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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 |
106-1 |
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授課對象 |
機械工程學系 |
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授課教師 |
蔡雅如 |
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課號 |
MATH1201 |
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課程識別碼 |
201 101A1 |
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班次 |
09 |
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學分 |
4.0 |
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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 |
星期三8,9,10(15:30~18:20)星期五1,2(8:10~10:00) |
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上課地點 |
新303新303 |
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備註 |
統一教學，大二以上限20人，三10為實習課
限本系所學生(含輔系、雙修生)
總人數上限：120人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1061MATH1201_09 |
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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 |
這是一個「線上實體混成課程」。老師會挑選某些主題，讓學生在課堂之前看線上課程自學。課堂中我們將進行活動、討論和解題練習，幫助學生熟練自學內容。這門課特別強調課堂參與，鼓勵學生和老師互動^^
The course will cover the following topics.
1. Functions and Models
2. Limits and Derivatives
3. Differentiation Rule
4. Applications of Differentiation
5. Integrals
6. Applications of Integration
7. Techniques of Integration
8. Differential Equations
9. Parametric Equations and Polar Coordinates |
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課程目標 |
After completing this course, students should be well versed in the mathematical language needed for applying the concepts of calculus to numerous applications in science and engineering. They should also be well prepared for courses in differential equations, linear algebra, or advanced calculus. |
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課程要求 |
Students should be skilled in high school math.
Students should attend and participate actively in lectures as well as discussion sections. |
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預期每週課後學習時數 |
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Office Hours |
每週一 10:00~12:00 備註： Office: Astro-Math building room 531 |
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指定閱讀 |
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參考書目 |
Textbook: James Stewart, Calculus Early Transcendentals, 8th edition.
其他相關資訊
微積分甲統一教學網站: http://www.math.ntu.edu.tw/~mathcal/a/
台大微甲考古題 http://www.math.ntu.edu.tw/~mathcal/a/?page_id=7
數學知識網站: http://episte.math.ntu.edu.tw/cgi/mathfield.pl?fld=cal
免費線上數學繪圖軟體 Desmos Calculator: https://www.desmos.com/calculator
免費知識型計算引擎: https://www.wolframalpha.com
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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 |
35% |
Nov 4 (Sat) 9:00-11:30 |
2. |
Final Exam |
35% |
Jan 6 (Sat) 9:00-11:30 |
3. |
Homework and quizzes |
30% |
There will be weekly homework and 6 quizzes (10/6, 10/18, 11/1, 11/22, 12/6, 12/27). |
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週次 |
日期 |
單元主題 |
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第1週 |
09/13, 09/15 |
1.4 Exponential Functions <br>
1.5 Inverse Functions and Logarithms<br>
2.1 The Tangent and Velocity Problems<br>
2.2 The Limit of a Function <br>
線上課程
https://courses.dlc.ntu.edu.tw/courses/course-v1:NTU+MATH1201+2017_T1/about
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第2週 |
09/20, 09/22 |
2.3 Calculating Limits Using the Limit Laws<br>
2.4 The Precise Definition of a Limit<br>
2.5 Continuity<br>
2.6 Limits at Infinity; Horizontal Asymptotes |
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第3週 |
09/27, 09/29 |
2.7 Derivatives and Rates of Change<br>
2.8 The Derivative as a Function<br>
3.1 Derivatives of Polynomials and Exponential Functions<br>
3.2 The Product and Quotient Rules <br>
線上課程
https://courses.dlc.ntu.edu.tw |
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第4週 |
10/04, 10/06 |
10/04 中秋節放假<br>
3.3 Derivatives of Trigonometric Functions<br>
3.4 The Chain Rule<br>
本週第一次小考（10/06） |
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第5週 |
10/11, 10/13 |
3.5 Implicit Differentiation<br>
3.6 Derivatives of Logarithmic Functions<br>
3.8 Exponential Growth and Decay (も)<br>
3.9 Related Rates |
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第6週 |
10/18, 10/20 |
3.10 Linear Approximations and Differentials<br>
3.11 Hyperbolic Functions (も)<br>
4.1 Maximum and Minimum Values <br>
4.2 The Mean Value Theorem<br>
線上課程
https://courses.dlc.ntu.edu.tw
<br>
本週第二次小考（10/18） |
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第7週 |
10/25, 10/27 |
4.3 How Derivatives Affect the Shape of a Graph<br>
4.4 Indeterminate Forms and L'Hospital's Rule<br>
4.5 Summary of Curve Sketching |
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第8週 |
11/01, 11/03 |
4.7 Optimization Problems<br>
4.9 Antiderivatives<br>
本週第三次小考（11/01） |
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第9週 |
11/08, 11/10 |
5.1 Areas and Distances (online course)<br>
5.2 The Definite Integral (online course)<br>
5.3 The Fundamental Theorem of Calculus<br>
5.4 Indefinite Integrals and the Net Change Theorem<br>
5.5 The Substitution Rule <br>
線上課程
https://courses.dlc.ntu.edu.tw
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第10週 |
11/15, 11/17 |
11/15 校慶停課<br>
6.1 Areas Between Curves<br>
6.2 Volume<br>
6.3 Volumes by Cylindrical Shells |
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第11週 |
11/22, 11/24 |
6.5 Average Value of a Function <br>
7.1 Integration by Parts<br>
7.2 Trigonometric Integrals<br>
7.3 Trigonometric Substitution<br>
線上課程
https://courses.dlc.ntu.edu.tw/courses/course-v1:NTU+MATH1201+2017_T1/about
<br>
本週第四次小考（11/22） |
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第12週 |
11/29, 12/01 |
7.4 Integration of Rational Functions by Partial Fractions<br>
7.5 Strategy for Integration<br>
7.8 Improper Integrals (online course) |
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第13週 |
12/06, 12/08 |
8.1 Arc Length (online course) <br>
8.2 Area of a Surface of Revolution (online course) <br>
線上課程
https://courses.dlc.ntu.edu.tw/courses/course-v1:NTU+MATH1201+2017_T1/about |
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第14週 |
12/13, 12/15 |
10.1 Curves Defined by Parametric Equations<br>
10.2 Calculus with Parametric Curves (online course)<br>
10.3 Polar Coordinates <br>
本週第五次小考（12/13）<br>
線上課程
https://courses.dlc.ntu.edu.tw/courses/course-v1:NTU+MATH1201+2017_T1/about |
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第15週 |
12/20, 12/22 |
10.4 Areas and Lengths in Polar Coordinates<br>
9.1 Modeling with Differential Equations |
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第16週 |
12/27, 12/29 |
9.3 Separable Equations<br>
9.4 Models for Population Growth<br>
本週第六次小考（12/27） |
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第17週 |
01/03, 01/05 |
9.5 Linear Equations |
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第8-2週 |
11/04 |
期中考 11/4(六) 09:00~11:30 考試範圍 1.4~4.9(英文命題) |
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第17-2週 |
01/06 |
期末考1/6(六) 09:00~11:30 考試範圍 5.1~10.4(英文命題) |
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