微積分甲(二)

數學的本質是理性思考,為落實思考內容、具體化抽象概念、操作而得感知、實踐數學的應用,數學的手作計算亦是數學的重要內容。但是數學絕不是機械化的計算;機械化的計算數學軟體(如 Maple, Mathematica, MATLAB)做的遠比人類好。本微積分課程除了數學的計算之外,也重視相關的數學概念,並強調數學的邏輯推理及論證;此教學內容對學生的數理素養與之後的用到數學理論的其他應用科學課程,具有關鍵的重要性。 第二學期的主要內容是多變數函數的微分與積分。

微積分(一)

無備註

將使用E3教學平台:補充說明、補充教材、討論與回應將置於E3

期末微積分會考佔30% 期中考 二次 各20 % 期末考 20 % 作業 10 %

• 課綱內容可能微調,以正式上課前公佈版本為準

• 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

• 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

• ◆Ch16 Vector Calculus (◆處為選教)

  ◆ 16.1 Vector Fields ◆ 16.2 Line integrals ◆ 16.3 The fundamental Theorem for line integrals ◆ 16.4 Green's Theorem

  講授：

  0 hour

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

地點

教師未提供此項資料

時間

教師未提供此項資料

聯絡方式

教師未提供此項資料