課程資訊
課程名稱
微積分乙上
Calculus (general Mathematics) (b)(1) 
開課學期
106-1 
授課對象
地理環境資源學系  
授課教師
劉瓊如 
課號
MATH1203 
課程識別碼
201 101B1 
班次
12 
學分
3.0 
全/半年
全年 
必/選修
必修 
上課時間
星期二1,2(8:10~10:00)星期四3,4(10:20~12:10) 
上課地點
新303新303 
備註
大二以上限20人.
限本系所學生(含輔系、雙修生)
總人數上限:140人 
Ceiba 課程網頁
http://ceiba.ntu.edu.tw/1061MATH1203_12 
課程簡介影片
 
核心能力關聯
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課程概述

Study the process of approximation and its limitation (errors), learn the tools and techniques for analyzing regular mappings with applications, and deepen the understanding of elementary functions.

 

課程目標
Study the process of approximation and its limitation (errors), learn the tools and techniques for analyzing regular mappings with applications, and deepen the understanding of elementary functions. 
課程要求
High School Mathematics 
預期每週課後學習時數
 
Office Hours
 
指定閱讀
待補 
參考書目
James Stewart, Calculus Early Transcendentals, 8th edition. (Metric version) 
評量方式
(僅供參考)
 
No.
項目
百分比
說明
1. 
平常 
30% 
作業,小考 
2. 
期中考 
35% 
 
3. 
期末考 
35% 
 
 
課程進度
週次
日期
單元主題
第1週
9/12,9/14  1.4 Exponential Functions
1.5 Inverse Functions and Logarithms
2.1 The Tangent and Velocity Problems
2.2 The Limit of a Function  
第2週
9/19,9/21  2.3 Calculating Limits Using the Limit Laws
2.4 The Precise Definition of a Limit
2.5 Continuity
2.6 Limits at Infinity; Horizontal Asymptotes  
第3週
9/26,9/28  2.7 Derivatives and Rates of Change
2.8 The Derivative as a Function
3.1 Derivatives of Polynomials and Exponential Functions
3.2 The Product and Quotient Rules  
第4週
10/03,10/05  3.3 Derivatives of Trigonometric Functions
3.4 The Chain Rule  
第5週
10/10,10/12  3.5 Implicit Differentiation
3.6 Derivatives of Logarithmic Functions
3.9 Related Rates  
第6週
10/17,10/19  3.10 Linear Approximations and Differentials
3.11 Hyperbolic Functions
4.1 Maximum and Minimum Values
4.2 The Mean Value Theorem  
第7週
10/24,10/26  4.3 How Derivatives Affect the Shape of a Graph
4.4 Indeterminate Forms and l''Hospital''s Rule
4.5 Summary of Curve Sketching  
第8週
10/31,11/02  4.7 Optimization Problems
4.9 Antiderivatives  
第9週
11/07,11/09  5.1 Areas and Distances
5.2 The Definite Integral
5.3 The Fundamental Theorem of Calculus
5.4 Indefinite Integrals and the Net Change Theorem
 
第10週
11/14,11/16  5.5 The Substitution Rule
6.1 Areas Between Curves
6.2 Volume
6.3 Volumes by Cylindrical Shells  
第11週
11/21,11/23  6.5 Average Value of a Function
7.1 Integration by Parts
7.2 Trigonometric Integrals
7.3 Trigonometric Substitution  
第12週
11/28,11/30  7.4 Integration of Rational Functions by Partial Fractions
7.5 Strategy for Integration
7.8 Improper Integrals 
第13週
12/05,12/07  8.1
Arc Length
8.2
Area of a Surface of Revolution 
第14週
12/12,12/14  8.1 Arc Length
 
第15週
12/19,12/21  9.1
Modeling with Differential Equations
9.3
Separable Equations
第十五週 12/20, 12/22
9.4
Models for Population Growth
9.5
Linear Equations 
第16週
12/26,12/28  10.1
Curves Defined by Parametric Equations
10.2
Calculus with Parametric Curves
10.3
Polar Coordinates
 
第17週
1/02,1/04  10.4
Areas and Lengths in Polar Coordinates