers already well-acquainted with problems from the theory of differential and integral equations gain insights into the classical notions and problems, including differential operators, characteristic surfaces, Levi functions, Green’s function, and Green’s formulas. Readers are also instructed in the extended potential theory in its three forms: the volume potential, the surface single-layer potential and the surface double-layer potential. Furthermore, the book presents the main initial boundary value problems associated with elliptic, parabolic and hyperbolic equations. The second part of the book, which is addressed first and foremost to those who are already acquainted with the notions and the results from the first part, introduces readers to modern aspects of the theory of partial differential equations.


Keywords

Green's function Differential operators characteristic surfaces Levi functions Green's formulas Parabolic equations Hyperbolic equations

Authors and affiliations

  • Marin Marin
    • 1
  • Andreas Öchsner
    • 2
  1. 1.Department of Mathematics and Computer ScienceTransilvania University of BrasovBrasovRomania
  2. 2.Faculty of Mechanical EngineeringEsslingen University of Applied SciencesEsslingenGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-90647-8
  • Copyright Information Springer International Publishing AG, part of Springer Nature 2019
  • Publisher Name Springer, Cham
  • eBook Packages Engineering
  • Print ISBN 978-3-319-90646-1
  • Online ISBN 978-3-319-90647-8
  • About this book