課程資訊

Calculus (general Mathematics) (a)(2)

107-2

MATH1202

201 101A2

02

4.0

Ceiba 課程網頁
http://ceiba.ntu.edu.tw/1072MATH1202

「微積分甲上」主要內容是「單變數函數」的微分與積分運算。
「微積分甲下」將推廣所討論的函數，介紹「向量值函數」，並著重於「多變數函數」的微分、積分，與其豐富的應用。

1. 具有「微積分甲上」的基礎。
2. 認真寫習題，上課參與討論。

Office Hours

James Stewart, Calculus Early Transcendentals, 8th edition.

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 No. 項目 百分比 說明 1. 平時成績 30% 包含WeBWork, 課堂小考 (十二次), 與回家作業 (六次) 2. 期中考 35% 4/20 9:00-11:30 共同考題 3. 期末考 35% 6/15 TBA 共同考題

 課程進度
 週次 日期 單元主題 第1週 2/18,2/20,2/22 Overview of Calculus in last semester. 12.6: Cylinders and Quadric Surfaces. 13.1: Vector Functions and Space Curves. 13.2: Derivatives and Integrals of Vector Functions. 13.3: Arc Length and Curvature. 第2週 2/25,2/27 Review of Chapter 13: Vector Functions. 14.1: Functions of Several Variables. 14.2: Limits and Continuity. 14.3: Partial Derivatives. 第3週 3/04,3/06,3/08 Overview Chapter 14: Partial Derivatives. 14.4: Tangent Planes and Linear Approximations. 14.5: The Chain Rule. 14.6: Directional Derivatives and the Gradient Vector. 第4週 3/11,3/13,3/15 14.7: Maximum and Minimum Values. 14.8: Lagrange Multipliers. Review of Chapter 14: Partial Derivatives. 第5週 3/18,3/20 15.1: Double Integrals over Rectangles. 15.2: Double Integrals over General Regions. 15.3: Double Integrals in Polar Coordinates. 第6週 3/25,3/27,3/29 15.4: Applications of Double Integrals. 15.5: Surface Area. 15.6: Triple Integrals. 第8週 4/08,4/10,4/12 15.7: Triple Integrals in Cylindrical Coordinates. 15.8: Triple Integrals in Spherical Coordinates. 15.9: Change of Variables in Multiple Integrals. 第9週 4/15,4/17,4/19 Review of Chapter 15: Multiple Integrals. Review of Midterm Exam. 第10週 4/22,4/24,4/26 16.1: Vector Fields. 16.2: Line Integrals. 16.3: The Fundamental Theorem for Line Integrals 第11週 4/29,5/01,5/03 16.4: Green's Theorem. 16.5: Curl and Divergence. 16.6: Parametric Surfaces and Their Areas. 第12週 5/06,5/08,5/10 16.7: Surface Integrals. 16.8: Stokes' Theorem. 16.9: The Divergence Theorem. 第13週 5/13,5/15,5/17 16.10: Summary. Review of Chapter 16: Vector Calculus. 11.1: Sequences. 第14週 5/20,5/22,5/24 11.2: Series. 11.3: The Integral Test and Estimates of Sums. 11.4: The Comparison Tests. 11.5: Alternating Series. 第15週 5/27,5/29,5/31 11.6: Absolute Convergence and the Ratio and Root Tests 11.7: Strategy for Testing Series. 11.8: Power Series. 第16週 6/03,6/05 11.9: Representations of Functions as Power Series. 11.10: Taylor and Maclaurin Series. 11.11: Applications of Taylor Polynomials. 第17週 6/10,6/12,6/14 Review of Chapter 11: Infinite Sequences and Series. Review of Final Exam.