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 中/英文 Semester 2024-FALL
Course Description 雖然現在電腦和網路越來越發達，已可在大多數情況下幫我們算出或搜到想要的計算結果，但如果不知道要怎麼輸入計算的指令或無法判斷計算的步驟，我們還是可能無法在如繁星般可能計算的過程中選出正確的計算方法並推導出我們想要的結果。為此，本課程希望大家能了解微積分各個符號的基本涵意，有推導微積分計算的基本能力，以在日後踫到微積分相關問題時，就算無法現場推導出結果，也有辦法自己找到答案，或在找到的答案分岐時有辦法判斷到底那個是對的或全都是錯的要自己導。
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. 學會正確計算普通物理學 [1]所需的微積分技巧。
Understand the calculus needed for General Physics [1].
2. 了解機率 [2]所需的級數和以及計算分佈的積分。
Understand the series and integration needed for Probability [2].
1.Having abilities on computer science literacy, information theory, and mathematical analysis.
100
Exercises
Lecturing
Assignment
Quiz
Course Content and Homework/Schedule/Tests Schedule
Week Course Content
Week 1 Section 1.1 Four Ways to Represent a Function
Section 1.2 Mathematical Models: A Catalog of Essential Functions
Week 2 Section 1.3 New Functions from Old Functions
Section 1.4 The Tangent and Velocity Problems
Week 3 Section 1.5 The Limit of a Function
Section 1.6 Calculating Limits Using the Limit Laws
Week 4 Section 1.7 The Precise Definition of a Limit
2024年10月02日因應山陀兒颱風臺中市停止上班上課
Classes in Taichung City Is Paused on October 2, 2024, Due to Typhoon KRATHON
Week 5 Section 1.8 Continuity
Section 2.1 Derivatives and Rates of Change
Week 6 Section 2.2 The Derivative as a Function
2024年10月16日期初考
Preliminary Exam on October 16, 2024
Week 7 Section 2.3 Differentiation Formulas
Section 2.4 Derivatives of Trigonometric Functions
Week 8 Section 2.5 The Chain Rule
Section 2.6 Implicit Differentiation
Week 9 Section 2.7 Rates of Change in the Natural and Social Sciences
Section 2.8 Related Rates
Section 2.9 Linear Approximations and Differentials
Week 10 Section 6.1 Inverse Functions and Their Derivatives
Section 6.2 Exponential Functions and Their Derivatives
Section 6.3 Logarithmic Functions
Week 11 Section 6.4 Derivatives of Logarithmic Functions
Section 6.8 Indeterminate Forms and l’Hospital’s Rule
Section 3.1 Maximum and Minimum Values
Week 12 Section 3.2 The Mean Value Theorem
Section 3.3 What Derivatives Tell Us about the Shape of a Graph
2024年11月27日期中考
Midterm Exam on November 27, 2024
Week 13 Section 3.4 Limits at Infinity; Horizontal Asymptotes
Section 3.5 Summary of Curve Sketching
2024年12月7日08:00停修截止
Course Withdrawal Deadline, 08:00, December 7, 2024
Week 14 Section 3.6 Graphing with Calculus and Technology
Section 3.7 Optimization Problems
Week 15 Section 4.1 The Area and Distance Problems
Section 4.2 The Definite Integral
Week 16 Section 4.3 The Fundamental Theorem of Calculus
Section 4.4 Indefinite Integrals and the Net Change Theorem
Section 4.5 The Substitution Rule
Final Exam
Week 17 自主學習
Self-Study
Section 5.1 Areas Between Curves
Section 5.2 Volumes
Week 18 自主學習
Self-Study
Section 5.3 Volumes by Cylindrical Shells
Section 5.5 Average Value of a Function
Evaluation
學期成績會取下列三個分數中最高的：
● 5% 出席狀況 + 30% 作業 + 25% 期初考 + 25% 期中考 + 15% 期末考、
● 5% 出席狀況 + 30% 作業 + 32.5% 期初考 + 35.5% 期末考、
● 5% 出席狀況 + 30% 作業 + 32.5% 期中考 + 32.5% 期末考。
對於全勤但上列三個分數中最高的還是 ＜ 60 分的學生，學期成績可視情況加到 60 分以通過這門課。

The overall grades will be the highest grade among the follow three grades:
● 5% Attendance + 30% Assignments + 25% Preliminary Exam + 25% Midterm Exam + 15% Final Exam,
● 5% Attendance + 30% Assignments + 32.5% Preliminary Exam + 32.5% Final Exam, and
● 5% Attendance + 30% Assignments + 32.5% Midterm Exam + 32.5% 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
其中 [3]是教科書。需要解釋變數及其範圍時，會參考 [4]。其他是參考書目。
Within the references, [3] is the textbook. If we need the idea of variables and scope, they will be explained according to [4]. The others are the general reference.

References
[1] D. Giancoli, Physics for Scientists and Engineers with Modern Physics, 5 ed., Pearson Education, 2023.
[2] 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.
[3] J. Stewart, D. Clegg and S. Watson, Calculus, Metric Version, 9 ed., Cengage Learning, Inc., 2021.
[4] K. N. King, C programming : a modern approach, 2 ed., W. W. Norton & Company, 2008.
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
● 學習諮詢預約服務 (https://cdtl.nchu.edu.tw/learningConsulting/)
● 星期二中午(12:10-13:00)、星期三第六節(14:10-15:00)於應用科技大樓336或資訊科學大樓611，依 Office Hour 前於應用科技大樓336上的微積分課下課後有沒有人留在教室問問題而定。
Sustainable Development Goals, SDGs
09.Industry, Innovation and Infrastructureinclude experience courses：N
Please respect the intellectual property rights and use the materials legally.Please repsect gender equality.
Update Date, year/month/day：2024/11/20 16:16:46 Printed Date, year/month/day：2024 / 11 / 21
The second-hand book website：http://www.myub.com.tw/