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
土木工程學系  
授課教師
朱樺 
課號
MATH1201 
課程識別碼
201 101A1 
班次
12 
學分
全/半年
全年 
必/選修
必帶 
上課時間
星期二7,8,9(14:20~17:20)星期四5,6(12:20~14:10) 
上課地點
新203新203 
備註
統一教學.二9為實習課.
限本系所學生(含輔系、雙修生)
總人數上限:130人 
Ceiba 課程網頁
http://ceiba.ntu.edu.tw/1001CalAChu 
課程簡介影片
 
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課程概述

課程大鋼
1. Functions and Models
2. Limit and Deriatives
3. Differentiation Rules
4. Applications of Differentiation
5. Integral
6. Applications of Integration
7. Techniques of Integraion
8. Further Applications of Integration
9. Differential Equations
10. Parametric Equations and Polar Coordinates 

課程目標
讓學生了解微積分的理論, 計算與應用 
課程要求
 
Office Hours
 
參考書目
Calculus, a complete course, seventh edition, Author: Robert A. Adams & Christopher Essex. Pearson Canada,Toronto 
指定閱讀
微積分統一教學網站:
www.math.ntu.edu.tw/~mathcal
課程教材網頁:
www.math.ntu.edu.tw/~hchu/Calculus 
評量方式
(僅供參考)
 
No.
項目
百分比
說明
1. 
習題課與小考 
20% 
各班助教給分 
2. 
期中考 
40% 
 
3. 
期末考 
40% 
 
 
課程進度
週次
日期
單元主題
第1週
09/13,09/15  1.1 Examples of Velocity, Growth Rate, and Area; <br> 1.2 Limit of Functions; <br> 1.3 Limits at Infinity and Infinite Limits; <br> 1.4 Continuity 
第2週
09/20,09/21  1.5 The Formal Definition of Limit; <br> 2.1 Tangent Lines and Their Slopes; <br> 2.2 The Derivative; <br> 2.3 Differentiation Rules 
第3週
9/27,9/29  2.4 The Chain Rule; <br> 2.5 Derivatives of Trigonometric Functions; <br> 2.6 Higher-Order Derivatives; <br> 2.7 Using Differentials and Derivatives; <br> 2.8 The Mean-Value Theorem 
第4週
10/04,10/06  2.9 Implicit Differentiation; <br> 2.10 Antiderivatives and Initial-Value Problems; <br> 2.11 Velocity and Acceleration; <br> 緩衝時間 
第5週
10/11,10/13  3.1 Inverse Functions; <br> 3.2 Exponential and Logarithmic Functions; <br> 3.3 The Natural Logarithm and Exponential; <br> 3.4 Growth and Decay 
第6週
10/18,10/20  3.5 The Inverse Trigonometric Functions; <br> 3.6 Hyperbolic Functions; <br> 4.1 Related Rates 
第7週
10/25,10/27  4.2 Finding Roots of Equations; <br> 4.3 Indeterminate Forms; <br> 4.4 Extreme Values; <br> 4.5 Concavity and Inflections 
第8週
11/01,11/03  4.6 Sketching the Graph of a Function; <br> 4.7 Graphing with Computers(※); <br> 4.8 Extreme-Value Problems; <br> 4.9 Linear Approximations 
第9週
11/08,11/10  4.10 Taylor Polynomials; <br> 4.11 Roundoff Error, Truncation Error, and Computers(※); <br> 緩衝時間; <br> 11/12(&#63953;) 09:00∼11:30 期中考考試範圍 1.1∼4.10 (英文命題) 
第10週
11/15,11/17  5.1 Sums and Sigma Notation; <br> 5.2 Areas as Limits of Sums; <br> 5.3 Definite Integral; <br> 5.4 Properties of the Definite Integral 
第11週
11/22,11/24  5.5 The Fundamental Theorem of Calculus; <br> 5.6 The Method of Substitution; <br> 5.7 Areas of Plane Regions; <br> 6.1 Integration by Parts 
第12週
11/29,12/01  6.2 Integrals of Rational Functions; <br> 6.3 Inverse Substitutions; <br> 6.4 Other Methods for Evaluating Integrals; <br> 6.5 Improper Integrals 
第13週
12/06,12/08  6.6 The Trapezoid and Midpoint Rules; <br> 6.7 Simpson's Rule; <br> 6.8 Other Aspects of Approximate Integration; <br> 緩衝時間 
第14週
12/13,12/15  7.1 Volumes by Slicing ─ Solids of Revolution; <br> 7.2 More Volumes by Slicing; <br> 7.3 Arc Length and Surface Area 
第15週
12/20,12/22  7.4 Mass, Moments, and Centre of Mass; <br> 7.5 Centroids(※); <br> 7.6 Other Physical Applications(※); <br> 7.7 Applications in Business, Finance, and Ecology(※); <br> 7.8 Probability(※); <br> 7.9 First-Order Differential Equations 
第16週
12/27,12/29  8.2 Parametric Curves; <br> 8.3 Smooth Parametric Curves and Their Slopes; <br> 8.4 Arc Lengths and Areas for Parametric Curves 
第17週
1/03,1/05  8.5 Polar Coordinates and Polar Curves; <br> 8.6 Slopes, Areas, and Arc Lengths for Polar Curves; <br> 緩衝時間; <br> 1/7(&#63953;) 09:00∼11:30 期末考考試範圍 5.1∼8.6 (英文命題)