課號：502 20002
班次：02
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)