工程數學(二)

臺北科技大學 114-2 學期課程，課號 355254。

課程大綱

先修課程：3002011或負責教授同意。特徵值、特徵向量及特徵函數，向量分析、向量微積分、傅立葉級數與邊界值問題、偏微分方程、複變函數。 Eigenvalue and Eigenfunction Problems, Vector Analyses, Calculus of Vectors, Fourier Series, Boundary Value Problems, Partial Differential Equations, Complex Analyses.

課程進度

週次 章節內容 01 Course introduction & Review. Matrices and Vectors. 02 Matrix Multiplication & Linear Systems of Equations. 03 Linear Independence & Solutions of Linear Systems. 04 Determinants (Second-/Third-order; Properties; Cramer’s Rule). 05 Inverse of a Matrix & Gauss–Jordan Elimination. (Quiz) 06 The Matrix Eigenvalue Problem & Applications. 07 Symmetric/Skew-symmetric/Orthogonal Matrices & Eigenbases. 08 Vectors in 2-Space and 3-Space; Inner Product; Vector Product. 09 Mid-term exam 10 Curves; Gradient; Directional Derivative. 11 Divergence; Curl. 12 Line Integrals; Path Independence; Double Integrals; Green’s Theorem. 13 Surfaces for Surface Integrals; Surface Integrals. 14 Fourier Series; Arbitrary Period. (Quiz) 15 Even/Odd Functions; Half-range Expansions; Fourier Integral. 16 Basic Concepts of PDEs; Separation of Variables; Wave Equation Modelling. 17 Solution of PDEs by Fourier Series. 18 Final exam

評量方式

平時45%(內含小考30%，平時出缺席考核與課堂行為觀察15%，點名缺席一次扣1%，最多扣至15%)，期中考25%，期末考30%。

教材

【遵守智慧財產權觀念，請使用正版教科書，不得使用非法影印教科書】 使用外文原文書：是 1. 自編教材 2. Erwin Kreyszig, Advanced Engineering Mathematics, 10th edition