|
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 |
4 |
|
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 |
|
|
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 |
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 |
|
|
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% |
|
|
|
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. |
|