Course Syllabus

Course Information：

Year-Semester	Course Number	Course Name	Phase	Credits	Hours	Required/Elective	Instructor	Class	Student NO.	Withdraw	Note
Fall Semester Year 2026	362975	Calculus	1	3.0	3	▲	Hong Huei-Lin	4EN1A	0	0

Course Plan：

Instructor	Hong Huei-Lin　Office Hours
Email	honger@ntut.edu.tw
Last Updated	2026-07-16 14:14:20
Course Objective	Course Description This course aims to provide students with a solid understanding of differential and integral calculus. It is designed to cultivate logical reasoning, inspire creative thinking, strengthen computational and deductive skills, and emphasize practical applications and graphing techniques. The goal is to build a strong mathematical foundation for future studies in engineering mathematics and related professional courses, ultimately achieving the objective of applying what is learned in real-world contexts. Course topics include: 1. Limits and Continuity 2. Derivatives and Their Applications 3. Indefinite and Definite Integrals 4. Transcendental Functions and Their Inverses 5. Integration Techniques 6. Indeterminate Forms and Improper Integrals 7. Applications of Definite Integrals 8. Solid Geometry and Vector Calculus 9. Partial Derivatives 10. Multiple Integrals 11. Series 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。
Course Schedule	Week 1 Definition of Functions and Limits Week 2 Techniques for Finding Limits and Infinite Limits Week 3 Continuity of Functions Week 4 Definition and Computation of Derivatives Week 5 Chain Rule Week 6 Implicit Differentiation and Higher-Order Derivatives Week 7 Derivatives of Trigonometric, Inverse Trigonometric Functions, Exponential and Logarithmic Functions Week 8 Extrema of Functions and Mean Value Theorem Week 9 Midterm Exam Week 10 Concavity, Curve Sketching, and Applications of Extrema Week 11 Introduction of Indefinite Integrals Week 12 Integration of Substitution Week 13 Fundamental Theorem of Calculus and Definite Integrals Week 14 Integration Techniques: Integration by Parts Week 15 Integration Techniques: Trigonometric Substitution Integration, Integral of Rational Functions and Partial Fractions Week 16 Final Exam Week 17~18 Flexible Self-Directed Learning
Evaluation and grading policy	Midterm Exam: 25% Final Exam: 25% Mathematics Proficiency Test: 10% Regular Performance: 35% (including class participation, homework, quizzes, etc.) Flexible Self-Directed Learning Project 5% Deductions (There is no limit to point deductions): Tardiness: 1 point per instance (遲到 -1/堂課) Unexcused Absence: 1 point per class session (曠課 -1節)) Sleeping in Class (head down): 2^n points for the nth offense Using Phone/Tablet Without Permission: 2^n points for the nth offense 打瞌睡(或趴著睡覺)或划手機或戴耳機 -2^n/第n次 請假請依學校規定，病假要有相關單據證明。
Materials	All right reserved. Do not reproduce without permission. Foreign-language textbooks:Yes Textbook: Calculus，2e, Huei-Lin Hong, Cheh-Chih Yeh，高立圖書 Reference: 1. Calculus 5e, James Stewart 2. Calculus, 6e, Larson, Hostetler and Edwards. 3. Calculus, Tan 4. Thomas' Calculus, Thomas, Weir and Hass. 5.微積分, 第四版, 洪揮霖著，高立圖書 6. 微積分， 林晶璟，劉國安編著，新頁圖書
The access to curricular consultation	上課方式依學校公告，課程會用Teams錄影，所有修課同學請務必加入line群組(開學後兩週內務必要加入群組)，訊息公告均利用line群組，群組連結如下: https://line.me/ti/g/TP5EYFC6Lx Office hours:二78、三67 共同科館602
Expanding teaching and resources	● 參與式創新教學 (Participatory & Innovative Teaching) 強調學生參與與產出，導入翻轉、PBL/專題、設計思考或遊戲化等策略。 Emphasizes student engagement and outcomes by adopting strategies such as Flipped Classroom, PBL (Problem/Project- Based Learning), Design Thinking, or Gamification. ● 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.
The course corresponds to the SDGs	SDG4：優質教育（Quality Education） SDG8：尊嚴就業與經濟發展（Decent Work and Economic Growth）
Does the course incorporate 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） ● 使用生成式AI進行課堂即時互動（Use generative AI for real-time classroom interaction）
Note	上課方式依學校公告，課程會用Teams錄影，所有修課同學請務必在第一週上課前加入line群組(開學後兩週內務必要加入群組)，訊息公告均利用line群組。Line 群組連結如下: https://line.me/ti/g/TP5EYFC6Lx 彈性自主學習 第17~18週 請同學利用AI與相關程式，應用微積分所學各種函數，設計一個幾何動態圖形或動畫(至少20秒以上不同視覺變化)，於18週結束前將作品連結網址上傳給老師。 本課程除了第9週期中考與第16週期末考外，每週課程內容均對應SDGs 課程指標：4優質教育, 8體面工作和經濟成長，有很大關係，因微積分內容為基礎科學教育必備的一環，應用層面甚廣，不僅可以幫助工作，更可以促進經濟成長。 另與教育部品德教育促進方案相呼應內容包含典範學習（Example）、啟發思辨（Explanation）、正向期許（Expectation）等，對應週次除了第8週期中考與第16週期末考外，其餘各週內容均有包含上述6E等教學方法。