微積分甲(二)

在探討(人文、社會、自然、資訊等)科學問題過程中,「數學」扮演關鍵的一環。這個學期微積分(二)將教授無窮級數及多變量函數的「極限」、「微分」與「積分」等課題,期待在學習這些主題後,建立基本數學觀念。在往後當遇到探究科學問題時,希望「微積分」的課程學習經驗能作為基礎或類比。

微積分(一)

無備註

(1) 課堂上進行理論架構介紹,搭配嚴格證明與簡易操作;課後同學自行主動學習,進行微積分教學小組勾選的習題之練習。 (2) 微積分有配搭課程助教,在同學學習上遇到問題時,助教諮詢時間可以協助。 (3) 課堂上,不實簽到、違反考試紀律者,按校規處理。 (4) 教學相關網站 http://www.math.nctu.edu.tw/~smchang/0802/C.html

(1) 作業:學生自行練習微積分教學小組勾選的習題。 (2) 考試:隨堂小考、3次期中考、1次會考(期末全校統一微積分會考)。 (3) 評量:平時隨堂小考(15%)、期中考(55%)、會考 (30%)。

• Ch11 Infinite Sequences and Series

  11.1 Sequences 11.2 Series 11.3 The Integral Test and Estimates of Sums 11.4 The Comparison Tests 11.5 Alternating Series 11.6 Absolute Convergence and the Ratio and Root Tests 11.7 Strategy for Testing Series 11.8 Power Series 11.9 Representations of Functions as Power Series 11.10 Taylor and Maclaurin Series 11.11 Applications of Taylor Polynomials

  講授：

  15 hours

• ◆Ch12 Vectors and the Geometry of Space (選教)

  12.1 Three-Dimensional Coordinate Systems 12.2 Vectors 12.3 The Dot Product 12.4 The Cross Product 12.5 Equations of Lines and Planes 12.6 Cylinders and Quadric Surface

  講授：

  3 hours

• Ch13 Vector Functions (◆處為選教)

  13.1 Vector Functions and Space Curves 13.2 Derivatives and Integrals of Vector Functions 13.3 Arc Length And ◆ Curvature ◆ 13.4 Motion in Space: Velocity and Acceleration

  講授：

  3 hours

• Ch10 Parametric Equations and Polar Coordinates

  10.3 Polar Coordinates 10.4 Areas and Lengths in Polar Coordinates

  講授：

  4hours

• Ch14 Partial Derivatives

  14.1 Functions of Several Variables 14.2 Limits and Continuity 14.3 Partial Derivatives 14.4 Tangent Plans and Linear Approximations 14.5 The Chain Rule 14.6 Directional Derivatives and the Gradient Vector 14.7 Maximum and Minimum Values 14.8 Lagrange Multipliers

  講授：

  16 hours

• Ch15 Multiple Integrals (◆處為選教)

  15.1 Double Integrals over Rectangles 15.2 Double Integrals over General Regions 15.3 Double Integrals in Polar Coordinates ◆15.4 Application of Double Integrals 15.5 Surface Area 15.6 Triple Integrals 15.7 Triple Integrals in Cylindrical Coordinates 15.8 Triple Integrals in Spherical Coordinates 15.9 Change of Variables in Multiple Integrals

  講授：

  11 hours

Calculus (Early Transcendentals), James Stewart, 8th Edition

地點

科學一館235室

時間

(四)12:20~13:10,欲前來晤談者,請事先用電子郵件預約。

聯絡方式

E-mail:smchang@math.nctu.edu.tw 校內分機:31216