國立中興大學教學大綱
課程名稱 (中) 微積分(二)(1260)
(Eng.) Calculus(II)
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 1132
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 series, double integrals, and (self-)study polar coordinates needed for Probability [1].
2、 Understand properties of sequences and series needed for Discrete Mathematics [2].
3、 Understand properties of partial derivatives, series, and (self-)study line integrals for General Physics [3].
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
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18週)
週次 授課內容
第1週 Introduction and Course Objectives
Section 6.6 Inverse Trigonometric Functions
第2週 Section 7.1 Integration by Parts
Section 7.2 Trigonometric Integrals
第3週 Section 7.3 Trigonometric Substitution
Section 7.4 Integration of Rational Functions by Partial Fractions
第4週 Section 7.8 Improper Integrals
第5週 Section 11.1 Sequences
Section 11.2 Series
Section 11.3 The Integral Test and Estimates of Sums
第6週 Preliminary Exam in March 24th, 2025
Section 11.4 The Comparison Tests
Course Dropping Deadline at 08:00, March 29th, 2025
第7週 Make-up holiday for University Anniversary and Annual Sports Meet
第8週 Section 11.5 Alternating Series and Absolute Convergence
Section 11.6 The Ratio and Root Tests
Section 11.7 Strategy for Testing Series
第9週 Section 11.8 Power Series
Section 11.9 Representations of Functions as Power Series
第10週 Section 11.10 Taylor and Maclaurin Series
Section 11.11 Application of Taylor Polynomials
第11週 Section 14.1 Functions of Several Variables
Section 14.2 Limits and Continuity
第12週 Section 14.3 Partial Derivatives
Section 14.4 Tangent Planes and Linear Approximations
第13週 Section 14.5 The Chain Rule
Midterm Exam Before the Course Withdrawal Deadline at 08:00, May 17th, 2025
第14週 Section 14.6 Directional Derivatives and the Gradient Vector
Section 14.7 Maximum and Minimum Values
第15週 Section 14.8 Lagrange Multipliers
Section 15.1 Double Integrals over Rectangles
第16週 Section 15.2 Double Integrals over General Regions
Section 15.3 Double Integrals in Polar Coordinates
第17週 Final Exam in June 12th, 2025
Self-Study
Section 10.3 Polar Coordinates
Section 10.4 Calculus in Polar Coordinates
第18週 Self-Study
Section 16.2 Line Integrals
Section 16.3 The Fundamental Theorem for Line Integrals
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)
Within the references, [4] is the textbook, and the others are the general references.

References
[1] R. D. Yates and D. J. Goodman, Probability and stochastic processes : a friendly introduction for electrical and computer engineers, 3 ed., John Wiley & Sons Singapore Pte. Ltd., 2015.
[2] K. Rosen, Discrete Mathematics and Its Applications, 8 ed., McGraw-Hill Education, 2019.
[3] D. Giancoli, Physics for Scientists and Engineers with Modern Physics, 5 ed., Pearson Education, 2023.
[4] J. Stewart, D. Clegg and S. Watson, Calculus, Metric Version, 9 ed., Cengage Learning, Inc., 2021.
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/ )
● 中興大學微積分教學網 ( http://amath2.nchu.edu.tw/cal/ )
● 微積分線上測驗系統 ( http://calctest.nchu.edu.tw/ )
課程輔導時間
● Monday (15:10-16:00) and Wednesday (14:10-15:00) at AT336
● Academic tutoring services ( https://cdtl.nchu.edu.tw/learningConsulting/ )
聯合國全球永續發展目標(連結網址)
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更新日期 西元年/月/日：2025/03/12 16:21:57 列印日期 西元年/月/日：2025 / 3 / 14
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