工程數學(2)

Engineering Mathematics(2)

學期

112-2

學分

3 學分

當期課號

910389

永久課號

SESE10027

開課單位

系統工程與科技學士學位學程

授課教師

楊順欽、石棟鑫

類別

必修

上課時間表

節	週二
2 09:00–09:50	工程數學(2) 3 節連堂
3 10:10–11:00
4 11:10–12:00

* 根據陽明交大上課時間表所列

概述

(中) 本課程將介紹工程數學的基本觀念,並教授學生如何利用應用相關知識解決工程問題。 (Eng.) This course will introduce some basic concepts of engineering mathematics, and teach students how to apply relevant knowledge to solve engineering problems.

評分方式

Three tests are scheduled. 3 Tests (each 30%) 90% Quizzes/Homeworks 10%

課程大綱

Chap-7, Linear Algebra: Matrices, Vectors, Determinants, Linear Systems,
Chap-8, Linear Algebra: Matrix Eigenvalue Problems,
Chap-9, Vector Differential Calculus, Grad, Div, Curl,
Chap-10, Vector Integral Calculus, Integral Theorems,
Chap-11,Fourier Analysis,
Exams

週次計畫

週次	主題
第 1 週	Chap-0, Introductions to the Course and Requirements,7.1 Matrices, Vectors: Addition and Scalar Multiplication&#x0B ,7.2 Matrix Multiplication&#x0B ,7.3 Linear Systems of Equations. Gauss Elimination,
第 2 週	7.3 Linear Systems of Equations. Gauss Elimination,&#x0B 7.4 Linear Independence. Rank of a Matrix. Vector Space,
第 3 週	和平紀念日連假
第 4 週	7.5 Solutions of Linear Systems: Existence, Uniqueness,7.6 For Reference: Second- and Third-Order Determinants,
第 5 週	7.7 Determinants. Cramer's Rule,&#x0B 7.8 Inverse of a Matrix. Gauss–Jordan Elimination,
第 6 週	Exam-1,8.1 The Matrix Eigenvalue Problem. Determining Eigenvalues and Eigenvectors,8.2 Some Applications of Eigenvalue Problems,
第 7 週	8.3 Symmetric, Skew-Symmetric, and Orthogonal Matrices,&#x0B 8.4 Eigenbases. Diagonalization. Quadratic Forms,
第 8 週	兒童節及民族掃墓節連假
第 9 週	9.1 Vectors in 2-Space and 3-Space,&#x0B 9.2 Inner Product(Dot Product)&#x0B ,9.3 Vector Product(Cross Product),
第 10 週	9.4 Vector and Scalar Functions and Their Fields Vector Calculus: Derivatives&#x0B ,9.5 Curves. Arc Length. Curvature. Torsion,&#x0B 9.6 Calculus Review: Functions of Several Variables,
第 11 週	9.7 Gradient of a Scalar Field. Directional Derivative,&#x0B 9.8 Divergence of a Vector Field&#x0B ,9.9 Curl of a Vector Field,
第 12 週	Exam-2,10.1 Line Integrals&#x0B ,10.2 Path Independence of Line Integrals&#x0B ,10.3 Calculus Review: Double Integrals,
第 13 週	10.4 Green's Theorem in the Plane,10.5 Surfaces for Surface Integrals&#x0B ,10.6 Surface Integrals,
第 14 週	10.7 Triple Integrals. Divergence Theorem of Gauss,10.8 Further Applications of the Divergence Theorem&#x0B ,10.9 Stokes's Theorem,
第 15 週	11.1 Fourier Series&#x0B ,11.2 Arbitrary Period. Even and Odd Functions. Half-Range Expansions,
第 16 週	11.3 Forced Oscillations&#x0B ,11.4 Approximation by Trigonometric Polynomials,
第 17 週	11.7 Fourier Integral&#x0B ,11.8 Fourier Cosine and Sine Transforms,&#x0B 11.10 Tables of Transforms,
第 18 週	Exam-3

教科書

Erwin Kreyszig, Advanced Engineering Mathematics, John Wiley & Sons, Inc. 10th Edition, 2018.

Office Hours

地點: Department of Civil Engineering, Engineering Building (II), Room 309.
時間: Wednesday, 10:00~12:00
聯絡方式: 03-5731917 dsshih@nctu.edu.tw