|
課程名稱 |
微積分甲下
Calculus (general Mathematics) (a)(2) |
|
開課學期 |
103-2 |
|
授課對象 |
物理學系 |
|
授課教師 |
李白飛 |
|
課號 |
MATH1202 |
|
課程識別碼 |
201 101A2 |
|
班次 |
05 |
|
學分 |
4 |
|
全/半年 |
全年 |
|
必/選修 |
必帶 |
|
上課時間 |
星期一9(16:30~17:20)星期二5,6(12:20~14:10)星期四7,8(14:20~16:20) |
|
上課地點 |
新505新303新303 |
|
備註 |
一9為實習課。
限本系所學生(含輔系、雙修生)
總人數上限：80人 |
|
Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1032MATH1202_05 |
|
課程簡介影片 |
|
|
核心能力關聯 |
核心能力與課程規劃關聯圖 |
|
課程大綱
|
|
為確保您我的權利,請尊重智慧財產權及不得非法影印
|
|
課程概述 |
1. Infinite Series. 2. Vector Functions. 3. Partial Differentiation. 4. Multiple Integration. 5. Line and Surface Integrals. |
|
課程目標 |
A relatively rigorous introduction of infinite series and calculus of functions of several variables and their applications to geometry and physics. |
|
課程要求 |
Calculus (A) 1. |
|
預期每週課後學習時數 |
|
|
Office Hours |
另約時間 |
|
指定閱讀 |
待補 |
|
參考書目 |
George B. Thomas, Maurice D. Weir, Joel R. Hass, Thomas' Calculus, Early Transcendentals. 12th ed. |
|
評量方式
(僅供參考) |
|
No. |
項目 |
百分比 |
說明 |
|
1. |
Quizes |
20% |
|
2. |
Midterm Examination |
40% |
|
3. |
Final Examination |
40% |
|
|
|
週次 |
日期 |
單元主題 |
|
第1週 |
2/24,2/26 |
Sequences. Infinite Series. Comparison and Limit Comparison Tests. Integral Test. Ratio and Root Tests. |
|
第2週 |
3/02,3/03,3/05 |
Alternating Series, Absolute and Conditional Convergence. Power Series. |
|
第3週 |
3/09,3/10,3/12 |
Taylor and MacLaurin Series. Convergence of Taylor Series. The Binomial Series and Applications of Taylor Series. |
|
第4週 |
3/16,3/17,3/19 |
The Cross Product. Curves in Space and Their Tangents. Arc Length in Space. |
|
第5週 |
3/23,3/24,3/26 |
Quiz 1. Curvature and Normal Vectors of a Curve. Tangential and Normal Components of Acceleration. Function of Several Variables. Limit and Continuity in Higher Dimension. Partial Derivatives. |
|
第6週 |
3/30,3/31 |
Directional Derivatives and Gradient Vectors. Differentiability. Chain Rules. |
|
第7週 |
4/07,4/09 |
Linear Approximation. Tangent Planes. Taylor's Formula for Two Variables. |
|
第8週 |
4/13,4/14,4/16 |
Quiz 2. Extreme Values and Saddle Points. |
|
第9週 |
4/20,4/21,4/23 |
Lagrange Multipliers. Midterm Examination. |
|
第10週 |
4/27,4/28,4/30 |
Improper Integrals. Double and Iterated Integrals over rectangles. Double Integrals over General Regions. |
|
第11週 |
5/04,5/05,5/07 |
Quiz 3. Double Integrals in Polar Form. Triple Integrals in Rectangular Coordinates. Moments and Centers of Mass. Triple Integrals in Cylindrical and Spherical Coordinates. |
|
第12週 |
5/11,5/12,5/14 |
Substitution in Multiple Integrals. Line Integrals. Vector Fields and Line Integrals.
Path Independence. |
|
第13週 |
5/18,5/19,5/21 |
Conservative Fields and Potential Function. Green's Theorem in the Plane. Surfaces and Surface Area. Surface Integrals. |
|
第14週 |
5/25,5/26,5/28 |
Quiz 4. The Divergence of a Vector Field. Gauss' Divergence Theorem. The Curl of a Vector Field. |
|
第15週 |
6/01,6/02,6/04 |
Stokes' Theorem. First Order Differential Equations. |
|
第16週 |
6/08,6/09,6/11 |
Second-Order Differential Equations. |
|
第17週 |
6/15,6/16,6/18 |
Quiz 5. Second-Order Differential Equations (Continued). |
|