工程數學（二）

臺北科技大學 114-2 學期課程，課號 355178。

課程大綱

本課程將介紹工程上、物理上系統解析的相關數學工具，內容包括：1. 向量幾何與分析：矩陣行列式及特徵問題。2. 傅立葉級數，積分及轉換。3. 偏微分方程及邊界值問題。

課程進度

週次 單元主題 1 Reviews; 7.1 Matrices, Vectors. 2 7.2 Matrix Multiplication; 7.3 Linear Systems of Equations; Gauss Elimination. 3 7.4 Linear Independence; Rank of a Matrix; 7.5 Solutions of Linear Systems. 4 7.6 Second- and Third-Order Determinants; 7.7 Determinants; Cramer’s Ruler. 5 7.8 Inverse of a Matrix; Gauss-Jordan Elimination; 8.1 Eigenvalues; Eigenvectors. 6 8.2 Some Applications of Eigenvalue Problems; 8.3 Symmetric, Skew-Symmetric Matrices. 7 9.1 Vectors in 2-Space and 3-Space; 9.2 Inner Product. 8 9.3 Vector Product; 9.4 Vector and Scalar Functions and Fields; Derivatives. 9 期中考 10 9.5 Curves; Arc Length; 9.7 Gradient of a Scalar Field; Directional Derivative. 11 9.8 Divergence of a Vector Field; 9.9 Curl of a Vector Field; 10.1 Line Integrals. 12 10.2 Path Independence of Line Integrals; 10.3 Double Integrals; 10.4 Green’s Theorem in the Plane. 13 10.5 Surfaces for Surface Integrals; 10.6 Surface Integrals. 14 11.1 Fourier Series; 11.2 Functions of Any Period p=2L 15 11.3 Even and Odd Functions; Half-Range Expansions; 11.7 Fourier Integral; 16 12.1 Basic Concepts; 12.3 Solution by Separating Variables 17 12.3 Solution by Separating Variables; Use of Fourier Series. 18 期末考

評量方式

平時50%(內含小考40%,平時出缺席考核與課堂行為觀察10%，點名缺席一次扣1%，最多扣至10%), 期中考25%, 期末考25%

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 Kreyszig, Adv. Engrg. Math.10th