資訊工程學系(Department of Computer Science and Information Engineering)
課程名稱(英文)
Engineering Mathematics
課程代碼
4102090_01
授課教師：
鍾菁哲
學分數
3
必/選修
選修
開課年級
大二
先修科目或先備能力：
微積分 (Calculus)
課程概述：
本課程著重於工程領域中常見的數學方法與其應用，主要涵蓋常微分方
程（Ordinary Differential Equation, ODE）、拉普拉斯轉換（Laplace
Transform），以及傅立葉級數、傅立葉積分與傅立葉轉換（Fourier
Series, Integral, and Transform）等主題。首先，將由一階常微分方
程開始，介紹其基本概念與解題技巧；接著探討二階線性常微分方程，
說明特徵方程及其通解的推導方式，並進一步延伸到高階線性常微分方
程，強調在工程實務中如何運用相應的解法與分析技巧。
在拉普拉斯轉換的部分，本課程將說明其定義、性質與逆轉換等重要觀
念，並著重於如何將常微分方程透過拉普拉斯轉換化為代數方程進行求
解；同時也會探討初始條件與邊界條件在應用上的影響。接著，課程將
介紹傅立葉級數及傅立葉轉換的基本原理與運算方法，並進一步延伸到
傅立葉積分，說明在處理周期性與非周期性訊號時的差異。藉由這些工
具，學生可以有效分析與處理各類工程問題，例如振動系統、波動傳遞
與訊號處理等。
透過本課程的學習，學生將能建立工程數學中的基礎概念與實用技巧，
為未來在控制系統、通訊工程、訊號與影像處理、電子電路分析以及其
他高階課程奠定扎實的理論根基。不論是致力於硬體設計或軟體開發，
本課程皆能在數學分析與工程應用的交界處，提供全面而必要的知識準
備。This course focuses on mathematical methods commonly
encountered in engineering and their applications, covering
topics such as Ordinary Differential Equations (ODEs), Laplace
Transforms, and Fourier Series, Integrals, and Transforms. It
begins with first-order ODEs, introducing fundamental
concepts and solution techniques. It then explores
second-order linear ODEs, detailing characteristic equations
and the derivation of general solutions, and extends to
higher-order linear ODEs, emphasizing their practical solution
approaches and analytical methods within engineering
contexts.
In the Laplace Transform, the course addresses key concepts
such as definitions, properties, and inverse transforms, with a
particular focus on how ODEs can be transformed into algebraic
equations through Laplace Transforms for more straightforward problem-solving. The influence of initial and
boundary conditions is also discussed. Next, the course
introduces the fundamentals of Fourier Series and Fourier
Transforms, along with their computational methods, before
extending to Fourier Integrals to clarify how to handle both
periodic and non-periodic signals. Through these tools,
students will learn to effectively analyze and address various
engineering problems, such as vibration systems, wave
propagation, and signal processing.
By completing this course, students will establish a solid
foundation of core concepts and practical techniques in
engineering mathematics, providing robust theoretical support
for advanced studies in control systems, communication
engineering, signal processing, electronic circuit analysis, and
beyond. Whether pursuing hardware design or software
development, this course offers comprehensive and essential
knowledge at the intersection of mathematical analysis and
engineering applications.
學習目標：
1. 了解常微分方程（包含一階、二階與高階）的求解方法，並能應用 於工程問題之分析與解決。[Understand the methods for solving o
2. 了解拉普拉斯轉換的基本原理與特性，並能將其應用於線性系統的 分析與工程實務問題之求解。[Understand the fundamental principl
3. 了解傅立葉分析（包含傅立葉級數、傅立葉積分與傅立葉轉換）的 概念與方法，並能應用於訊號處理、振動與波動分析等工程相關領 域 。 [Understand the
Chapter 06: Laplace Transforms (Convolution, Differentiation and Integration of
Transforms)
3
1.11.21.32.12.22.33.13.23.34.14.2
Chapter 11: Fourier Analysis (Fourier Series of Period 2pi functions, General Fourier
Series and Convergence, Even-Odd Functions and Half-Range Extensions)
3
1.11.21.32.12.22.33.13.23.34.14.2
Chapter 11: Fourier Analysis (Fourier Integral, Fourier Cosine and Sine Transforms,
Fourier Transform)
3
1.11.21.32.12.22.33.13.23.34.14.2
Chapter 11: Fourier Analysis (Fourier Transforms, DFT and FFT)
1.1.具有資訊工程相關基礎知識之吸收與了解的能力(Capability to grasp foundational knowledge in computer science.)
1.2.具有運用資訊工程理論及應用知識，分析與解決相關問題的能力(Capability to use computer science theory and application knowledge to analyze and solve related problems.)
1.3.在資訊工程的許多領域中，具有至少某一項專業能力，例如：硬體、軟體、多媒體、系統、網路、理論等(Professional in at least one area, including hardware, software, multimedia, system, networking, and theory.)
2.1.具有資訊工程實作技術及使用計算機輔助工具的能力(Capability to perform computer science implementations and use computer-aided tools.)
2.2.具有設計資訊系統、元件或製程的能力(Capability to design computer systems, components, or processes.)
2.3.具有科技寫作與簡報的能力。(Capability to write and present technical materials.)
3.1.具有除了已有的應用領域之外，亦可以將自己的專業知識應用於新的領域或跨多重領域，進行研發或創新的能力。(Capability to apply one’s professional knowledge to a new application domain or across multiple different application domains.)
3.2.具有領導或參與一個團隊完成一項專案任務的能力並且具有溝通、協調與團隊合作的能力。(Capability to lead or participate in group projects, with effective communication, coordination, and teamwork.)
3.3.具有因應資訊科技快速變遷之能力，培養自我持續學習之能力。(Capability to adapt to rapidly changing computer science technology and to develop self-learning capabilities.)
4.1.具有社會責任、人文素養及奉獻精神。(The awareness of social responsibilities, humanity, and contribution.)
4.2.具有工程倫理、宏觀能力、國際觀及前瞻視野。(The awareness of engineering ethics, broad capabilities, and global and contemporary vision.)
在資訊工程的許多領域中，具有至少某一項專業能力，例如：硬體、軟體、多媒體、系統、網路、理論等(Professional in at least one area, including hardware, software, multimedia, system, networking, and theory.)