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課程名稱 |
微積分甲上
Calculus (general Mathematics) (a)(1) |
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開課學期 |
101-1 |
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授課對象 |
材料科學與工程學系 |
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授課教師 |
容志輝 |
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課號 |
MATH1201 |
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課程識別碼 |
201 101A1 |
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班次 |
02 |
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學分 |
4 |
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全/半年 |
全年 |
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必/選修 |
必修 |
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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) |
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上課地點 |
新203新203新203 |
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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 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1011calculus_I_02 |
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課程簡介影片 |
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核心能力關聯 |
核心能力與課程規劃關聯圖 |
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課程大綱
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為確保您我的權利,請尊重智慧財產權及不得非法影印
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課程概述 |
http://www.math.ntu.edu.tw/~mathcal/download/991/991A1.pdf |
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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. |
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課程要求 |
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預期每週課後學習時數 |
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Office Hours |
另約時間 |
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指定閱讀 |
Salas, Hille, and Etgen, Calculus, one and several variables, tenth edition. |
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參考書目 |
1. Apostol, Calculus, vol. 1 and 2.
2. Courant and John, Introduction to Calculus and Analysis.
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評量方式
(僅供參考) |
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No. |
項目 |
百分比 |
說明 |
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1. |
Homework and Quiz |
20% |
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2. |
Midterm Exam |
40% |
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3. |
Final Exam |
40% |
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週次 |
日期 |
單元主題 |
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第1週 |
9/10,9/12,9/14 |
Limits, The Pinching Theorem. |
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第2週 |
9/17,9/19,9/21 |
Continuity, Sequences, Bolzano-Weierstrass Theorem, The Completeness of Real Numbers. |
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第3週 |
9/24,9/26,9/28 |
Intermediate-Value Theorem, Bolzano Theorem, Extreme-Value Theorem, Differentiation. |
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第4週 |
10/01,10/03,10/05 |
The Chain Rule, Implicit Differentiation, The Mean-Value Theorem. |
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第5週 |
10/08,10/10,10/12 |
Quiz, Local Extreme Values. |
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第6週 |
10/15,10/17,10/19 |
Concavity and Inflection, Limits at Infinity, Infinite Limits, Asymptotes, Curve Sketching, Absolute Extreme Value. |
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第7週 |
10/22,10/24,10/26 |
Extreme-Value Problem, Differentials. Antiderivatives, Riemann Integral. |
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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. |
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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. |
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第10週 |
11/12,11/14,11/16 |
Inverse Function Theorem, Natural Logarithmic Function and Natural Exponential Function. |
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第11週 |
11/19,11/21,11/23 |
Exponential Growth and Decay, Inverse Trigonometric Functions, Hyperbolic Functions, Inverse Hyperbolic Functions, Techniques of Integration. |
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第12週 |
11/26,11/28,11/30 |
Quiz, First-Order Linear Ordinary Differential Equations(ODEs), Separable First-Order ODEs. |
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第13週 |
12/03,12/05,12/07 |
Second-Order Linear ODEs with Constant Coefficients, Polar Coordinates. |
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第14週 |
12/10,12/12,12/14 |
Quiz, Area in Polar Coordinates, Parameterized Curves. |
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第15週 |
12/17,12/19,12/21 |
Arc Length, Reparameterization, Area of Surface of Revolution. |
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第16週 |
12/24,12/26,12/28 |
Indeterminate Forms, Improper Integrals. |
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第17週 |
12/31,1/02,1/04 |
Monotone Sequences Convergence Theorem, Cauchy Criterion, Proof of Bolzano-Weierstrass Theorem. |
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