課程講義
講義封面     修課名單     歷屆資訊
講義 為何要學複數與複變 SVD Complex 操作
複數相關術語 Direction derivative&Analytic complex function
　 複數操作與其幾何意義 limit, continuity and complex function
Poles and residues (x, y)與(z, z bar) (1) (2)
　 General forms of Cauchy Riemann equations
　 Solution in complex form Harmonic function
　 Application of complex variable to solve the Laplace solution Elementary function
　 Complex integration for complex function Complex integrals
　 Exponential functions and logarithms Derivation of Poisson integral formula using Cauchy integral formula
　 　 圓形邊界積分
　 Cauchy integral formula Circular boundary integrals using Poisson integral formula
　 Hadamard integral formula Poisson 積分式 (外域)

Poisson 積分式 (內域)
　 Solve ODE using residue theorem  Inverse Laplace transform (Single pole)

 Inverse Laplace transform (Double pole)
　 Power,Taylor,Maclaurine and Laurent series conformal mapping
　 Integrals using complex variable 　
　 ln積分(內外) 　
　 內外域轉換(1)

內外域轉換(2)

 　
　 PDE for solving annular and eccentric circle (1)

PDE for solving annular and eccentric circle (2)

 　
Table Comparisons of time domain and frequency domain approaches-1 　
　 Comparisons of time domain and frequency domain approaches-2 　
　 Comparisons of time domain and frequency domain for viscous damping & hysterestic damping 　
Fourier transform &Hilbert transform with Complex variable (Hilbert transform)
Constraint in Frequency Domain Geometric meaning for Fourier Transform
Geometric meaning for Hilbert Transform Time Domain versus Frequency Domain
Hilbert transform Hilbert&Fourier
Proof of Hilbert Transform 四次操作會回來的運算元
Last course 　
參考論文
複數與簡諧振動(陳永祥教授提供) 複數與工程    (賴添盛技師---取自技師報)
從柯西積分公式談起(數學傳播, 第27卷宗  第1期, 程守慶） 從三次方程到構作正七邊形
應用論文:Dual boundary element analysis using complex variables for potential problems with or without a degenerate boundary A new point of view for the polar decomposition using singular value decomposition
Alternative derivations for the Poisson integral formula 第三十卷第一期--從解三次方程到構作正七邊形
第十一卷第一期--由三次函數圖形探討三次方程式的根 複變函數論方法的應用簡介
複變函數史話