NCHU Course Outline
Course Name (中) 微積分(一)(1226)
(Eng.) Calculus(I)
Offering Dept Department of Applied Mathematics
Course Type Required Credits 3 Teacher Yu-Tsung Tai
Department Department of Computer Science and Engineering/Undergraduate Language English Semester 2025-FALL
Course Description There are tremendous online and offline computational resources now a day. Although their results may sometimes be correct as we expected, these results are wrong other times; in the other situation, they are not what we expected but still are some other correct answers. No matter which situation, we need to have some knowledge to understand how to justify these answers, and modify them into the form we want. To have this ability, we will introduce the meaning of symbols in Calculus and their complex relationships and interactions, so that students will not be afraid of these symbols and could trace and fix Calculus computations.
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
1. Understand properties of limit and exponential functions to derive the big-O relations among functions used in 𝐷𝑖𝑠𝑐𝑟𝑒𝑡𝑒 𝑀𝑎𝑡ℎ𝑒𝑚𝑎𝑡𝑖𝑐𝑠 [1].
2. Understand the series and integration needed for 𝑃𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 [2].
3. Understand the calculus needed for 𝐺𝑒𝑛𝑒𝑟𝑎𝑙 𝑃ℎ𝑦𝑠𝑖𝑐𝑠 [3].
4. Understand the variables and scope needed for 𝐶𝑜𝑚𝑝𝑢𝑡𝑒𝑟 𝑃𝑟𝑜𝑔𝑟𝑎𝑚𝑚𝑖𝑛𝑔 [4].
1.Having abilities on computer science literacy, information theory, and mathematical analysis.
100
Exercises
Lecturing
Networking/Distance Education
Assignment
Quiz
Attendance
Course Content and Homework/Schedule/Tests Schedule
Week Course Content
Week 1 Introduction
Variables and Scope [4]
Week 2 Section 1.5 The Limit of a Function [5]
Section 1.6 Rules of Inference [1]
Section 1.7 Introduction to Proofs [1]
Week 3 Section 1.6 Calculating Limits Using the Limit Laws [5]
Section 1.4 Predicates and Quantifiers [1]
Section 1.5 Nested Quantifiers [1]
Week 4 Section 1.7 The Precise Definition of a Limit [5]
Section 1.8 Continuity [5]
Week 5 Section 2.1 Derivatives and Rates of Change [5]
Preliminary Exam on 2025-10-08 12:10 ~ 14:00
Week 6 Section 2.2 The Derivative as a Function [5]
Section 2.3 Differentiation Formulas [5]
Course Dropping Deadline at 2025-10-18 08:00
Week 7 Section 2.4 Derivatives of Trigonometric Functions [5]
Section 2.5 The Chain Rule [5]
Section 2.6 Implicit Differentiation [5]
Week 8 Section 2.9 Linear Approximations and Differentials [5]
Section 3.1 Maximum and Minimum Values [5]
Section 3.2 The Mean Value Theorem [5]
Week 9 Section 3.3 What Derivatives Tell Us about the Shape of a Graph [5]
Section 3.4 Limits at Infinity; Horizontal Asymptotes [5]
Section 3.5 Summary of Curve Sketching [5]
Week 10 Section 3.7 Optimization Problems [5]
Section 3.9 Antiderivatives [5]
Section 4.1 The Area and Distance Problems [5]
Week 11 Section 4.2 The Definite Integral [5]
Section 4.3 The Fundamental Theorem of Calculus [5]
Week 12 Section 4.4 Indefinite Integrals and the Net Change Theorem [5]
Section 4.5 The Substitution Rule [5]
Week 13 Section 6.1 Inverse Functions and Their Derivatives [5]
Midterm Exam on 2025-12-03 12:10 ~ 14:00
Course Withdrawal Deadline at 2025-12-06 08:00
Week 14 Section 6.2 Exponential Functions and Their Derivatives / Section 6.3* The Natural Exponential Function [5]
Section 6.3 Logarithmic Functions / Section 6.2* The Natural Logarithmic Function [5]
Week 15 Section 6.4 Derivatives of Logarithmic Functions / Section 6.4* General Logarithmic and Exponential Functions [5]
Section 6.6 Inverse Trigonometric Function [5]
Week 16 Section 6.8 Indeterminate Forms and l’Hospital’s Rule [5]
Final Exam on 2025-12-24 12:10 ~ 14:00
self-directed
learning		 Section 10.3 Polar Coordinates [5]
Section 10.4 Calculus in Polar Coordinates [5]
Evaluation
The overall grades will be the highest grade among the follow three grades:
● 5% Attendance + 25% Assignments + 35% Preliminary Exam + 35% Midterm Exam ,
● 5% Attendance + 25% Assignments + 35% Preliminary Exam + 35% Final Exam , and
● 5% Attendance + 25% Assignments + 35% Midterm Exam + 35% Final Exam .
For those who attends every class and whose highest grade among the previous three grades is still ＜ 60 , your overall grade might be adjusted to pass this course.
