應用數學

物理系｜周雄

課程大綱 Course syllabus
1.Coordinate system
2.Ordinary Differential Equations
3.Linear Algebra
4.Laplace
5.Fourier Series and Transforms
6.Partial Differential Equation
7.Complex

課程目標 Objectives

讓學生在本學期中認識所教內容,並會基本的應用

參考書/教科書/閱讀文獻 Reference book/ textbook/ documents
1. Erwin Kreyszig Advanced Engineering Mathematics 9th Edition John Wiley & sons, Inc (歐亞代理)
2. Advanced Engineering Mathematics by Erwin Kreyszig

本課程共79講：

座標系統-01

座標系統-01 座標系統-02 積分單元&一階線性微分方程一階線性微分方程-01 一階線性微分方程-02 二階線性微分方程-01 二階線性微分方程-02 二階線性微分方程-03 二階線性微分方程-04 二階線性非齊次方程-01

二階線性非齊次方程-02 Partial Differential Equation Linear ODE & Legendre's Eguation Legendre's differential equation Bessel ODE-01 Bessel ODE-02 Linear Algebra-01 Linear Algebra-02 Linear system of equations,Gauss Elimination review

Linear Indep Homog. Linear System Linear system of equations,Gauss Elimination review Linear Indep Homog. Linear System Eigenvalues and Eigenvectors skew-symmetric and orthogonal matrics-01 skew-symmetric and orthogonal matrics-02 Laplace Transformation-01

Laplace Transformation-02 Laplace Transformation-03 Laplace Transformation-04 Laplace Transformation-05 Fourier Series. Integrals & Transformations Fourier Series and Transforms-01 Fourier Series and Transforms-02 Fourier Series and Transforms-03 Fourier Series and Transforms-04 Partial Differential Equation-01

Partial Differential Equation-02 Partial Differential Equation-03 Partial Differential Equation-04 Partial Differential Equation-05 Partial Differential Equation-06 Partial Differential Equation-07 Partial Differential Equation-08 Partial Differential Equation-09 Partial Differential Equation-10 Partial Differential Equation-11

Partial Differential Equation-12 Partial Differential Equation-13 Partial Differential Equation-14 Review the exam Complex-01 Complex-02 Complex-03 Complex-04 Complex-05 Complex-Power series and Taylor series-01

Complex-Power series and Taylor series-02 Complex-Power series-01 Complex-Power series-02 Complex-Singularity and zeros, Infinity Complex-Laurent series-01 Complex-Laurent series-02 Complex-Laurent Th-01 Complex-Laurent Th-02 Complex-Laurent Th-03 Complex-Laurent Th-04

ComplexConformal Mapping Complex-Linear fractional transformation Complex- Super linear fractional transformation Conformal Mapping by other function Conformal Mapping Potantial theory-Ectrostatic field Electrostatic Fields-01 Electrostatic Fields-02 Review the exam