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課程資訊

課程名稱	微積分甲下 Calculus (general Mathematics) (a)(2)
開課學期	101-2
授課對象	土木工程學系
授課教師	郭鴻文
課號	MATH1202
課程識別碼	201 101A2
班次	11
學分	4
全/半年	全年
必/選修	必帶
上課時間	星期二7,8,9(14:20~17:20)星期四5,6(12:20~14:10)
上課地點	新203新203
備註	統一教學.二9為實習課. 限本系所學生(含輔系、雙修生) 總人數上限：130人
Ceiba 課程網頁	http://ceiba.ntu.edu.tw/1012calculus_a11
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課程概述	Study the process of approximation and its limitation (errors), learn the tools and techniques for analyzing regular mappings with applications, and deepen the understanding of elementary functions.
課程目標	Study the process of approximation and its limitation (errors), learn the tools and techniques for analyzing regular mappings with applications, and deepen the understanding of elementary functions.
課程要求	High School Mathematics
預期每週課後學習時數
Office Hours
指定閱讀
參考書目	Textbook Calculus: One And Several Variables, tenth edition.
評量方式 (僅供參考)

課程進度

週次	日期	單元主題
第1週	2/19,2/21	[12.1] Sigma Notation. [12.2] Infinite Series. [12.3] The Integral Test; Basic Comparison, Limit Comparison. [12.4] The Root Test; The Ratio Test. [12.5] Absolute and Conditional Convergence; Alternating Series.
第2週	2/26,2/28	[12.6] Taylor Polynomials in x; Taylor Series in x. [12.7] Taylor Polynomials and Taylor Series in x–a.
第3週	3/05,3/07	[12.8] Power Series. [12.9] Differentiation and Integration of Power Series. [13.3] The Dot Product. [13.4] The Cross Product.
第4週	3/12,3/14	[13.5] Lines. [13.6] Planes. [13.7] Higher Dimensions. [14.1] Limit, Continuity, Vector Derivative. [14.2] The Rules of Differentiation.
第5週	3/19,3/21	[14.3] Curves. [14.4] Arc Length. [14.5] Curvilinear Motion; Curvature. [14.6] Vector Calculus in Mechanics.
第6週	3/26,3/28	[15.1] Elementary Examples. [15.3] Graphs; Level Curves and Level Surfaces. [15.4] Partial Derivatives. [15.5] Open Sets and Closed Sets. [15.6] Limits and Continuity; Equality of Mixed Partials.
第7週	4/02,4/04	[16.1] Differentiability and Gradient. [16.2] Gradients and Directional Derivatives.
第8週	4/09,4/11	[16.3] The Mean-Value Theorem; the Chain Rule. [16.4] The Gradient as a Normal; Tangent Lines and Tangent Planes.
第9週	4/16,4/18	[16.5] Local Extreme Values. [16.6] Absolute Extreme Values. [16.7] Maxima and Minima with Side Conditions.
第10週	4/23,4/25	[16.8] Differentials. [16.9] Reconstructing a Function from Its Gradient.
第11週	4/30,5/02	[17.1] Multiple-Sigma Notation. [17.2] Double Integrals. [17.3] The Evaluation of Double Integrals by Repeated Integrals.
第12週	5/07,5/09	[17.4] The Double Integral as the Limit or Riemann Sums; Polar Coordinates. [17.5] Further Applications of Double Integration. [17.6] Triple Integrals. [17.7] Reduction to Repeated Integrals.
第13週	5/14,5/16	[17.8] Cylindrical Coordinates. [17.9] The Triple Integral as the Limit of Riemann Sums; Spherical Coordinates. [17.10] Jacobians; Changing Variables in Multiple Integration.
第14週	5/21,5/23	[18.1] Line Integrals. [18.2] The Fundamental Theorem for Line Integrals. [18.3] Work-Energy Formula; Conservation of Mechanical Energy.
第15週	5/28,5/30	[18.4] Another Notation for Line Integrals; Line Integrals with Respect to Arc Length. [18.5] Green’s Theorem.
第16週	6/04,6/06	[18.6] Parametrized Surfaces; Surface Area. [18.7] Surface Integrals. [18.8] The Vector Differential Operator .
第17週	6/11,6/13	[18.9] The Divergence Theorem. [18.10] Stokes’s Theorem.