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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 |
95-2 |
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授課對象 |
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授課教師 |
張志中 |
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課號 |
MATH1202 |
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課程識別碼 |
201 101A2 |
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班次 |
05 |
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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 |
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備註 |
*統一教學。限電機、資工、資管等 系學生修習
總人數上限：120人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/952calculusA05 |
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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 |
Sequence and infinite series (various tests for convergence/divergence, power
series, Taylor series, and applications), theory of multi-variable functions
(limit, continuity, partial and directional derivatives, tangent planes and
differentiability, gradient vectors, maximum and minimum values, Lagrange
multipliers, iterated and multiple integrals, change of variables,
applications), and vector calculus (vector fields, line and surface integrals,
curl and divergence, Green’s, Stokes’, and the divergence theorems.) |
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課程目標 |
Study sequences and series to understand the process of approximation; learn
to estimate and control the errors of approximation; acquaint with the tools
and techniques for analyzing regular multi-variable mappings and vector
fields. |
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課程要求 |
Course prerequisite: Calculus A 1. |
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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 |
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參考書目 |
M. D. Weir, J. Hass, F. R. Giordano: Thomas’ Calculus, 11th Edition. Pearson,
Addison Wesley, 2005. |
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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. |
期中考 |
40% |
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2. |
期末考 |
40% |
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3. |
平時成績 |
20% |
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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 ;
11.2 Infinite Series; |
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第2週 |
3/07,3/09 |
11.3 The Integral Test ;
11.4 Comparison Test ; |
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第3週 |
3/14,3/16 |
11.5 The Ratio and Root Test ;
11.6 Alternating Series, Absolute and Conditional COnvergence ;
11.7 Power Series ; |
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第4週 |
3/21,3/23 |
11.8 Taylor and Maclaurin Series ;
11.9 Convergence of Taylor Series; Error Estimates ;
11.10 Applications of Power Series ;
11.11 Fourier Series ; |
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第5週 |
3/28,3/30 |
14.1 Functions of Serveral Variables ;
14.2 Limits and Continuity in Higher Dimensions ;
14.3 Partial Derivatives ;
14.4 The Chain Rule ; |
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第6週 |
4/04,4/06 |
14.5 Directional Derivatives and Gradient Vectors ;
14.6 Tangent Planes and Differentials ; |
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第7週 |
4/11,4/13 |
14.7 Extreme Values and Saddle Points ;
14.8 Lagrange Multipliers; |
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第9週 |
4/25,4/27 |
期中考 ;
15.1 Double Integrals |
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第10週 |
5/02,5/04 |
15.2 Areas, average value (跳過Moments and Center of Mass)
15.3 Double Integrals in Polar Form ;
15.4 Triple Integrals in Rectangle Coordinates ; |
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第11週 |
5/09,5/11 |
15.6 Triple Integrals in Cylindrical and Spherical Coordinates ;
15.7 Substitutions ain Multiple Integrals ; |
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第12週 |
5/16,5/18 |
16.1 Line Integrals (跳過Mass and Moment Calculations) ;
16.2 Vector Fields, Works, Circulation, and Flux ; |
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第13週 |
5/23,5/25 |
16.3 Path Independence, Potential Functions, and Conservative Fields ; |
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第16週 |
6/13,6/15 |
16.8 The Divergence Theorem and a Unified Theory |
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第17週 |
6/20 |
期末考 |
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