1. 簡介與基礎數學複習
1.1 脈衝與步階函數
1.2 無限級數
1.3 代數與線性代數
1.4 迴旋積分(連續與離散)

2. 複數分析
2.1 複數
2.2 複數函數
2.3 微分與積分

3. 傅立葉級數
3.1 週期函數之傅立葉級數
3.2 傅立葉級數之收斂
3.3 傅立葉級數之近似
3.4 傅立葉級數之微分與積分
3.5 離散頻譜
3.6 Parseval定理

4. 連續時間之傅立葉轉換
4.1 傅立葉級數到傅立葉轉換
4.2 有限函數之傅立葉轉換
4.3 傅立葉轉換特性
4.4 重要範例

*5. 離散時間傅立葉級數與轉換 [ 時間不足可不敎 ]
5.1 離散時間傅立葉級數
5.2 離散時間傅立葉級數特性
5.3 離散時間傅立葉轉換
5.4 離散時間傅立葉轉換特性

*6. 離散傅立葉轉換[ 時間不足可不敎 ]
6.1 離散時間傅立葉轉換之取樣
6.2 離散傅立葉轉換特性

7. 常微分方程
7.1 一階常微分方程
7.2 二階常微分方程
7.3 級數解

8. Laplace轉換
8.1 定義與基本特性
8.2 解常微分方程
8.3 使用Laplace轉換做迴旋積分

1. Introduction and Groundwork
1.1 Delta function and step function
1.2 Infinite series
1.3 Algebra and Linear Algebra
1.4 Convolution (continuous and discrete)

2. Complex Analysis
2.1 Complex numbers
2.2 Complex functions
2.3 Derivative and integration

3. Fourier Series (FS)
3.1 Fourier series for periodic function
3.2 Convergence of Fourier series (Dirichlet condition)
3.3 Approximation by Finite Fourier series
3.4 Differentiation and Integration of Fourier series
3.5 Discrete frequency spectra
3.6 Parseval's Theorem

4. Continuous-Time Fourier Transform (CT-FT)
4.1 From Fourier Series to Fourier Transform
4.2 Continuous-Time Fourier Transform for finite support function
4.3 Properties
4.4 Important Examples

*5. Discrete-Time Fourier Series (DFS) and Transform (DT-FT) [ 時間不足可不敎 ]
5.1 Representation of periodic sequences: the discrete Fourier series (DFS)
5.2 Properties of DFS
5.3 The Discrete-Time Fourier transform (DT-FT)
5.4 Properties of DT-FT

*6. Discrete Fourier Transform (DFT) [ 時間不足可不敎 ]
6.1 Sampling the DFT
6.2 Properties of DFT

7. Ordinary Differential Equation
7.1 First-order Ordinary Differential Equation
7.2 Second-order Ordinary Differential Equation
7.3 Series solution

8. Laplace Transform
8.1 Definition and basic properties
8.2 Solving ODE using Laplace transform
8.3 Convolution using Laplace transform

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