課程資訊
課程名稱
 微積分1
CALCULUS (1) 
開課學期
 113-1 
授課對象
 生命科學系  
授課教師
 蔡國榮 
課號
 MATH4006 
課程識別碼
 201E49810 
班次
 16 
學分
 2.0 
全/半年
 半年 
必/選修
 必修 
上課時間
 第1,2,3,4,5,6,7,8 週
星期二1(8:10~9:00)星期四8,9,10(15:30~18:20) 
上課地點
 普102普102 
備註
 本課程以英語授課。密集課程。英文授課.統一教學.實習課另安排.初選將直接帶入此班次的微積分2.加退選階段請自行加選微積分2.
限本系所學生(含輔系、雙修生)
總人數上限：150人 
  
課程簡介影片
 
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課程概述

This course will be conducted in English.

Calculus was independently founded by Isaac Newton and Gottfried Leibniz to describe and study the change of functions with respect to their variables. This subject has found applications and become fundamental in fields such as physics, chemistry, and engineering. In the first module of this Calculus series (MATH4006-4009), we will introduce differentiation of functions in one real variable.

Specifically, we will define the derivative of a function, derive basic rules and techniques of differentiation, analyze extrema of a function, discuss the statement and applications of the Mean Value Theorem(s), and sketch the graph of a function.

Key definitions are discussed, and important theorems are derived in lectures to help students develop their abilities in logical deduction and analysis. Practical applications of Calculus in various fields are illustrated to promote an organic interaction between the theory of Calculus and students’ own fields of study.

This course also provides TA classes, where students can enhance their proficiency in handling Calculus calculations under the guidance of our teaching assistants.

Provisional Schedule :

Week 1 Functions and Limits
1.4 Exponential Functions (Brief)
1.5 Inverse Functions and Logarithms
2.1 The Tangent Problem
2.2 The Limit of a Function
2.3 Calculating Limits Using the Limit Laws

Week 2 More on Limits and Derivatives
2.5 Continuity
2.6 Limits at Infinity; Horizontal Asymptotes
2.7 Derivatives and Rates of Change
2.8 The Derivative as a Function
3.1 Derivatives of Polynomials and Exponential Functions
9/12, Thu, Quiz 1 (Coverage : 1.4-2.3)

Week 3 Differentiation (I)
3.2 The Product and Quotient Rules
3.3 Derivatives of Trigonometric Functions
3.10 Linear Approximations and Differentials
9/19, Thu, Worksheet 1 (Derivatives in Economics)

Week 4 Differentiation (II)
3.4 The Chain Rule
3.5 Implicit Differentiation
3.6 Derivatives of Logarithmic and Inverse Trigonometric Functions
9/26, Thu, Exam 1 (Coverage : Week 1-3, WS1)

Week 5 MVT and L’Hospital’s Rule
3.7 Rates of Change in Natural and Social Science (Biology and Economics)
4.2 The Mean Value Theorem
4.4 Indeterminate Forms and L’Hospital Rule

Week 6 Curve Sketching and Optimization Problems (I)
4.1 Maximum and Minimum Values
4.3 What Derivatives Tell Us about the Shape of a Graph
10/8, Tue, Quiz 2 (Coverage 3.4-3.6)

Week 7 Curve Sketching and Optimization Problems (II)
4.5 Summary of Curve Sketching
4.7 Optimization Problems
10/17, Thu, Worksheet 2 (Higher order approximations)

Week 8 Exam Week
4.9 Antiderivatives(*)
10/24, Thu, Exam 2 (Coverage : Week 4-7, WS2) 

課程目標
 Students will be familiar with Calculus as a tool and be able to apply it in various subjects after finishing this course. Calculus 1, 2, 3, 4 provide a basis for the study of various advanced courses like Engineering Mathematics, Mathematical Analysis and Differential Equations.

