From Ordinary to Partial Differential Equations

  • Giampiero Esposito

Part of the UNITEXT book series (UNITEXT, volume 106)

Also part of the La Matematica per il 3+2 book sub series (UNITEXTMAT, volume 106)

Table of contents

  1. Front Matter
    Pages i-xxi
  2. Ordinary Differential Equations

    1. Front Matter
      Pages 1-1
    2. Giampiero Esposito
      Pages 3-23
    3. Giampiero Esposito
      Pages 25-37
  3. Linear Elliptic Equations

    1. Front Matter
      Pages 39-39
    2. Giampiero Esposito
      Pages 41-52
    3. Giampiero Esposito
      Pages 53-69
    4. Giampiero Esposito
      Pages 71-83
    5. Giampiero Esposito
      Pages 85-102
    6. Giampiero Esposito
      Pages 103-112
    7. Giampiero Esposito
      Pages 113-121
    8. Giampiero Esposito
      Pages 123-134
    9. Giampiero Esposito
      Pages 135-155
    10. Giampiero Esposito
      Pages 157-173
  4. Calculus of Variations

    1. Front Matter
      Pages 175-175
    2. Giampiero Esposito
      Pages 177-182
    3. Giampiero Esposito
      Pages 183-200
  5. Linear and Non-linear Hyperbolic Equations

    1. Front Matter
      Pages 201-201
    2. Giampiero Esposito
      Pages 203-219
    3. Giampiero Esposito
      Pages 221-232

About this book

Introduction

This book is addressed to mathematics and physics students who want to develop an interdisciplinary view of mathematics, from the age of Riemann, Poincaré and Darboux to basic tools of modern mathematics. It enables them to acquire the sensibility necessary for the formulation and solution of difficult problems, with an emphasis on concepts, rigour and creativity. It consists of eight self-contained parts: ordinary differential equations; linear elliptic equations; calculus of variations; linear and non-linear hyperbolic equations; parabolic equations; Fuchsian functions and non-linear equations; the functional equations of number theory; pseudo-differential operators and pseudo-differential equations. The author leads readers through the original papers and introduces new concepts, with a selection of topics and examples that are of high pedagogical value.

Keywords

Partial differential equations Ordinary differential equations Riemann's zeta function Fuchsian functions Characteristic conoid Fundamental solution Green function Parametrix Kirchhoff formulae Pseudoholomorphic functions

Authors and affiliations

  • Giampiero Esposito
    • 1
  1. 1.University of Naples Federico IIINFN, Sez.Napoli, Compl.Univ. M.S.Angelo NaplesItaly

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-57544-5
  • Copyright Information Springer International Publishing AG 2017
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-57543-8
  • Online ISBN 978-3-319-57544-5
  • Series Print ISSN 2038-5714
  • Series Online ISSN 2532-3318
  • About this book