Course Syllabus

Course Information：

Year-Semester	Course Number	Course Name	Phase	Credits	Hours	Required/Elective	Instructor	Class	Student NO.	Withdraw	Note
Spring Semester Year 2026	354864	Engineering Mathematics (II)	1	3.0	3	▲	WEN-SHYUE CHEN	4EE2B	45	0

Course Plan：

Instructor	WEN-SHYUE CHEN　Office Hours
Email	wschen@ntut.edu.tw
Last Updated	2025-12-17 15:41:56
Course Objective	This course intends to introduce the mathematical principles and practices that today\'s engineers need to know. The course contents are: Ordinary Differential Eqs: 1st order, 2nd order and higher order ODEs. Laplace transform, series solution, special function, vector analysis, Fourier analysis and partial differential equations. 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：一常微分方程式：一階、二階及高階常微分方程，拉譜拉斯轉換，特殊函數二級數解三向量幾何與分析四傅立葉級數五偏微分方程式
Course Schedule	Week 1 Introduction; Vector Functions of One Variable, Velocity and Curvature 第1週課程介紹；單變數之向量函數、速度、曲率 Week 2 The Gradient Field, Divergence and Curl 第2週梯度場、散度及旋度 Week 3 Line Integrals, Green’s Theorem 第3週線積分、格林定理 Week 4 Independence of Path and Potential Theory 第4週與積分路徑無關之線積分及位能定理 Week 5 Surface Integrals, Applications of Surface Integrals, Gauss’s Divergence Theorem, Stokes’s Theorem 第5週面積分、面積分的應用；高斯散度定理、史托克定理 Week 6 Fourier Series on [–L, L], Fourier Sine and Fourier Cosine Series 第6週區間–L～L的傅立葉級數、傅立葉正弦與餘弦級數 Week 7 Fourier Series on [–L, L], Fourier Sine and Fourier Cosine Series 第7週區間–L～L的傅立葉級數、傅立葉正弦與餘弦級數 Week 8 Properties of Fourier Coefficients, Phase Angle Form, Complex Fourier Series 第8週傅立葉係數、相角型式的傅立葉級數、複數型的傅立葉級數 Week 9 Mid-term Exam. 第9週期中考試 Week 10 ※The Fourier Integral, Fourier Cosine and Sine Integrals, The Fourier Transform 第10週 ※傅立葉積分、傅立葉正弦與餘弦積分式、傅立葉轉換 Week 11 Wave Motion on a Bounded Interval 第11週有界區間之波的運動 Week 12 Wave Motion in an Unbounded Medium 第12週無界介質之波的運動 Week 13 The Wave Equation with a Forcing Term K(x, t) 第13週具有強迫項K(x, t)的波動方程式 Week 14 Diffusion Problems in a Bounded Medium 第14週有界介質的擴散問題 Week 15 The Heat Equation with a Forcing Term F(x, t) 第15週具有強迫項F(x, t) 的熱傳方程式 Week 16 The Heat Equation on the Real Line and Half-Line 第16週實數線與半實數線上的熱傳方程式 Week 17 The Two-Dimensional Heat Equation 第17週二維度的熱傳方程式 Week 18 Final Exam. 第18週期末考試
Evaluation and grading policy	1. Homework 作業 20% 2. Attendance 出席 20% 3. Mid-term exam. 期中考試 30% 4. Final exam. 期末考試 30%
Materials	All right reserved. Do not reproduce without permission. Foreign-language textbooks:Yes Textbook: Advanced Engineering Mathematics 8th SI Custom Solutions Edition Peter V. O’Neil Reference Book：Differential Equations with Boundary-Value Problems 7th Ed. Dennis G. Zill and Michael R. Cullen
The access to curricular consultation	學生諮商時間：每週二13:00~16:00於綜合科館314-1室及每週四16:00~19:00於綜合科館417-2室
Expanding teaching and resources
The course corresponds to the SDGs	SDG4：優質教育（Quality Education） SDG9：產業創新與基礎設施（Industry, Innovation and Infrastructure）
Does the course incorporate AI	● 無（None）
Note	若受疫情的影響，可能調整授課順序、講授內容、教授方式、評量方式及配分比例等。若因疫情而暫停實體上課時，將使用Microsoft Teams 於原定上課時間遠距上課，會議網址與細節，將公告於北科i學園+。若有其他問題，聯絡方式：wschen@ntut.edu.tw或02-27712171轉2138