教學大綱與進度

課程基本資料：

學年期	課號	課程名稱	階段	學分	時數	修	教師	班級	人	撤	備註
115-1	363099	微積分	1	3.0	3	▲	林光暉	能源一	0	0

教學大綱與進度：

教師姓名	林光暉
Email	kuanghui0510@gmail.com
最後更新時間	2026-08-14 09:21:26
課程大綱	This course aims at developing comprehension of Derivation and Integral、activating capabilities of Logic Inference and Induction、enlightening confidence and independence、strengthening calculating abilities with an emphasis on its application and diagram、furnishing a sound basis for future specialty. The content includes: 1.Limits and Continuity, 2.Derivative and Application, 3.Indefinite and Definite Integral, 4.Transcendental Functions and their Inverses, 5.Techniques of Integration, 6.Indeterminate Forms and Improper Integral, 7.Application of Integration, 8.Basic Vector Analysis, 9.Partial Derivative, 10.Multiple Integration. 本課程希望在一學年中，能使學生對微分及積分有充分的瞭解、培養邏輯推理、啟發思考創造、強化計算演繹並注重應用與作圖，以建立同學未來學習工程數學及相關專業課程之數學基礎，充分達到學以致用的目的。課程內容包括：1.極限與連續，2.導數及其應用，3.不定積分與定積分，4.超越函數及其反函數，5.積分法則，6.不定型與瑕積分，7.定積分的應用，8.空間幾何與向量微積分，9.偏導數，10.重積分。
課程進度 (1-16週)	Week 1~ 2: Chapter 1: Functions and Models Week 3~ 4: Chapter2: Limits and Derivatives Week 5~ 7: Chapter 3: Differentiation Rules Week 8~ 10: Chapter 4: Applications of Differentiation Week11~12: Chapter 5: Integrals Week 13~15: Chapter 6: Applications of Integration Week 16: Final exam Week 17-18: Flexible Learning Week
彈性學習 (17-18週)	類別 ● 線上數位教材學習(Coursera、edX、磨課師等)(Online digital learning (Coursera, edX, MOOCs, etc.)) ● AI 輔助學習與工具應用(AI-assisted learning and tool application) 內容 The final two weeks integrate digital resources and AI. Week 17 ("Online Digital Learning") uses platforms to review Calculus concepts. Week 18 ("AI-Assisted Learning") applies MathGPT, Gemini, and Claude for problem-solving and visualization. Students conclude by submitting an "AI & Math" project, showcasing human-AI collaborative problem-solving and critical verification. 時數 (小時) 6 學習成果 Students will build "digital self-learning" to reinforce Calculus concepts and use "AI tools" for problem-solving and visualization. They will develop "critical verification thinking" to audit AI outputs for logical accuracy. Finally, the "AI & Math" project showcases their human-AI collaborative problem-solving skills. 評量比例 AI&Math: 10%
評量方式與標準	(1) Midterm Exam: 30% (2) Final Exam: 30% (3) Homework Assignments: 20% (4) AI&Math: 10% (5) Mathematics Standardized Test (10/14): 10% To be announced in the class for further details.
使用教材、參考書目或其他	【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 Essential Calculus: Early Transcendentals, Metric Version 2e(Custom Solutions), James Stewart, Daniel Clegg, Saleem Watson
課程諮詢管道	1. Office hour 2. Make an appointment 3. Email: kuanghui0510@ntut.edu.tw 4. After class or before class (20 minutes)
延伸教學與資源	● 數位科技融入 (Digital Technology Integration) 運用生成式AI、VR/AR、IoT、IRS等新興科技輔助教學與評量。 Utilizes emerging technologies such as Generative AI, VR/AR, IoT, and IRS (Interactive Response Systems) to facilitate teaching and assessment. ● 數位教材資源應用 (Application of Digital Resources) 採用影音多媒體或具開放授權之資源（如OCW、開放教科書）作為主要或輔助教材。 Adopts multimedia or open-licensed resources (e.g., OCW, Open Textbooks) as primary or supplementary teaching materials.
課程對應SDGs指標	SDG4：優質教育（Quality Education） SDG8：尊嚴就業與經濟發展（Decent Work and Economic Growth） SDG9：產業創新與基礎設施（Industry, Innovation and Infrastructure）
課程是否導入AI	● 使用生成式AI作為教學過程的輔助工具（Use generative AI tools as an aid to the teaching process） ● 鼓勵學生使用生成式AI工具（Encourage students to use generative AI tools） ● 簡單介紹AI的基本概念（Briefly introduce the basic concept of AI）
備註	學習規範請假、遲到、按照學校規定。 & To be announced in the class