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 355543 Calculus 2 3.0 3 ▲ Tzu-Hsuan Tsai 4MMRE1B 43 0 　

Year-Semester	Course Number	Course Name	Phase	Credits	Hours	Required/Elective	Instructor	Class	Student NO.	Withdraw	Note
Spring Semester Year 2026	355543	Calculus	2	3.0	3	▲	Tzu-Hsuan Tsai	4MMRE1B	43	0

Course Plan：

Instructor Tzu-Hsuan Tsai　Office Hours

Email tzhtsai@ntut.edu.tw

Last Updated 2026-02-08 13:44:40

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 2nd Semester Week 01： Series & Taylor series Week 02： Applications of Integration Week 03-04： Parametric Equations Week 05-06： Calculus with Parametric Curves Week 07-08： Polar Coordinates Week 09-10： Vectors & the Geometry of Space Week 11-12： Partial Derivatives Week 13-14： Directional Derivatives Week 15-16： Double Integrals & Triple Integrals Week 17-18： Multiple Integrals

Evaluation and grading policy Midterm Exam (around 9th week) 35-40% Final Exam (around 18th week) 35-40% Others (Homework, Exercise in-class & Attendance, etc.) 20-30%

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 推薦科普閱讀蔡聰明，微積分的歷史步道，三民書局

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.

Expanding teaching and resources

The course corresponds to the SDGs SDG1：消除貧窮（No Poverty）
SDG4：優質教育（Quality Education）

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
相關課程講義將於開學後置於北科IPLUS學園。
Relevant course materials will be uploaded to the NTUT iPLUS platform after the semester begins.

Instructor	Tzu-Hsuan Tsai　Office Hours
Email	tzhtsai@ntut.edu.tw
Last Updated	2026-02-08 13:44:40
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	2nd Semester Week 01： Series & Taylor series Week 02： Applications of Integration Week 03-04： Parametric Equations Week 05-06： Calculus with Parametric Curves Week 07-08： Polar Coordinates Week 09-10： Vectors & the Geometry of Space Week 11-12： Partial Derivatives Week 13-14： Directional Derivatives Week 15-16： Double Integrals & Triple Integrals Week 17-18： Multiple Integrals
Evaluation and grading policy	Midterm Exam (around 9th week) 35-40% Final Exam (around 18th week) 35-40% Others (Homework, Exercise in-class & Attendance, etc.) 20-30%
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 推薦科普閱讀蔡聰明，微積分的歷史步道，三民書局
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.
Expanding teaching and resources
The course corresponds to the SDGs	SDG1：消除貧窮（No Poverty） SDG4：優質教育（Quality Education）
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	相關課程講義將於開學後置於北科IPLUS學園。 Relevant course materials will be uploaded to the NTUT iPLUS platform after the semester begins.