課程資訊
課程名稱
微積分甲上
Calculus (general Mathematics) (a)(1) 
開課學期
100-1 
授課對象
物理學系  
授課教師
李白飛 
課號
MATH1201 
課程識別碼
201 101A1 
班次
06 
學分
全/半年
全年 
必/選修
必帶 
上課時間
星期一9(16:30~17:20)星期二5,6(12:20~14:10)星期五7,8(14:20~16:20) 
上課地點
新505新505新505 
備註
一9為實習課.
限本系所學生(含輔系、雙修生)
總人數上限:80人 
Ceiba 課程網頁
http://ceiba.ntu.edu.tw/1001phlee 
課程簡介影片
 
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課程概述

1.Limits and Continuity 2.Differentiation 3.Applications of Derivatives 4.Integration 5.Transcendental Functions 6.Techniques of Integration 7. Applications of Integration 8. Parametric Curves and Polar Curves. 

課程目標
A relatively rigorous introduction of differentiation and integration of functions of a single variable and some applications to geometry and physics. 
課程要求
 
Office Hours
 
參考書目
E. Landau:Foundation of Analysis.
T. Apostol : Calculus, Vol.1.
曹亮吉等 微積分 
指定閱讀
R.A.Adams: Calculus, a Complete Course, 7th ed. 
評量方式
(僅供參考)
 
No.
項目
百分比
說明
1. 
Mid-Term 
40% 
 
2. 
Final Examination 
40% 
 
3. 
Quizzes 
20% 
 
 
課程進度
週次
日期
單元主題
第1週
9/13,9/16  Sequences and Convergence. Limits of Functions. 
第2週
9/19,9/20,9/23  One-Sided Limits. Limt at Infinity and Infinite Limits. Continuity. Complete Axiom. The Max-Min Theorem. The Intermiate-Value Theorem. The Derivative. 
第3週
9/26,9/27,9/30  Differential Rules. The Chain Rule. Derivatives of Trigonometric Functions. Higher-Order derivatives. Implicit Differentiation. The Mean-Value Theorem. 
第4週
10/03,10/04,10/07  Quiz 1. Increasing and Decreasing Functions. Extreme Values. Concativity and Inflections. 
第5週
10/10,10/11,10/14  Asymptotes. Sketching the Graph of a Function. Extreme-Value Problems. Related Rates. Using Differentials and Derivatives. Linear Approximations. 
第6週
10/17,10/18,10/21  The Definite Integral. 
第7週
10/24,10/25,10/28  Quiz 2. Exercises. 
第8週
10/31,11/01,11/04  Properties of the Definite Integrals. The Fundamental Theorem of Calculus. 
第9週
11/07,11/08,11/11  Midterm Examination. Areas of Plane Regions. 
第10週
11/14,11/15,11/18  Inverse Functions. The Natural Logarithm and Exponential. Exponential and Logarithmic Functions. The Inverse Trigonometric Functions. 
第11週
11/21,11/22,11/25  Cauchy's Mean-Value Theorem. Taylor Polynomials. Indeterminate Forms. 
第12週
11/28,11/29,12/02  The Method of Substitution. Integration by Parts. Reduction Formulas. 
第13週
12/05,12/06,12/09  Integration of Rational Functions. Integrals Transformable to Thoses of Rational Functions. The Trapezoid and Midpoint Rules. 
第14週
12/12,12/13,12/16  Simpson's Rule. Volume by Slicing--Solids of Revolution. More on Volumes by Slicing. 
第15週
12/19,12/20,12/23  Arc Length and Surface Area. Mass, Moments and Center of Mass. 
第16週
12/26,12/27,12/30  Centroids. Parametric Curves. Smooth Parametric Curves and Their Slopes. 
第17週
1/02,1/03,1/06  Arc Lengths and Areas of Parametric Curves. Polar Coordinates and Polar Curves. Slopes, Arc Lengths and Areas for Polar Curves.