• 學分： (上) 3
• 課程碼： E620630
• 必/選修： 選修
• 授課語言： 中文
• 授課教師： 陳東陽
• 課程大綱：

歷年開課

課程目標：

熟悉傅立葉級數，轉換，偏微分方程式。

課程內容概要：

I. Fourier series, integrals, and transforms:

Periodic functions, trigonometric series, Fourier series, functions of any period, Even and odd functions, half-range expansions, approximations by trigonometric polynomials, Fourier integrals, Fourier cosine and sine transforms, Fourier transforms, etc.

II. Sturm-Liouville problems:

Sturm-Liouville problems, the orthogonality theorem, non-homogeneous boundary value problem.

III. Partial differential equations:

Basic concepts, vibrating string, wave equations, separation of variables, D’Alembert’s solutions of the wave equation, heart equations by Fourier series and integrals, membrane, 2-D wave equation, rectangular membrane, circular membrane, Fourier-Bessel Series, Laplace’s equations, Laplacian in spherical coordinates, Legendre’s equation, solutions by Laplace and Fourier transforms.

IV. Topics in higher-dimensional calculus:

Partial differentiation, implicit function, functional dependence, Taylor series, maximum and minimum, constraints and Lagrange multipliers, etc.

成績計算方式：

(a) 2 mid-term exams.................................................................................. 67%

(b) 1 final exam.......................................................................................... 33%

教科書或主要參考書：

(a) Kreyszig, E., 1999, Advanced Engineering Mathematics. 8th ed., John Wiley & Sons, New York.

(b) Hildebrand, F. B., 1976, Advanced Calculus for Applications. Prentice-Hall, New Jersey.

適合選修對象：

大三選修

建議先修基礎課程：

微積分、工程數學(一) (二)