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Partial differential equations of mathematical physics
Uravnenii︠a︡ matematicheskoĭ fiziki. English
1 online resource (x, 427 pages) : illustrations
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.
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.
S.L. Sobolev ; translated from the 3d Russion ed. by E.R. Dawson. English translation edited by T.A.A. Broadbent.
Translation of Uravnenii︠a︡ matematicheskoĭ fiziki.
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Sobolev, S.L. (Sergeĭ Lʹvovich), 1908-1989.
Adiwes international series in mathematics