Generalized functions : theory and applications（广义函数理论与应用）
发布日期:2006-04-07 浏览次
[内容简介]
This third edition of Generalized Functions expands the treatment of fundamental concepts and theoretical background material and delineates connections to a variety of applications in mathematical physics, elasticity, wave propagation, magnetohydrodynamics, linear systems, probability and statistics, optimal control problems in economics, and more. In applying the powerful tools of generalized functions to better serve the needs of physicists, engineers, and applied mathematicians, this work is quite distinct from other books on the subject.
Key new topics and important features:
- Examination of the Poisson Summation Formula and the concepts of differential forms and the delta distribution on wave fronts
- Enhanced presentation of the Schroedinger, Klein-Gordon, Helmholtz, heat and wave equations
- Exposition driven by additional examples and exercises
- Comprehensive bibliography and index
- Prerequisites: advanced calculus, ordinary and partial differential equations
[目次]
The Dirac Delta Function and Delta Sequences.
- The Schwartz-Sobolev Theory of Distributions.
- Additional Properties of Distributions.- Distributions Defined by Divergent Integrals
- Distributional Derivatives of Functions with Jump Discontinuities.
- Tempered Distributions and the Fourier Transforms.
- Direct Products and Convolutions of Distributions.
- The Laplace Transform.
- Applications to Ordinary Differential Equations.
- Applications to Partial Differential Equations.
- Applications to Boundary Value Problems.
- Applications to Wave Propagation.
- Interplay between Generalized Functions and the Theory of Moments.
- Linear Systems.- Miscellaneous Topics.
- References.- Index.
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