課程資訊
課程名稱
工程數學下
ENGINEERING MATHEMATICS (2) 
開課學期
94-2 
授課對象
機械工程學系  
授課教師
伍次寅 
課號
ME2002 
課程識別碼
502 20002 
班次
02 
學分
全/半年
全年 
必/選修
必修 
上課時間
星期一3,4(10:20~12:10)星期三2(9:10~10:00) 
上課地點
工綜215 
備註
限本系所學生(含輔系、雙修生)
總人數上限:65人 
 
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課程概述

課號:502 20002
班次:01
主授教授:伍次寅
學分: 3
課程名稱:工程數學 (下)
教科書: `Advanced Engineering Mathematics`,
P.V. O`neil, 5th ed. 2003, Thomson Brooks/Cole.
課程大綱:

1. Systems of Linear Differential Equations:
homogeneous systems, fundamental matrix, solutions by eigenvalues and eigenvectors, solutions in exponential matrix form, nonhomogeneous systems, method of diagonalization, method of variation of parameters

2. Vector Calculus:
vector functions, differentiation of vector functions, curves and surfaces, tangents and normals, integration of vector functions, line integrals, surface integrals, gradient, divergence and curl, Green`s theorem, Gauss` theorem, Stokes` theorem, potential theory

3. Fourier Analysis:
Fourier series, convergence of Fourier series, Fourier integrals, Fourier transforms, properties of Fourier transform, complex Fourier transforms, Fourier spectra, power spectra, discrete Fourier transform

4. Orthogonal Expansions:
special functions (Legendre, Bessel), orthogonal polynomials, Sturm-Liouville theory, eigenfunction expansions

5. Linear Partial Differential Equations:
separation of variables, eigenvalue problems, eigen-solutions, heat equations, wave equations, Laplace equations, Laplace and Fourier transforms for solving boundary-value problems

6. Complex Analysis:
complex variables and complex functions, analytic functions, differentiation and integration of complex functions,
Cauchy integral theorem, power series, Taylor and Laurent series representation of functions, singularities, residue theorem,
multi-valued functions, branch point and branch cut, application on real integrals

成績評量方式:
1. 小考(6至7次) 佔 70%
2. 期末考 佔 30~40%
3. 作業(指定但不予評分) 

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(僅供參考)
   
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