NCHU Course Outline
Course Name (中) 微積分(一)(1207)
(Eng.) Calculus(I)
Offering Dept Department of Applied Mathematics
Course Type Required Credits 3 Teacher CHEN,KUEN-TSANN
Department Department of Physics (Optoelectronics Program)/Undergraduate Language English Semester 2026-FALL
Course Description This course aims to familiarize students with the establishment of mathematical models for engineering physics problems, and introduces various formulas for limits, continuity, basic differentials and basic integrals of single-variable functions, as well as problem types and techniques, and related graphical transformations and plotting. This will enable them to be adept at applying these concepts in engineering practice, and to become proficient in using scientific computing software suites for engineering problems and the Python data analysis language.
Prerequisites
self-directed learning in the course Y
Relevance of Course Objectives and Core Learning Outcomes(%) Teaching and Assessment Methods for Course Objectives
Course Objectives Competency Indicators Ratio(%) Teaching Methods Assessment Methods
The objectives of this course are:
1. cultivating students’ comprehensive, rigorous, and logical thinking for developing their abilities to process and analyze things in the future.
2. nourishing students’ capabilities of computations for enhancing their confidence and efficiency while solving mathematical problems.
3. establishing students’ mathematical competencies for future professional learning
2.Professional knowledge and skills
3.Problem analysis and logical deduction
50
50
Lecturing
Networking/Distance Education
Assignment
Quiz
Written Presentation
Course Content and Homework/Schedule/Tests Schedule
Week Course Content
Week 1 Chapter 1：Limits and Their Properties
Week 2 1.3 Evaluating Limits Analytically
1.4 Continuity and One-Sided Limits
Week 3 Chapter 2： Differentiation
2.2 Basic Differentiation Rules and Rates of Change
2.3 Product and Quotient Rules and Higher-Order Derivatives
Week 4 2.4The Chain Rule
2.5 Implicit Differentiation
2.6 Related Rates
Week 5 Chapter 3：Applications of Differentiation
3.2 Rolle’s Theorem and the Mean Value Theorem
Week 6 3.3 Increasing and Decreasing Functions and the First Derivative Test
3.4 Concavity and the Second Derivative Test
Week 7 3.6 A Summary of Curve Sketching
3.7 Optimization Problems
Week 8 3.8 Newton’s Method
3.9 Differentials
Midterm Exam
Week 9 Chapter 4：Integration
4.1 Antiderivatives and Indefinite Integration
4.2 Area
Week 10 4.3 Riemann Sums and Definite Integrals
4.4 The Fundamental Theorem of Calculus
4.5Integration by Substitution
Week 11 Chapter 5：Logarithmic, Exponential, and Other Transcendental Functions
5.3 Inverse Functions
Week 12 5.4 Exponential Functions: Differentiation and Integration
5.5 Bases Other Than e and Applications
5.6 Indeterminate Forms and L’Hôpital’s Rule
Week 13 5.7 Inverse Trigonometric Functions: Differentiation
5.8 Inverse Trigonometric Functions: Integration
5.9 Hyperbolic Functions
Week 14 Chapter 7：Applications of Integration
7.1 Area of a Region Between Two Curves
7.2 Volume: The Disk Method
7.4 Arc Length and Surfaces of Revolution
Week 15 Chapter 8：Integration Techniques and Improper Integrals
8.2 Integration by Parts
8.3 Trigonometric Integrals
8.4 Trigonometric Substitution
Week 16 8.8 Improper Integrals
Final Exam
self-directed
learning		    03.Preparing presentations or reports related to industry and academia.
自主學習01~人工智慧程式語言Python之入門與實作
~Python之安裝與函數圖形繪製指令介紹、微分及其應用之指令實作
自主學習02~人工智慧程式語言Python之實作與熟習
~六大函數的積分及其應用之Python指令實作
Evaluation
(1) Attendance：30%(Roll call 、Quiz #4)
(2) Midterm：30%
(3) Final Exam： 40%
Textbook & other References
1. Textbook:
“Calculus,” 12E. Metric Version By Ron Larson, & Bruce Edwards,2022 東華書局。
2. References Books
「微積分 Calculus」第一版，陳焜燦、陳志偉著，偉文出版社(2026)
and
「微積分 Calculus」第三版(3rd Edition)，陳焜燦、陳緯著，東華書局出版。
(1) 團購寄書：0952-135332黃雅慧經理(東華書局)
(2) 學校圖書館敦煌書局(~個人去買也是團購價)。
(3) 博客來網站購買
Teaching Aids & Teacher's Website
My Youtube Channel address：
http://www.amath.nchu.edu.tw/member/room/508/course.htm

Lesson (「微積分 Calculus」第三版(3rd Edition)，陳焜燦、陳緯著，東華書局出版。)每章末所附考題集錦，其詳細解答請至中興大學應數系網頁兼任老師陳焜燦網頁內下載)，網址如下：http://amath2.nchu.edu.tw/ktchen/course.htm
Office Hours
Tuesday (9:10~12:00)
Sustainable Development Goals, SDGs(Link URL)
include experience courses：N
Please respect the intellectual property rights and use the materials legally.Please respect gender equality.
Update Date, year/month/day：2026/08/02 23:35:38 Printed Date, year/month/day：2026 / 8 / 18
The second-hand book website：http://www.myub.com.tw/