課程資訊
課程名稱
 微積分甲上
Calculus (general Mathematics) (a)(1) 
開課學期
 103-1 
授課對象
 生物環境系統工程學系  
授課教師
 劉瓊如 
課號
 MATH1201 
課程識別碼
 201 101A1 
班次
 13 
學分
 4 
全/半年
 全年 
必/選修
 必修 
上課時間
 星期一5,6(12:20~14:10)星期五1,2(8:10~10:00) 
上課地點
 新103新103 
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：100人 
Ceiba 課程網頁
 http://ceiba.ntu.edu.tw/1031MATH1201_13 
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課程概述

課程大綱
1. Limits and continuity,
2. Differentiation,
3. Application of Differentiation,
4. Integration,
5. Application of integrals,
6. Transcendental functions,
7. Techniques of Integration,
8. Infinte Series
9. Function of Several Variables
10. Multiple Integration
11. Vector Analysis
 

課程目標
 學生能從此課程中學習到微積分的理論與應用 
課程要求
 待補 
預期每週課後學習時數
  
Office Hours
  
參考書目
 課本
Calculus: Early Transcendentals 7th edition,
作者： James Stewart 
指定閱讀
 待補 
評量方式
(僅供參考)
    
課程進度
週次
日期
單元主題
第1週
 9/15,9/19  [1.5] Exponential Functions [1.6] Inverse Functions and Logarithms
2. Limits and Derivatives
[2.1] The Tangent and Velocity Problems
[2.2] The Limit of a Function
[2.3] Calculating Limits Using the Limit Laws 
第2週
 9/22,9/26  [2.4] The Precise Definition of a Limit
[2.5] Continuity
[2.6] Limits at Infinity; Horizontal Asymptotes
[2.7] Derivatives and Rates of Change 
第3週
 9/29,10/03  [2.8] The Derivative as a Function [3.1] Derivatives of Polynomials and Exponential Functions
[3.2] The Product and Quotient Rules
[3.3] Derivatives of Trigonometric Functions 
第4週
 10/06,10/10  [3.4] The Chain Rule
[3.5] Implicit Differentiation 
第5週
 10/13,10/17  [3.6] Derivatives of Logarithmic Functions
[3.8] Exponential Growth and Decay
[3.9] Related Rates
[3.10] Linear Approximations and Differentials 
第6週
 10/20,10/24  [4.1] Maximum and Minimum Values
[4.2] The Mean Value Theorem 
第7週
 10/27,10/31  [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
[4.7] Optimization Problems 
第8週
 11/03,11/07  [4.9] Antiderivatives
[5.1] Areas and Distances 
第9週
 11/10,11/14  期中考 
第10週
 11/17,11/21  [5.2] The Definite Integral
[5.3] The Fundamental Theorem of Calculus
[5.4] Indefinite Integrals and the Net Change Theorem
[5.5] The Substitution Rule 
第11週
 11/24,11/28  [6.1] Areas Between Curves
[6.2] Volumes
[6.3] Volumes by Cylindrical Shells
[6.5] Average Value of a Function 
第12週
 12/01,12/05  [7.1] Integration by Parts
[7.2] Trigonometric Integrals
[7.3] Trigonometric Substitution
[7.4] Integration of Rational Functions by Partial Fractions 
第13週
 12/08,12/12  [7.5] Strategy for Integration
[7.8] Improper Integrals
[8.1] Arc Length 
第14週
 12/15,12/19  [8.2] Area of a Surface of Revolution
[9.1] Modeling with Differential Equations
[9.2] Direction Fields and Euler’s Method 
第15週
 12/22,12/26  [9.3] Separable Equations
[9.4] Models for Population Growth
[9.5] Linear Equations 
第16週
 12/29,1/02  [10.1] Curves Defined by Parametric Equations
[10.2] Calculus with Parametric Curves 
第17週
 1/05,1/09  [10.3] Polar Coordinates
[10.4] Areas and Lengths in Polar Coordinates
[10.6] Conic Sections in Polar Coordinates 
第18週
 1/12  期末考