Cargando…
Generalized functions : theory and technique /
Generalized functions : theory and technique.
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
New York :
Academic Press,
1983.
|
| Colección: | Mathematics in science and engineering ;
v. 171. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Front Cover; Generalized Functions: Theory and Technique; Copyright Page; Contents; PREFACE; CHAPTER 1. THE DIRAC DELTA FUNCTION AND DELTA SEQUENCES; 1.1 The Heaviside Function; 1.2 The Dirac Delta Function; 1.3 The Delta Sequences; 1.4 A Unit Dipole; 1.5 The Heaviside Sequences; Exercises; CHAPTER 2. THE SCHWRTZ-SOBOLEV THEORY OF DISTRIBUTIONS; 2.1 Some Introductory Definitions; 2.2 Test Functions; 2.3 Linear Functionals and the Schwartz-Sobolev Theory of Distributions; 2.4 Examples; 2.5 Algebraic Operations on Distributions; 2.6 Analytic Operations on Distributions; 2.7 Examples
- 2.8 The Support and Singular Support of a Distribution Exercises; CHAPTER 3. ADDITIONAL PROPERTIES OF DISTRIBUTIONS; 3.1 Transformation Properties of the Delta Distribution; 3.2 Convergence of Distributions; 3.3 Delta Sequences with Parametric Dependence; 3.4 Fourier Series; 3.5 Examples; 3.6 The Delta Function as a Stieltjes Integral; Exercises; CHAPTER 4. DISTRIBUTIONS DEFINED BY DIVERGENT INTEGRALS; 4.1 Introduction; 4.2 The Pseudofunction H(x)/xn, n = 1, 2, 3, . . .; 4.3 Functions with Algebraic Singularity of Order m; 4.4 Examples; Exercises
- CHAPTER 5. DISTRIBUTIONAL DERIVATIVES OF FUNCTIONS WITH JUMP DISCONTINUITIES5.1 Distributional Derivatives in R1; 5.2 Rn, n = 2; Moving Surfaces of Discontinuity; 5.3 Surface Distributions; 5.4 Various Other Representations; 5.5 First-Order Distributional Derivatives; 5.6 Second-Order Distributional Derivatives; 5.7 Higher-Order Distributional Derivatives; 5.8 The Two-Dimensional Case; 5.9 Examples; CHAPTER 6. TEMPERED DISTRIBUTIONS AND THE FOURIER TRANSFORMS; 6.1 Preliminary Concepts; 6.2 Distributions of Slow Growth (Tempered Distributions); 6.3 The Fourier Transform; 6.4 Examples
- ExercisesCHAPTER 7. DIRECT PRODUCTS AND CONVOLUTIONS OF DISTRIBUTIONS; 7.1 Definition of the Direct Product; 7.2 The Direct Product of Tempered Distributions; 7.3 The Fourier Transform of the Direct Product of Tempered Distributions; 7.4 The Convolution; 7.5 The Role of Convolution in the Regularization of the Distributions; 7.6 Examples; 7.7 The Fourier Transform of the Convolution; Exercises; CHAPTER 8. THE LAPLACE TRANSFORM; 8.1 A Brief Discussion of the Classical Results; 8.2 The Laplace Transform of Distributions
- 8.3 The Laplace Transform of the Distributional Derivatives and Vice Versa8.4 Examples; Exercises; CHAPTER 9. APPLICATIONS TO ORDINARY DIFFERENTIAL EQUATIONS; 9.1 Ordinary Differential Operators; 9.2 Homogeneous Differential Equations; 9.3 Inhomogeneous Differential Equations: The Integral of a Distribution; 9.4 Examples; 9.5 Fundamental Solutions and Green's Functions; 9.6 Second-Order Differential Equations with Constant Coefficients; 9.7 Eigenvalue Problems; 9.8 Second-Order Differential Equations with Variable Coefficients; 9.9 Fourth-Order Differential Equations