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	362892	Calculus	1	3.0	3	▲	Tzu-Hsuan Tsai	4MMRE1A	0	0	下學期物理實驗周三上午

Course Plan：

Instructor	Tzu-Hsuan Tsai　Office Hours
Email	tzhtsai@ntut.edu.tw
Last Updated	2026-08-15 22:00:38
Course Objective	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。 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.
Course Schedule (Week 1-16)	1st Semester Week 01 Functions and Models Week 02 Limits and Derivatives Week 03-04 Differentiation Rules Week 05-06 Inverse Functions Week 07-08 Applications of Differentiation Week 09-10 Integrals Week 11-12 Fundamental Theorem of Calculus Week 13-14 Techniques of Integration Week 15 Improper Integrals Week 16 Series & Taylor series 2nd Semester Week 01-02 Applications of Integration Week 03-04 Parametric Equations Week 05-06 Polar Coordinates Week 07-08 Vector & the Geometry of Space Week 09-10 Directional Derivatives & Gradient Vector Week 11-12 Partial Derivatives Week 13-14 Double Integrals Week 15-16 Triple Integrals
Flexible Learning (Week 17-18)	Category ● 參與課程相關作業、作品、實驗、田野調查(Participation in course-related assignments, works, experiments, or field research) ● 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) Content 規劃 1. 學習用GEOGEBRA繪圖，完成指定函數繪圖。 2. 學習用EXCEL處理數據以及其函數功能，完成指定數據分析。 3. 看完指定教學影片，自學MATLAB，完成自學報告。 Hours 6 Learning Outcomes 1.GEOGEBRA：提供自建的GEOGEBRA帳號連結，評分者將點閱指定任務結果。 2.EXCEL：繳交指定的數據分析報告(含數據圖與文字)至本課程LINE官方帳號 (交PDF檔)。 3.MATLAB：繳交自學筆記(含學習重點與練習截圖)至本課程LINE官方帳號(交PDF檔)。 Assessment Percentage 1. GEOGEBRA：1-2%。 2. EXCEL：2-3%。 3. MATLAB：3-5%。
Evaluation and grading policy	Midterm Exam (around 9th week) 30-35% Final Exam (around 18th week) 30-35% Others (Homework, Exercise in-class & Attendance, etc.) 20-30% Uniform examination: 10%
Materials	All right reserved. Do not reproduce without permission. Foreign-language textbooks:Yes Textbook James Stewart, Essential Calculus (Metric Version) Early Transcendental (2e), Taiwan exclusive, 2022. Reference J. Hass, C. Heil, P. Bogacki, M. D. Weir, G. B. Thomas, University Calculus Early Transcendentals,4e
The access to curricular consultation	本課程開學後會提供LINE官方帳號，同學可由LINE官方帳號發問。 After the course begins, an official LINE account will be provided, through which students can ask questions. 相關課程講義將於開學後置於北科IPLUS學園。
Expanding teaching and resources	● 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	SDG1：消除貧窮（No Poverty） SDG3：良好健康和福祉（Good Health and Well-being） 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	● 鼓勵學生使用生成式AI工具（Encourage students to use generative AI tools）
Note	第17週提供自學範圍與練習單。 第18週提供自學範圍與練習單。