工程數學(二)

臺北科技大學 114-2 學期課程，課號 354812。

課程大綱

This course will introduce the mathematical principles in engineering, including following topics: Matrices, Vectors, Linear Systems, Determinants, and Matrix Eigenvalue Problems in Linear Algebra; Vector Differential and Integral Calculus; Fourier Series and Fourier Integral; and Partial Differential Equations and Boundary Value Problems.

課程進度

1 Course introduction & Review. Matrices and Vectors. 2 Matrix Multiplication & Linear Systems of Equations. 3 Linear Independence & Solutions of Linear Systems. 4 Second- and Third-Order Determinants & Determinants. 5 Inverse of a Matrix & Vector Spaces. 6 In-class quiz 1. The Matrix Eigenvalue Problem & Their Applications. 7 Symmetric, Skew-Symmetric, and Orthogonal Matrices & Eigenbases. 8 Vectors in 2-Space and 3-Space & Inner Product & Vector Product. 9 Vector and Scalar Functions and Their Fields. Mid-term exam. 10 Curves & Gradient of a Scalar Field. 11 Divergence of a Vector Field & Curl of a Vector Field. 12 Line Integrals & Path Independence of Line Integrals & Green’s Theorem in the Plane. 13 Surfaces for Surface Integrals & Surface Integrals & Triple Integrals. 14 In-class quiz 2. Fourier Series & For Arbitrary Period. 15 Even and Odd Functions in Fourier Series & Fourier Integral. 16 Basic Concepts of PDEs & Vibrating String, Wave Equation Modelling. 17 Solution of PDEs by Fourier Series. 18 Final exam.

評量方式

Attendance 15% + In-class quizzes 1&2 25% + Mid-term exam 30% + Final exam 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 Kreyszig, Erwin. “Advanced engineering mathematics.” 10th ed.