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課程名稱 |
微積分3
CALCULUS (3) |
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開課學期 |
109-2 |
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授課對象 |
物理學系 |
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授課教師 |
張志中 |
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課號 |
MATH4008 |
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課程識別碼 |
201 49830 |
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班次 |
05 |
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學分 |
2.0 |
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全/半年 |
半年 |
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必/選修 |
必修 |
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上課時間 |
第1,2,3,4,5,6,7,8,9 週
星期一10(17:30~18:20)星期二6,7(13:20~15:10)星期四8,9(15:30~17:20) |
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上課地點 |
新303新303新303 |
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備註 |
本課程中文授課,使用英文教科書。密集課程。密集課程，統一教學，一10為實習課，期考於周末舉辦。
限本系所學生(含輔系、雙修生)
總人數上限：80人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1092MATH4008_05 |
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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 |
*Vector Functions:
Derivatives, Integrals, Arc Length, Curvature
*Partial Derivatives:
Limits, Continuity, Partial Derivatives, Linear Approximations, Chain Rule, Directional Derivatives, Maximum and Minimum Values, Lagrange Multipliers
*Multiple Integrals:
Double Integrals, Triple Integrals, Change of Variables |
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課程目標 |
Students would be familiar with Calculus as a tool and be able to apply it in various subjects after finishing this course. "Calculus 1, 2, 3, 4" provide the basis for the study of various advanced courses like Engineering Mathematics, Analysis and Differential Equations. |
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課程要求 |
Calculus 1, 2 |
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預期每週課後學習時數 |
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Office Hours |
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指定閱讀 |
Textbook: James Stewart, Daniel Clegg, and Saleem Watson, Calculus Early Transcendentals, 9th edition. |
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參考書目 |
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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. |
期考 |
50% |
4/24(六) 09:00~11:30 |
2. |
小考1 |
20% |
暫定 第6週 |
3. |
小考2 |
20% |
暫定 第9週 |
4. |
WeBWorK作業 |
10% |
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週次 |
日期 |
單元主題 |
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第1週 |
2/22,2/23,2/25 |
2/23, 2/25: 12.6, 13.1 - 13.3 Frenet-Serret formulas (p. 915)
==================
12.6 Cylinders and Quadric Surfaces
13.1 Vector Functions and Space Curves
13.2 Derivatives and Integrals of Vector Functions |
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第2週 |
3/01,3/02,3/04 |
3/02: 13.3 formulas and an example (helix)
3/04: 14.1 and 14.2 (general definitions of limit and continuity in metric spaces are given)
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13.3 Arc Length and Curvature
13.4 Motion in Space: Velocity and Acceleration (✽)
3/01(一) 補假 |
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第3週 |
3/08,3/09,3/11 |
3/09: 14.3 Partial Derivatives (Proof of Clairaut's theorem is given) and 14.4 definition of differentiable functions, tangent planes, and linear approximation
3/11: 14.5 The Chain Rule (multi-dimensional version is introduced)
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14.1 Functions of Several Variables
14.2 Limits and Continuity
14.3 Partial Derivatives |
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第4週 |
3/15,3/16,3/18 |
3/16: 14.6 Directional Derivatives and the Gradient Vector
3/18: 14.7 Maximum and Minimum Values
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14.4 Tangent Planes and Linear Approximations
14.5 The Chain Rule
14.6 Directional Derivatives and the Gradient Vector |
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第5週 |
3/22,3/23,3/25 |
3/23: 14.8 Lagrange Multipliers
3/25: 15.1 &15.2 Double Integrals over Rectangles and General Regions
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14.7 Maximum and Minimum Values
14.8 Lagrange Multipliers |
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第6週 |
3/29,3/30,4/01* |
3/30: 15.6 Triple Integrals and the beginning of 15.3 Double Integrals in Polar Coordinates
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15.1 Double Integrals over Rectangles
15.2 Double Integrals over General Regions
15.3 Double Integrals in Polar Coordinates
4/01(四) 溫書假 |
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第7週 |
4/05*, 4/06*, 4/08 |
4/08: 15.3, 15.4 Applications of Double Integrals, and 15.5 surface area
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4/05(一) 補假
4/06(二) 溫書假
4/09(五) 微積分3停修截止 |
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第8週 |
4/12,4/13,4/15 |
4/13: 15.7 Triple Integrals in Cylindrical Coordinates and 15.8 Triple Integrals in Spherical Coordinates
4/15: 15.8 and 15.9 Change of Variables in Multiple Integrals
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15.4 Applications of Double Integrals
15.5 Surface Area
15.6 Triple Integrals |
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第9週 |
4/19,4/20,4/22 |
4/20: Review (Jacobian of n dimensional spherical coordinates, Taylor theorem, Taylor expansions of multiple variable functions, and the proof of second derivative test)
4/22: Quiz 2
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15.7 Triple Integrals in Cylindrical Coordinates
15.8 Triple Integrals in Spherical Coordinates
15.9 Change of Variables in Multiple Integrals
期考 4/24(六) 09:00~11:30 |
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