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課程名稱 |
微積分甲下
Calculus (general Mathematics) (a)(2) |
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開課學期 |
106-2 |
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授課對象 |
化學工程學系 |
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授課教師 |
蔡雅如 |
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課號 |
MATH1202 |
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課程識別碼 |
201 101A2 |
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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/1062MATH1202_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。課堂中我們將分組寫學習單，進行討論和解題練習，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^^
教學影片在 NTU COOL 課程網站
https://cool.ntu.edu.tw/courses/course-v1:NTU+MATH1202+2018_S/
This course will cover the following topics:
1. Infinite sequences, series, and power series
2. Vector functions
3. Functions of several variables
4. Multiple integrals
5. Vector calculus ( Green's theorem, Stokes' theorem and the divergence theorem ) |
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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 |
待補 |
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預期每週課後學習時數 |
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Office Hours |
每週一 10:30~12:30 備註： 天數館 531 |
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指定閱讀 |
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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參考書目 |
待補 |
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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 Quizzes |
30% |
There will be weekly homework and 6 quizzes (3/21, 4/11, 5/2, 5/23, 6/6, 6/20) given in the discussion sections. Some homework will be assigned on WebWork.
WebWork:
http://webwork.math.ntu.edu.tw/webwork2/ |
2. |
Midterm Exam |
35% |
5/5 (Sat) 9:00-11:30 |
3. |
Final Exam |
35% |
6/23 (Sat) 9:00-11:30 |
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週次 |
日期 |
單元主題 |
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第1週 |
2/28,3/02 |
11.1: Sequences
教學影片 11-1：
https://cool.ntu.edu.tw/courses/course-v1:NTU+MATH1202+2018_S/ |
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第2週 |
3/07,3/09 |
11.2: Series
11.3: The Integral Test and Estimates of Sums
11.4: The Comparison Tests |
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第3週 |
3/14,3/16 |
11.5: Alternating Series
11.6: Absolute Convergence and the Ratio and Root Tests
11.7: Strategy for Testing Series |
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第4週 |
3/21 (Quiz 1), 3/23 |
11.8: Power Series
11.9: Representations of Functions as Power Series |
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第5週 |
3/28,3/30 |
11.10: Taylor and Maclaurin Series
11.11: Applications of Taylor Polynomials
12.6: Cylinders and Quadric Surfaces |
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第6週 |
3/31 (補課), 4/04,4/06(Spring Break) |
13.1: Vector Functions and Space Curves
13.2: Derivatives and Integrals of Vector Functions |
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第7週 |
4/11 (Quiz 2), 4/13 |
13.3: Arc Length and Curvature
14.1: Functions of Several Variables
14.2: Limits and Continuity |
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第8週 |
4/18,4/20 |
14.3: Partial Derivatives
14.4: Tangent Planes and Linear Approximation
14.5: The Chain Rule |
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第9週 |
4/25,4/27 |
14.6: Directional Derivatives and the Gradient Vector
14.7: Maximum and Minimum Values |
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第10週 |
5/02 (Quiz 3), 5/04 |
14.8: Lagrange Multipliers
Midterm on 5/05 |
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第11週 |
5/09,5/11 |
15.1:Double Integrals over Rectangles
15.2: Double Integrals over General Regions
15.3: Double Integrals in Polar Coordinates |
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第12週 |
5/16,5/18 |
15.4: Applications of Double Integrals
15.5: Surface Area
15.6: Triple Integrals |
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第13週 |
5/23 (Quiz 4), 5/25 |
15.7: Triple Integrals in Cylindrical Coordinates
15.8: Triple Integrals in Spherical Coordinates
15.9: Change of Variables in Multiple Integrals |
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第14週 |
5/30,6/01 |
16.1: Vector Fields
16.2: Line Integrals
16.3: The Fundamental Theorem for Line Integrals |
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第15週 |
6/06 (Quiz 5), 6/08 |
16.4: Green's Theorem
16.5: Curl and Divergence
16.6: Parametric Surfaces and Their Areas |
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第16週 |
6/13,6/15 |
16.7: Surface Integrals
16.8: Stokes' Theorem
16.9: The Divergence Theorem |
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第17週 |
6/20 (Quiz 6) , 6/22 |
16.10: Summary
Final Exam on 6/23. |
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