Partial differential equations of mathematical physics /

Partial Differential Equations of Mathematical Physics emphasizes the study of second-order partial differential equations of mathematical physics, which is deemed as the foundation of investigations into waves, heat conduction, hydrodynamics, and other physical problems.

Bibliographic Details
Call Number:Libro Electrónico
Main Author: Sobolev, S. L. (Serge�i L�vovich), 1908-1989
Format: Electronic eBook
Language:Inglés
Ruso
Published: 1964.
Series:Adiwes international series in mathematics.
Subjects:
Mathematical physics.
Differential equations, Partial.
Physique math�ematique.
�Equations aux d�eriv�ees partielles.
Mathematische Physik
Partielle Differentialgleichung
Parti�ele differentiaalvergelijkingen.
Mathematische fysica.
Fisica Matematica.
Online Access:Texto completo
Table of Contents:
  • Derivation of the fundamental equations
  • The formulation of problems of mathematical physics. Hadamard's example
  • The classification of linear equations of the second order
  • The equation for a vibrating string and its solution by D'Alembert's method
  • Riemann's method
  • Multiple integrals: Lebesgue integration
  • Integrals dependent on a parameter
  • The equation of heat conduction
  • Laplace's equation and Poisson's equation
  • Some general consequences of Green's formula
  • Poisson's equation in an unbounded medium: Newtonian potential
  • The solution of the Dirichlet problem for a half-space
  • The wave equation and the retarded potential
  • Properties of the potentials of single and double layers
  • Reduction of the Dirichlet problem and the Neumann problem to integral equations
  • Laplace's equation and Poisson's equation in a plane
  • The theory of integral equations
  • Application of the theory of Fredholm equations to the solution of the Dirichlet and Neumann problems
  • Green's function
  • Green's function for the Laplace operator
  • Correctness of formulation of the boundary-value problems of mathematical physics
  • Fourier's method
  • Integral equations with real, symmetric kernels
  • The bilinear formula and the Hilbert-Schmidt theorem
  • The inhomogeneous integral equation with a symmetric kernel
  • Vibrations of a rectangular parallelepiped
  • Laplace's equation in curvilinear coordinates. Examples of the use of Fourier's method
  • Harmonic polynomials and spherical functions
  • Some elementary properties of Spherical functions.

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