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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 |
99-1 |
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授課對象 |
電機工程學系 |
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授課教師 |
張志中 |
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課號 |
MATH1201 |
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課程識別碼 |
201 101A1 |
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班次 |
03 |
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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303新103新103 |
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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：100人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/991cal03 |
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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 |
One variable calculus
統一教學網站: http://www.math.ntu.edu.tw/~mathcal/a/ |
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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 |
High School Mathematics |
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預期每週課後學習時數 |
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Office Hours |
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參考書目 |
James Stewart, Calculus Early Transcendentals, 6th edition. |
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指定閱讀 |
James Stewart, Calculus Early Transcendentals, 6th edition. |
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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. |
Midterm Exam |
40% |
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2. |
Final Exam |
40% |
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3. |
Quizzes and Participation |
20% |
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週次 |
日期 |
單元主題 |
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第1週 |
9/13,9/15,9/17 |
[1.5] Exponential Functions [1.6] Inverse Functions and Logarithms [2.1] The Tangent and Velocity Problems [2.2] The Limit of a Function |
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第2週 |
9/20,9/22,9/24 |
[2.3] Calculating Limits Using the Limit Laws
[2.4] The Precise Definition of a Limit |
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第3週 |
9/27, 9/29, 10/01 |
[2.5] Continuity
[2.6] Limits at Infinity; Horizontal Asymptotes
[2.7] Derivatives and Rates of Change
[2.8] The Derivative as a Function
[3.1] Derivatives of Polynomials and Exponential Functions |
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第4週 |
10/04,10/06,10/08 |
[3.2] The Product and Quotient Rules
[3.3] Derivatives of Trigonometric Functions
[3.4] The Chain Rule
[3.5] Implicit Differentiation |
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第5週 |
10/11,10/13,10/15 |
[3.6] Derivatives of Logarithmic Functions
[3.8] Exponential Growth and Decay
[3.9] Related Rates
[3.10] Linear Approximations and Differentials |
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第6週 |
10/18,10/20,10/22 |
[4.1] Maximum and Minimum Values
[4.2] The Mean Value Theorem |
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第7週 |
10/25,10/27,10/29 |
[4.3] How Derivatives Affect the Shape of a Graph
[4.4] Indeterminate Forms and L’Hospital’s Rule
[4.5] Summary of Curve Sketching
[4.6] Graphing with Calculus and Calculators
[4.7] Optimization Problems |
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第8週 |
11/01,11/03,11/05 |
[4.9] Antiderivatives
[5.1] Areas and Distances
[5.2] The Definite Integral
[5.3] The Fundamental Theorem of Calculus |
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第9週 |
11/08,11/10,11/12 |
[5.4] Indefinite Integrals and the Net Change Theorem
[5.5] The Substitution Rule
** Midterm Exam: 11/13 (Sat.) 13:30~16:00** |
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第10週 |
11/15,11/17,11/19 |
[6.1] Areas between Curves
[6.2] Volumes
[6.3] Volumes by Cylindrical Shells |
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第11週 |
11/22,11/24,11/26 |
[6.5] Average Value of a Function
[7.1] Integration by Parts
[7.2] Trigonometric Integrals |
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第12週 |
11/29,12/01,12/03 |
[7.3] Trigonometric Substitution
[7.4] Integration of Rational Functions by Partial Fractions |
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第13週 |
12/06,12/08,12/10 |
[7.5] Strategy for Integration
[7.6] Integration Using Tables and Computer Algebra Systems
[7.7] Approximate Integration
[7.8] Improper Integrals |
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第14週 |
12/13,12/15,12/17 |
[8.1] Arc Length
[8.2] Area of a Surface of Revolution |
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第15週 |
12/20,12/22,12/24 |
[9.1] Modeling with Differential Equations
[9.2] Direction Fields and Euler’s Method
[9.3] Separable Equations
[9.4] Models for Population Growth |
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第16週 |
12/27,12/29,12/31 |
[9.5] Linear Equations
[10.1] Curves Defined by Parametric Equations
[10.2] Calculus with Parametric Curves |
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第17週 |
1/03,1/05,1/07 |
[10.3] Polar Coordinates
[10.4] Areas and Lengths in Polar Coordinates
** Final Exam: 1/9 (Sun.) 13:30~16:00 ** |
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