Distributions and Fourier Transforms. Part 2

Автор(ы):Goncharova O.
06.10.2007
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:
Distributions and Fourier Transforms. Part 2 — обложка книги. Обложка книги.
1 Fourier Series and Fourier Transforms [4]
  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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