|
課程名稱 |
微積分甲上
Calculus (general Mathematics) (a)(1) |
|
開課學期 |
101-1 |
|
授課對象 |
電機工程學系 |
|
授課教師 |
容志輝 |
|
課號 |
MATH1201 |
|
課程識別碼 |
201 101A1 |
|
班次 |
02 |
|
學分 |
4 |
|
全/半年 |
全年 |
|
必/選修 |
必修 |
|
上課時間 |
星期一9(16:30~17:20)星期三5,6(12:20~14:10)星期五5,6(12:20~14:10) |
|
上課地點 |
新203新203新203 |
|
備註 |
統一教學.大二以上限20人.一9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/1011calculus_I_02 |
|
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 |
http://www.math.ntu.edu.tw/~mathcal/download/991/991A1.pdf |
|
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 |
|
|
預期每週課後學習時數 |
|
|
Office Hours |
另約時間 |
|
參考書目 |
1. Apostol, Calculus, vol. 1 and 2.
2. Courant and John, Introduction to Calculus and Analysis.
|
|
指定閱讀 |
Salas, Hille, and Etgen, Calculus, one and several variables, tenth edition. |
|
評量方式
(僅供參考) |
|
No. |
項目 |
百分比 |
說明 |
|
1. |
Homework and Quiz |
20% |
|
2. |
Midterm Exam |
40% |
|
3. |
Final Exam |
40% |
|
|
|
週次 |
日期 |
單元主題 |
|
第1週 |
9/10,9/12,9/14 |
Limits, The Pinching Theorem. |
|
第2週 |
9/17,9/19,9/21 |
Continuity, Sequences, Bolzano-Weierstrass Theorem, The Completeness of Real Numbers. |
|
第3週 |
9/24,9/26,9/28 |
Intermediate-Value Theorem, Bolzano Theorem, Extreme-Value Theorem, Differentiation. |
|
第4週 |
10/01,10/03,10/05 |
The Chain Rule, Implicit Differentiation, The Mean-Value Theorem. |
|
第5週 |
10/08,10/10,10/12 |
Quiz, Local Extreme Values. |
|
第6週 |
10/15,10/17,10/19 |
Concavity and Inflection, Limits at Infinity, Infinite Limits, Asymptotes, Curve Sketching, Absolute Extreme Value. |
|
第7週 |
10/22,10/24,10/26 |
Extreme-Value Problem, Differentials. Antiderivatives, Riemann Integral. |
|
第8週 |
10/29,10/31,11/02 |
Quiz, Uniform Continuity, Riemann Sum, Mean-Value and Intermediate-Value Theorem for Integrals, The Fundamental Theorem of Calculus. |
|
第9週 |
11/05,11/07,11/09 |
Change of Variables, Area Problems, Volumes by Slicing and Solids of Revolution, Centroid, Pappus's Theorem, One-to-One Function, Midterm Exam. |
|
第10週 |
11/12,11/14,11/16 |
Inverse Function Theorem, Natural Logarithmic Function and Natural Exponential Function. |
|
第11週 |
11/19,11/21,11/23 |
Exponential Growth and Decay, Inverse Trigonometric Functions, Hyperbolic Functions, Inverse Hyperbolic Functions, Techniques of Integration. |
|
第12週 |
11/26,11/28,11/30 |
Quiz, First-Order Linear Ordinary Differential Equations(ODEs), Separable First-Order ODEs. |
|
第13週 |
12/03,12/05,12/07 |
Second-Order Linear ODEs with Constant Coefficients, Polar Coordinates. |
|
第14週 |
12/10,12/12,12/14 |
Quiz, Area in Polar Coordinates, Parameterized Curves. |
|
第15週 |
12/17,12/19,12/21 |
Arc Length, Reparameterization, Area of Surface of Revolution. |
|
第16週 |
12/24,12/26,12/28 |
Indeterminate Forms, Improper Integrals. |
|
第17週 |
12/31,1/02,1/04 |
Monotone Sequences Convergence Theorem, Cauchy Criterion, Proof of Bolzano-Weierstrass Theorem. |
|