國立中興大學教學大綱

課程名稱	(中) 微積分(一)(1226)
	(Eng.) Calculus(I)
開課單位	應數系
課程類別	必修	學分	3	授課教師	戴淯琮
選課單位	資工系 / 學士班	授課使用語言	英文	英文/EMI	Y	開課學期	1141
課程簡述	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.
先修課程名稱						課程含自主學習	Y

課程與核心能力關聯配比(%)

課程目標之教學方法與評量方法

課程目標

核心能力

配比(%)

教學方法

評量方法

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.具備資訊科學素養、資訊理論與數學分析之能力

100

習作

講授

網路/遠距教學

作業

測驗

出席狀況

授課內容(單元名稱與內容、習作/每週授課、考試進度-共16週加自主學習)

週次	授課內容
第1週	Introduction Section 1.5 The Limit of a Function [5] Section 1.6 Calculating Limits Using the Limit Laws [5]
第2週	Section 1.1 Propositional Logic [1] Section 1.4 Predicates and Quantifiers [1] Section 1.5 Nested Quantifiers [1]
第3週	Section 1.6 Rules of Inference [1] Section 1.7 Introduction to Proofs [1] Section 1.7 The Precise Definition of a Limit [5]
第4週	Section 1.8 Continuity [5] Section 2.1 Derivatives and Rates of Change [5]
第5週	Section 2.2 The Derivative as a Function [5] Section 2.3 Differentiation Formulas [5]
第6週	Section 2.4 Derivatives of Trigonometric Functions [5] Preliminary Exam Before the Course Dropping Deadline at 2025-10-18 08:00
第7週	Section 2.5 The Chain Rule [5] Section 2.6 Implicit Differentiation [5]
第8週	Section 2.9 Linear Approximations and Differentials [5] Section 6.1 Inverse Functions and Their Derivatives [5]
第9週	Section 6.2 Exponential Functions and Their Derivatives [5] Section 6.3 Logarithmic Functions [5] Section 6.4 Derivatives of Logarithmic Functions [5]
第10週	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]
第11週	Section 3.2 The Mean Value Theorem [5] Section 3.3 What Derivatives Tell Us about the Shape of a Graph [5]
第12週	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]
第13週	Section 3.7 Optimization Problems [5] Section 3.9 Antiderivatives [5] Midterm Exam Before the Course Withdrawal Deadline at 2025-12-06 08:00
第14週	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]
第15週	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]
第16週	Section 6.3* The Natural Exponential Function [5] Section 6.4* General Logarithmic and Exponential Functions [5] Final Exam
自主學習內容	Section 10.3 Polar Coordinates [5] Section 10.4 Calculus in Polar Coordinates [5]

學習評量方式

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.

教科書＆參考書目(書名、作者、書局、代理商、說明)

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] 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 [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.

課程教材（教師個人網址請列在本校內之網址）

中興大學微積分教學網 (http://amath2.nchu.edu.tw/cal/)
iLearning 3.0 (https://lms2020.nchu.edu.tw/)

課程輔導時間

● 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.

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更新日期西元年/月/日：2025/07/31 19:41:38	列印日期西元年/月/日：2025 / 8 / 03
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