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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
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參考書目	Robert A. Adams, Calculus, A Complete Course. 6th ed.
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.