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A Course on Partial Differential Equations
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Librairie Eyrolles - Paris 5e
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A Course on Partial Differential Equations

A Course on Partial Differential Equations

Walter Craig

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205 pages, parution le 29/01/2019
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Indisponible

Résumé

Many laws of physics are formulated in terms of differential equations. This book puts together the three main aspects of the topic of partial differential equations, namely theory, phenomenology, and applications, from a contemporary point of view.Does entropy really increase no matter what we do? Can light pass through a Big Bang? What is certain about the Heisenberg uncertainty principle? Many laws of physics are formulated in terms of differential equations, and the questions above are about the nature of their solutions. This book puts together the three main aspects of the topic of partial differential equations, namely theory, phenomenology, and applications, from a contemporary point of view. In addition to the three principal examples of the wave equation, the heat equation, and Laplace's equation, the book has chapters on dispersion and the Schrodinger equation, nonlinear hyperbolic conservation laws, and shock waves.

The book covers material for an introductory course that is aimed at beginning graduate or advanced undergraduate level students. Readers should be conversant with multivariate calculus and linear algebra. They are also expected to have taken an introductory level course in analysis. Each chapter includes a comprehensive set of exercises, and most chapters have additional projects, which are intended to give students opportunities for more in-depth and open-ended study of solutions of partial differential equations and their properties.
  • Introduction
  • Wave equations
  • The heat equation
  • Laplace's equation
  • Properties of the Fourier transform
  • Wave equations on $\mathbb{R}^n$
  • Dispersion
  • Conservation laws and shocks
  • Bibliography
  • Index
 Walter Craig , McMaster University, Hamilton, ON, Canada, and Fields Institute, Toronto, ON, Canada.

Caractéristiques techniques

  PAPIER
Éditeur(s) American mathematical society
Auteur(s) Walter Craig
Parution 29/01/2019
Nb. de pages 205
EAN13 9781470442927

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