Distributions and Fourier Transforms. Part 2
| Автор(ы): | Goncharova O.
06.10.2007
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| Год изд.: | 2002 |
| Описание: | Математическое хокку! Знаете ли вы что Косинус "пи пополам" Равняется ноль? :) Вот приблизительно об этом эта книга. Distributions and Fourier Transforms. Part 2 – все что Вы хотели знать о математике, но боялись спросить. Основные темы издания: Fourier Series and Fourier Transforms; Fourier – Transforms; Distribution Solutions to Differential Equations; Partial Differential Equations; Fourier Analysis. |
| Оглавление: |
Обложка книги.
1.1 From Fourier Series to Fourier Integrals [4] 1.1.1 Convergence of the Trigonometric Fourier Series [5] 1.1.2 Sine and Cosine Series [6] 1.1.3 Change of Scale [7] 1.2 The Fourier Transform [9] 1.2.1 Sine- and Cosine- Fourier Integrals [11] 2 Fourier - Transforms [13] 2.1 Introduction to the Fourier Transform of (?) - Functions [13] 2.2 Basic Definitions for Case (?) [15] 2.3 The Schwartz Class S [16] 2.3.1 Fourier Transform in (?) [18] 2.4 Computing with Fourier Transforms [19] 2.4.1 Inversion Formula in Space S(R) [19] 2.4.2 The Linearity Property [19] 2.4.3 Translation property [20] 2.4.4 Differentiation [20] 2.4.5 Convolution Product [22] 2.5 Fourier Transforms of Tempered Distributions [25] 2.5.1 Fourier Transform of Distributions with Compact Support [27] 2.5.2 Examples of the Calculation of Fourier Transforms [28] 3 Distribution Solutions to Differential Equations [32] 3.1 Distribution Solutions to Ordinary Differential Equations [32] 3.2 Ordinary Linear Differential Equations [35] 4 Partial Differential Equations [39] 4.1 Elliptic Problems [39] 4.1.1 Potential Equation [43] 4.2 Diffusion Problems [46] 4.2.1 Heat Equation in one Space Dimension [49] 5 Fourier Analysis [51] 5.1 The Riemann - Lebesgue Lemma [51] 5.2 Paley - Wiener Theorems [51] 5.3 The Poisson Summation Formula [51] 5.4 Hermite Functions [51] 5.5 Radial Fourier Transforms and Bessel Functions [51] 5.6 Integral Equations [51] 5.7 Laplace Transforms [51] |
| Формат: | djvu |
| Размер: | 202195 байт |
| Язык: | ENG |
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| Открыть: | Ссылка (RU) |