課程資訊
課程名稱
 微積分甲上
Calculus (general Mathematics) (a)(1) 
開課學期
 101-1 
授課對象
 數學系  
授課教師
 李白飛 
課號
 MATH1201 
課程識別碼
 201 101A1 
班次
 06 
學分
 4 
全/半年
 全年 
必/選修
 必帶 
上課時間
 星期二5,6(12:20~14:10)星期四5,6,9(12:20~17:20) 
上課地點
 新103新103 
備註
 四9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/1011phlee 
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
  
預期每週課後學習時數
  
Office Hours
  
指定閱讀
 R.A.Adams: Calculus, a Complete Course, 7th ed. 
參考書目
 E. Landau：Foundation of Analysis.
T. Apostol : Calculus, Vol.1.
曹亮吉等 微積分 
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
 9/11,9/13  Sequences and Convergence. Limits of Functions. One-Sided Limits. Limits at Infinity. Infinite Limits. 
第2週
 9/18,9/20  Continuity. Complete Axiom. The Max-Min Theorem. The
Intermiate-Value Theorem. The Derivative. Differential Rules. 
第3週
 9/25,9/27  The Chain Rule. Derivatives of Trigonometric Functions. Higher-Order derivatives. Implicit
Differentiation. 
第4週
 10/02,10/04  The Mean Value Theorem. Increasing and Decreasing Functions. Extreme Values. Concativity and Inflections. Quiz 1. 
第5週
 10/09,10/11  Asymptotes. Sketching the Graph of a Function. Related Rates. Extreme-Value Problems. Using Differentials and
Derivatives. Linear Approximations. Definite Integrals. 
第6週
 10/16,10/18  Properties of the Definite Integral. 
第7週
 10/23,10/25  Fundamental Theorem of Calculus. Integrability of Continuous Functions. Riemann Sums. Inverse Functions. Quiz 2. 
第8週
 10/30,11/01  The Natural Logarithm and Exponential. Exponential and Logarithmic Functions. The Inverse Trigonometric Functions. The Method of Substitution. 
第9週
 11/06,11/08  Integration by Parts. Reduction Formulas. Midterm Examination. 
第10週
 11/13  Integration of Rational Functions. 
第11週
 11/20,11/22  Rationalization. The Trapezoid and Midpoint Rules. Simpson Rule. Quiz 3. 
第12週
 11/27,11/29  Areas of Plane Regions. Volumes by Slicing. Solid of Revolution. Arc Length and Surface Area. Mass. 
第13週
 12/04,12/06  Moments and Center of Mass. Centroid. Cauchy's Mean Value Theorem. Taylor Polynomials. Quiz 4. 
第14週
 12/11,12/13  Indeterminate Forms. Conics. Smooth Parametric Curves and Their Slopes. Arc Lengths of Parametric Curves. 
第15週
 12/18,12/20  Areas Bounded by Parametric Curves. Curves Defined by Implicit Functions. 
第16週
 12/25,12/27  Curves Defined by Quadratic Forms. Polar Coordinates and Polar Curves. Quiz 5. 
第17週
 1/03  Slopes, Areas and Arc Length for Polar Curves.