To be specific, upon completing the course, students are expected to be able to

1. Understand the notion of the limits of a function
2. Use limits to describe properties of a function, including continuity and asymptotic behaviors
3. Define the derivative of a function and determine the differentiability of a function
4. Understand the geometric and physical meanings of differentiation
5. Use chain rule to differentiate composed functions and implicit functions
6. Apply Mean Value Theorem to derive properties of a function from its derivatives
7. Derive and apply the L’Hospital’s rule to compute limits of more sophisticated functions
 
課程要求
 Students are expected to be proficient in high school mathematics, including all topics covered in Pre-U/MATH4012 Pre-Calculus.

Before the course begins, students should complete the online Precalculus Self-Diagnostic Test, designed for NTU freshmen.

Students who receive unsatisfactory results on the Diagnostic Test should consider enrolling in MATH4012 Pre-Calculus and consult the instructor for advice as soon as possible. 
預期每週課後學習時數
 Besides the 4-hour lectures per week, students should expect to spend around 2-3 hours weekly in digesting the lecture materials as well as completing exercises offered by the lecturer or the teaching assistant(s).  
Office Hours
  
指定閱讀
 Textbook:
Stewart, Clegg, Watson, CALCULUS: EARLY TRANSCENDENTALS, Metric, 9th Edition.

ISBN : 0357113519

This course will be supplemented by instructor's lecture notes.  
參考書目
 NTUOCW on Calculus 1 :
https://ocw.aca.ntu.edu.tw/ntu-ocw/ocw/cou/111S102 
評量方式
(僅供參考)
  
No.
項目
百分比
說明
1. 
 Exam 1 
25% 
  
2. 
 Exam 2 
25% 
  
3. 
 Quiz 1 
10% 
  
4. 
 Quiz 2 
10% 
  
5. 
 Assessment 
30% 
  
 
針對學生困難提供學生調整方式
  
上課形式
 以錄影輔助
作業繳交方式
考試形式
其他
 由師生雙方議定
課程進度
週次
日期
單元主題
Week 1
   Functions and Limits
1.4 Exponential Functions (Brief)
1.5 Inverse Functions and Logarithms
2.1 The Tangent Problem
2.2 The Limit of a Function
2.3 Calculating Limits Using the Limit Laws 
Week 2
   More on Limits and Derivatives
2.5 Continuity
2.6 Limits at Infinity; Horizontal Asymptotes
2.7 Derivatives and Rates of Change
2.8 The Derivative as a Function
3.1 Derivatives of Polynomials and Exponential Functions

9/12, Thu, Quiz 1 (Coverage : 1.4-2.3)  
Week 3
   Differentiation (I)
3.2 The Product and Quotient Rules
3.3 Derivatives of Trigonometric Functions
3.10 Linear Approximations and Differentials

9/19, Thu, Worksheet 1 (Derivatives in Economics) 
Week 4
   Differentiation (II)
3.4 The Chain Rule
3.5 Implicit Differentiation
3.6 Derivatives of Logarithmic and Inverse Trigonometric Functions

9/26, Thu, Exam 1 (Coverage : Week 1-3, WS1) 
Week 5
   MVT and L’Hospital’s Rule
3.7 Rates of Change in Natural and Social Science (Biology and Economics)
4.2 The Mean Value Theorem
4.4 Indeterminate Forms and L’Hospital Rule 
Week 6
   Curve Sketching and Optimization Problems (I)
4.1 Maximum and Minimum Values
4.3 What Derivatives Tell Us about the Shape of a Graph

10/8, Tue, Quiz 2 (Coverage 3.4-3.6)  
Week 7
   Curve Sketching and Optimization Problems (II)
4.5 Summary of Curve Sketching
4.7 Optimization Problems

10/17, Thu, Worksheet 2 (Higher order approximations) 
Week 8
   Exam Week
4.9 Antiderivatives(*)

10/24, Thu, Exam 2 (Coverage : Week 4-7, WS2)