傅立葉分析專題

There cannot be a language more universal and more simple, more free from errors and obscurities,….more worthy to express the invariable relations of natural things than mathematics. It interprets all phenomena by the same language, as if to attest the unity and simplicity of the plan of the universe, and to make still more evident that unchangeable order which presides over all natural causes.

― Joseph Fourier, The Analytical Theory of Heat

 

函數空間簡介：

• 從幾何向量空間到函數空間
• Legendre 多項式

歐拉公式的證明：

• 歐拉恆等式──最優美的數學定理

傅立葉分析始於傅立葉級數：

• 傅立葉級數 (上)
• 傅立葉級數 (下)

離散傅立葉轉換的推導與簡介：

• 離散傅立葉轉換
• 特殊矩陣 (七)：循環矩陣

摺積簡介：

• 摺積與離散傅立葉轉換

快速傅立葉轉換介紹：

• 快速傅立葉轉換