Partial differential equations
著者
書誌事項
Partial differential equations
（AMS/IP studies in advanced mathematics, v. 6）
American Mathematical Society , International Press, c1997
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注記
Bibliography: p. 701
Includes index
内容説明・目次
内容説明
The subject matter, partial differential equations (PDEs), has a long history (dating from the 18th century) and an active contemporary phase. An early phase (with a separate focus on taut string vibrations and heat flow through solid bodies) stimulated developments of great importance for mathematical analysis, such as a wider concept of functions and integration and the existence of trigonometric or Fourier series representations. The direct relevance of PDEs to all manner of mathematical, physical and technical problems continues. This book presents a reasonably broad introductory account of the subject, with due regard for analytical detail, applications and historical matters.
目次
Introduction Partial differentiation Solutions of PDE's and their specification PDE's and related arbitrary functions Particular solutions of PDE's Similarity solutions Correctly set problems Some preliminary aspects of linear first order PDE's First order PDE's, linear First order nonlinear PDE's Some technical problems and related PDE's First order PDE's, general theory First order PDE's with multiple independent variables Original detaials of the Fourier approach to boundary value problems Eigenfunctions and eigenvalues Eigenfunctions and eigenvalues, continued Non-orthogonal eigenfunctions Further example of Fourier style analysis Inhomogeneous problems Local heat sources An inhomogeneous configuration Other eigenfunction/eigenvalue problems Uniqueness of solutions Alternative representations of solutions Other differential equations and inferences therefrom Second order ODE's Boundary value problems and Sturm-Liouville theory Green's functions and boundary value problems Green's functions and generalizations PDE's, Green's functions, and integral equations Singular and infinite range problems Orthogonality and its ramifications Fourier expansions: Generalities Fourier expansions: Varied examples Fourier integrals and transforms Applications of Fourier transforms Legendre polynomials and related expansions Bessel functions and related expansions Hyperbolic equations Afterwords Bibliography Index.
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