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 of other correct answers. No matter in which situation, we need to have some knowledge to understand how to justify the answer we get, and modify these answers into the form we want. To have this ability, we will introduce the meaning of each symbol in Calculus and their complex relationship 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
Section 1.5 The Limit of a Function [5]
Section 1.6 Calculating Limits Using the Limit Laws [5]
Week 2 Section 1.1 Propositional Logic [1]
Section 1.4 Predicates and Quantifiers [1]
Section 1.5 Nested Quantifiers [1]
Week 3 Section 1.6 Rules of Inference [1]
Section 1.7 Introduction to Proofs [1]
Section 1.7 The Precise Definition of a Limit [5]
Week 4 Section 1.8 Continuity [5]
Section 2.1 Derivatives and Rates of Change [5]
Week 5 Section 2.2 The Derivative as a Function [5]
Section 2.3 Differentiation Formulas [5]
Week 6 Section 2.4 Derivatives of Trigonometric Functions [5]
Preliminary Exam Before the Course Dropping Deadline at 2025-10-18 08:00
Week 7 Section 2.5 The Chain Rule [5]
Section 2.6 Implicit Differentiation [5]
Week 8 Section 2.9 Linear Approximations and Differentials [5]
Section 6.1 Inverse Functions and Their Derivatives [5]
Week 9 Section 6.2 Exponential Functions and Their Derivatives [5]
Section 6.3 Logarithmic Functions [5]
Section 6.4 Derivatives of Logarithmic Functions [5]
Week 10 Section 6.6 Inverse Trigonometric Function [5]
Section 6.8 Indeterminate Forms and l'Hospital's Rule [5]
Section 3.1 Maximum and Minimum Values [5]
Week 11 Section 3.2 The Mean Value Theorem [5]
Section 3.3 What Derivatives Tell Us about the Shape of a Graph [5]
Week 12 Section 3.4 Limits at Infinity; Horizontal Asymptotes [5]
Section 3.5 Summary of Curve Sketching [5]
Section 3.6 Graphing with Calculus and Technology [5]
Week 13 Section 3.7 Optimization Problems [5]
Section 3.9 Antiderivatives [5]
Midterm Exam Before the Course Withdrawal Deadline at 2025-12-06 08:00
Week 14 Section 4.1 The Area and Distance Problems [5]
Section 4.2 The Definite Integral [5]
Section 4.3 The Fundamental Theorem of Calculus [5]
Week 15 Section 4.4 Indefinite Integrals and the Net Change Theorem [5]
Section 4.5 The Substitution Rule [5]
Section 6.2* The Natural Logarithmic Function [5]
Week 16 Section 6.3* The Natural Exponential Function [5]
Section 6.4* General Logarithmic and Exponential Functions [5]
Final Exam
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 + 25% Preliminary Exam + 25% Midterm Exam + 20% Final 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 a limit, we will cover the necessary idea in Chapter 1 The Foundations: Logic and Proofs in Discrete Mathematics and Its Applications [1] before dive into our main textbook Calculus [5]. If a proof of a theorem is not covered in Calculus [5], we might refer An Introduction to Analysis [6] , but these materials will not be in exams. The others are the general reference.

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] Kim N. King, C programming : a modern approach, 2nd ed.: W. W. Norton & Company, 2008.
[5] James Stewart, Daniel Clegg, and Saleem Watson, Calculus, Metric Version, 9th ed.: Cengage Learning, Inc., 2021.
[6] 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
中興大學微積分教學網 (http://amath2.nchu.edu.tw/cal/)
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
Please respect the intellectual property rights and use the materials legally.Please respect gender equality.
Update Date, year/month/day：2025/07/11 04:15:59 Printed Date, year/month/day：2025 / 7 / 12
The second-hand book website：http://www.myub.com.tw/