Cover Image

Partial Differential Equations / by Fritz John.

Show other versions (5)

The book has been completely rewritten for this new edition. While most of the material found in the earlier editions has been retained, though in changed form, there are considerable additions, in which extensive use is made of Fourier transform techniques, Hilbert space, and finite difference meth...

Full description

Saved in:
Bibliographic Details
Online Access: Full Text (via Springer)
Main Author: John, Fritz
Format: eBook
Language:English
Published: New York, NY : Springer US, 1978.
Edition:Third edition.
Series:Applied mathematical sciences (Springer-Verlag New York Inc.) ; v. 1.
Subjects:
Mathematics.
Table of Contents:
  • 1 The single first-order equation
  • 1. Introduction
  • 2. Examples
  • 3. Analytic Solution and Approximation Methods in a Simple Example
  • 4. Quasi-linear Equations
  • 5. The Cauchy Problem for the Quasi-linear Equation
  • 6. Examples
  • 7. The General First-order Equation for a Function of Two Variables
  • 8. The Cauchy Problem
  • 9. Solutions Generated as Envelopes
  • 2 Second-order equations: hyperbolic equations for functions of two independent variables
  • 1. Characteristics for Linear and Quasi-linear Second-order Equations
  • 2. Propagation of Singularities
  • 3. The Linear Second-order Equation
  • 4. The One-Dimensional Wave Equation
  • 5. Systems of First-order Equations (Courant-Lax Theory)
  • 6. A Quasi-linear System and Simple Waves
  • 3 Characteristic manifolds and the Cauchy problem
  • 1. Notation of Laurent Schwartz
  • 2. The Cauchy Problem
  • 3. Cauchy-Kowalewski Theorem
  • 4. The Lagrange-Green Identity
  • 5. The Uniqueness Theorem of Holmgren
  • 6. Distribution Solutions
  • 4 The Laplace equation
  • 1. Green's Identity, Fundamental Solutions
  • 2. The Maximum Principle
  • 3. The Dirichlet Problem, Green's Function, and Poisson's Formula
  • 4. Proof of Existence of Solutions for the Dirichlet Problem Using Subharmonic Functions ('Perron's Method')
  • 5. Solution of the Dirichlet Problem by Hilbert-Space Methods
  • 5 Hyperbolic equations in higher dimensions
  • 1. The Wave Equation in n-dimensional Space
  • 2. Higher-order Hyperbolic Equations with Constant Coefficients
  • 3. Symmetric Hyperbolic Systems
  • 6 Higher-order elliptic equations with constant coefficients
  • 1. The Fundamental Solution for Odd n
  • 2. The Dirichlet Problem
  • 7 Parabolic equations
  • 1. The Heat Equation
  • 2. The Initial-value Problem for General Second-order Linear Parabolic Equations.

Similar Items