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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	數學系
授課教師	李白飛
課號	MATH1202
課程識別碼	201 101A2
班次	06
學分	4
全/半年	全年
必/選修	必帶
上課時間	星期二5,6(12:20~14:10)星期四5,6,9(12:20~17:20)
上課地點	新103新103
備註	四9為實習課。四9教室更動為新生202。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/1012phlee
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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
參考書目	Robert A. Adams, Calculus, A Complete Course. 6th ed.
指定閱讀
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	Infinite Sequences. Infinite Series. Convergence Tests for Positive Series. Alternating Series.
第2週	2/26	Absolute Convergence and Conditional convergence. Power Series.
第3週	3/05,3/07	Differentiation and Integration of Power Series. Taylor and MacLaurin Series. The Binomial Series. Quiz 1.
第4週	3/12,3/14	Improper Integrals. The Cross Product in 3-Space. Planes and Lines in 3-Space.
第5週	3/19,3/21	Vector Functions of One Variable. Curves and Parametrizations. Curvature. Functions of Several Variables. Limits and Continuity. Partial Derivatives. Directional Derivatives.
第6週	3/26,3/28	Differentialbility. Chain Rule. Linear Approximation. Tangent Planes. Gradients. Higher-Order Derivatives. Quiz 2.
第7週	4/02	Taylor Polynomials. Implicit Differentiation.
第8週	4/09,4/11	Extreme Values. Lagrange Multipliers. Boundedness of Continuous Functions.
第9週	4/16,4/18	Existence of Extreme Values. Second Derivative Test. Double Integrals over Rectangular Region. Integrability of Continuous Functions.
第10週	4/23,4/25	Midterm Examination. Double Integrals over Nonrectangular Region. Improper Integrals. Quiz 3.
第11週	4/30,5/02	Double Integrals in Polar Coordinates. Triple Integrals.
第12週	5/07,5/09	Cylindrical and Spherical Coordinates. Change of Variables in Triple Integrals. Applications of Multiple Integrals. Line Integrals of Scalar Fields.
第13週	5/14,5/16	Line Integrals of Vector Fields. Conservative Vector Fields. Green Theorem. Quiz 4.
第14週	5/21,5/23	Surface Integrals. Divergence. The Divergence Theorem in 3-Space.
第15週	5/28,5/30	Curl. Stokes Theorem. Differential Equations. Solving First-Order Equations. Solving Second-Order Equations.
第16週	6/04,6/06	Linear Differential Equations. Series Solutions of Differential equations. Quiz 5.
第17週	6/11,6/13	Review.