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
化學系  
授課教師
莊正良 
課號
MATH1201 
課程識別碼
201 101A1 
班次
09 
學分
全/半年
全年 
必/選修
必修 
上課時間
星期三7,8,9(14:20~17:20)星期五1,2(8:10~10:00) 
上課地點
新303新303 
備註
統一教學.大二以上限20人.三9為實習課.
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_09 
課程簡介影片
 
核心能力關聯
核心能力與課程規劃關聯圖
課程大綱
為確保您我的權利,請尊重智慧財產權及不得非法影印
課程概述

上學期:單變數微積分
1. Functions and Models
2. Limits and Derivatives
3. Differentiation Rules
4. Applications of Differentiation
5. Integrals
6. Applications of Integration
7. Techniques of Integration
8. Further Applications of Integration
9. Differential Equations
10. Parametric Equations and Polar Coordinates 

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
高中數學 
Office Hours
備註: Tuesday, Thursday 9:00--11:00. 
參考書目
Please see 統一教學網站. 
指定閱讀
無 
評量方式
(僅供參考)
 
No.
項目
百分比
說明
1. 
期中考 
40% 
 
2. 
期末考 
40% 
 
3. 
平常成績(含小考) 
20% 
 
 
課程進度
週次
日期
單元主題
第1週
9/17,9/19  <html> <head> <title> </title> </head> <body> [1.5] Exponential Functions <br> [1.6] Inverse Functions and Logarithms <br> [2.1] The Tangent and Velocity Problems <br> [2.2] The Limit of a Function <br> [2.3] Calculating Limits Using the Limit Laws <br> </body> </html> 
第2週
9/24,9/26  <html> <head> <title> </title> </head> <body> [2.4] The Precise Definition of a Limit <br> [2.5] Continuity<br> [2.6] Limits at Infinity; Horizontal Asymptotes <br> [2.7] Derivatives and Rates of Change <br> </body> </html> 
第3週
10/01,10/03  <html> <head> <title> </title> </head> <body> [2.8] The Derivative as a Function <br> [3.1] Derivatives of Polynomials and Exponential Functions <br> [3.2] The Product and Quotient Rules <br> [3.3] Derivatives of Trigonometric Functions <br> </body> </html> 
第4週
10/08,10/10  <html> <head> <title> </title> </head> <body> [3.4] The Chain Rule <br> [3.5] Implicit Differentiation <br> 10/10(五)國慶紀念日放假一天 <br> </body> </html> 
第5週
10/15,10/17  <html> <head> <title> </title> </head> <body> [3.6] Derivatives of Logarithmic Functions <br> [3.7] Rates of Change in the Natural and Social Sciences(※) <br> [3.8] Exponential Growth and Decay <br> [3.9] Related Rates <br> [3.10] Linear Approximations and Differentials <br> [3.11] Hyperbolic Functions(※) <br> </body> </html> 
第6週
10/22,10/24  <html> <head> <title> </title> </head> <body> 緩衝時間 <br> [4.1] Maximum and Minimum Values <br> [4.2] The Mean Value Theorem <br> </body> </html> 
第7週
10/29,10/31  <html> <head> <title> </title> </head> <body> [4.3] How Derivatives Affect the Shape of a Graph <br> [4.4] Indeterminate Forms and L’Hospital’s Rule <br> [4.5] Summary of Curve Sketching <br> [4.6] Graphing with Calculus and Calculators(※) <br> [4.7] Optimization Problems <br> </body> </html> 
第8週
11/05,11/07  <html> <head> <title> </title> </head> <body> [4.8] Newton’s Method(※) <br> [4.9] Antiderivatives <br> [5.1] Areas and Distances <br> 緩衝時間 <br> 11/8 (六) 09:00~11:30 期中考 (1.5~4.9)<br> </body> </html> 
第9週
11/12,11/14  <html> <head> <title> </title> </head> <body> [5.2] The Definite Integral <br> [5.3] The Fundamental Theorem of Calculus <br> [5.4] Indefinite Integrals and the Net Change Theorem <br> [5.5] The Substitution Rule <br> </body> </html> 
第10週
11/19,11/21  <html> <head> <title> </title> </head> <body> [6.1] Areas Between Curves <br> [6.2] Volumes <br> [6.3] Volumes by Cylindrical Shells <br> [6.4] Work(※)<br> [6.5] Average Value of a Function <br> </body> </html> 
第11週
11/26,11/28  <html> <head> <title> </title> </head> <body> [7.1] Integration by Parts <br> [7.2] Trigonometric Integrals <br> [7.3] Trigonometric Substitution <br> [7.4] Integration of Rational Functions by Partial Fractions <br> </body> </html> 
第12週
12/03,12/05  <html> <head> <title> </title> </head> <body> [7.5] Strategy for Integration <br> [7.6] Integration Using Tables and Computer Algebra Systems(※)<br> [7.7] Approximate Integration(※)<br> [7.8] Improper Integrals <br> [8.1] Arc Length <br> </body> </html> 
第13週
12/10,12/12  <html> <head> <title> </title> </head> <body> 緩衝時間 <br> [8.2] Area of a Surface of Revolution <br> [8.3] Applications to Physics and Engineering <br> [8.4] Applications to Economics and Biology(※)<br> [8.5] Probability(※) <br> </body> </html> 
第14週
12/17,12/19  <html> <head> <title> </title> </head> <body> [9.1] Modeling with Differential Equations <br> [9.2] Direction Fields and Euler's Method <br> [9.3] Separable Equations <br> [9.4] Models for Population Growth <br> </body> </html> 
第15週
12/24,12/26  <html> <head> <title> </title> </head> <body> [9.5] Linear Equations <br> [9.6] Predator-Prey Systems(※)<br> 緩衝時間 <br> </body> </html> 
第16週
12/31,1/02  <html> <head> <title> </title> </head> <body> [10.1] Curves Defined by Parametric Equations <br> [10.2] Calculus with Parametric Curves <br> [10.3] Polar Coordinates <br> [10.4] Areas and Lengths in Polar Coordinates <br> [10.6] Conic Sections in Polar Coordinates <br> </body> </html> 
第17週
1/07,1/09  <html> <head> <title> </title> </head> <body> 緩衝時間 <br> 1/10 (六) 09:00~11:30 期末考(5.1~10.6)<br> </body> </html> 
第20週
  餘零班投影片 
第20-2週
  餘零班講義