國立中興大學教學大綱

課程名稱	(中) 微積分(一)(1226)
課程名稱	(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	授課語言	英文	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 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.
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 Variables and Scope [4]
第2週	Section 1.5 The Limit of a Function [5] Section 1.6 Rules of Inference [1] Section 1.7 Introduction to Proofs [1]
第3週	Section 1.6 Calculating Limits Using the Limit Laws [5] Section 1.4 Predicates and Quantifiers [1] Section 1.5 Nested Quantifiers [1]
第4週	Section 1.7 The Precise Definition of a Limit [5] Section 1.8 Continuity [5]
第5週	Section 2.1 Derivatives and Rates of Change [5] Preliminary Exam on 2025-10-08 12:10 ~ 14:00
第6週	Section 2.2 The Derivative as a Function [5] Course Dropping Deadline at 2025-10-18 08:00
第7週	Section 2.3 Differentiation Formulas [5] Section 2.4 Derivatives of Trigonometric Functions [5]
第8週	Section 2.5 The Chain Rule [5] Section 2.6 Implicit Differentiation [5]
第9週	Section 2.9 Linear Approximations and Differentials [5] Section 3.1 Maximum and Minimum Values [5]
第10週	Section 3.2 The Mean Value Theorem [5] Section 3.3 What Derivatives Tell Us about the Shape of a Graph [5] Section 3.4 Limits at Infinity; Horizontal Asymptotes [5]
第11週	Section 3.5 Summary of Curve Sketching [5] Section 3.7 Optimization Problems [5] Section 3.9 Antiderivatives [5]
第12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13週	Section 4.4 Indefinite Integrals and the Net Change Theorem [5] Section 4.5 The Substitution Rule [5] Midterm Exam on 2025-12-03 12:10 ~ 14:00 Course Withdrawal Deadline at 2025-12-06 08:00
第14週	Section 6.1 Inverse Functions and Their Derivatives [5] 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]
第15週	Section 6.4 Derivatives of Logarithmic Functions / Section 6.4* General Logarithmic and Exponential Functions [5] Section 6.6 Inverse Trigonometric Function [5]
第16週	Section 6.8 Indeterminate Forms and l’Hospital’s Rule [5] Final Exam on 2025-12-24 12:10 ~ 14:00
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 + 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.

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] 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.

課程教材（教師個人網址請列在本校內之網址）

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.

聯合國全球永續發展目標(連結網址)

09.工業、創新基礎建設

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更新日期西元年/月/日：2025/11/05 16:14:44	列印日期西元年/月/日：2025 / 11 / 05
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