Textbook & other References
To fully explain the definition of limit, we will cover necessary idea in Chapter 1 The Foundations: Logic and Proofs in 𝐷𝑖𝑠𝑐𝑟𝑒𝑡𝑒 𝑀𝑎𝑡ℎ𝑒𝑚𝑎𝑡𝑖𝑐𝑠 𝑎𝑛𝑑 𝐼𝑡𝑠 𝐴𝑝𝑝𝑙𝑖𝑐𝑎𝑡𝑖𝑜𝑛𝑠 [1] with logic notations [6,7] before diving into our main textbook 𝐶𝑎𝑙𝑐𝑢𝑙𝑢𝑠 [5]. If the proof of a theorem is not covered in 𝐶𝑎𝑙𝑐𝑢𝑙𝑢𝑠 [5], we might refer 𝐴𝑛 𝐼𝑛𝑡𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑜𝑛 𝑡𝑜 𝐴𝑛𝑎𝑙𝑦𝑠𝑖𝑠 [8] , but these materials will not be in exams. The others are the general references.

𝖱𝖾𝖿𝖾𝗋𝖾𝗇𝖼𝖾𝗌
[1] Kenneth Rosen, 𝐷𝑖𝑠𝑐𝑟𝑒𝑡𝑒 𝑀𝑎𝑡ℎ𝑒𝑚𝑎𝑡𝑖𝑐𝑠 𝑎𝑛𝑑 𝐼𝑡𝑠 𝐴𝑝𝑝𝑙𝑖𝑐𝑎𝑡𝑖𝑜𝑛𝑠, 8th ed.: McGraw-Hill Education, 2019.
[2] Roy D. Yates and David J. Goodman, 𝑃𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 𝑎𝑛𝑑 𝑠𝑡𝑜𝑐ℎ𝑎𝑠𝑡𝑖𝑐 𝑝𝑟𝑜𝑐𝑒𝑠𝑠𝑒𝑠 : 𝑎 𝑓𝑟𝑖𝑒𝑛𝑑𝑙𝑦 𝑖𝑛𝑡𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑜𝑛 𝑓𝑜𝑟 𝑒𝑙𝑒𝑐𝑡𝑟𝑖𝑐𝑎𝑙 𝑎𝑛𝑑 𝑐𝑜𝑚𝑝𝑢𝑡𝑒𝑟 𝑒𝑛𝑔𝑖𝑛𝑒𝑒𝑟𝑠, 3rd ed. International Student Version: John Wiley & Sons Singapore Pte. Ltd., 2015.
[3] Douglas Giancoli, 𝑃ℎ𝑦𝑠𝑖𝑐𝑠 𝑓𝑜𝑟 𝑆𝑐𝑖𝑒𝑛𝑡𝑖𝑠𝑡𝑠 𝑎𝑛𝑑 𝐸𝑛𝑔𝑖𝑛𝑒𝑒𝑟𝑠 𝑤𝑖𝑡ℎ 𝑀𝑜𝑑𝑒𝑟𝑛 𝑃ℎ𝑦𝑠𝑖𝑐𝑠, 5th ed.: Pearson Education, 2023.
[4] 錦輝 陳, 𝐶語言初學指引, 6th ed. 新北市: 博碩文化股份有限公司, 2024.
[5] James Stewart, Daniel Clegg, and Saleem Watson, 𝐶𝑎𝑙𝑐𝑢𝑙𝑢𝑠, 𝑀𝑒𝑡𝑟𝑖𝑐 𝑉𝑒𝑟𝑠𝑖𝑜𝑛, 9th ed.: Cengage Learning, Inc., 2021.
[6] Alan Hausman, Howard Kahane, and Paul Tidman, 𝐿𝑜𝑔𝑖𝑐 𝑎𝑛𝑑 𝑃ℎ𝑖𝑙𝑜𝑠𝑜𝑝ℎ𝑦 : 𝑎 𝑚𝑜𝑑𝑒𝑟𝑛 𝑖𝑛𝑡𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑜𝑛, 12th ed. Boston, MA, USA: Wadsworth, Cengage Learning, 2013.
[7] Harry J. Gensler, 𝐼𝑛𝑡𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑜𝑛 𝑡𝑜 𝑙𝑜𝑔𝑖𝑐, 3rd ed.: Routledge, 2017.
[8] William R. Wade, 𝐴𝑛 𝐼𝑛𝑡𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑜𝑛 𝑡𝑜 𝐴𝑛𝑎𝑙𝑦𝑠𝑖𝑠, 3rd ed. Upper Saddle River, New Jersey, U.S.A.: Pearson Prentice Hall, Inc., 1995.
Teaching Aids & Teacher's Website
iLearning 3.0 (https://lms2020.nchu.edu.tw/)
Office Hours
● Academic tutoring services (https://cdtl.nchu.edu.tw/learningConsulting/)
● Office hour for Prof. Tai is on Tuesday Noon (12:10-13:00) and Wednesday (14:10-15:00) at AT336.
Sustainable Development Goals, SDGs(Link URL)
09.Industry, Innovation and Infrastructureinclude experience courses：N
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Update Date, year/month/day：2025/10/15 15:14:17 Printed Date, year/month/day：2025 / 10 / 19
The second-hand book website：http://www.myub.com.tw/