微積分甲（二）A、B時段

  • 發布日期：115-07-03
  • 更新日期：115-07-31
  • 發布單位：應用數學系
用書：Calculus(Early Transcendentals), James Stewart, 9th Edition
(◆ 標示之章節，由老師決定是否講授，不列入微積分會考範圍)
 
  1. Parametric Equations and Polar Coordinates -- 2 hours
         10.3 Polar Coordinates
         10.4 Calculus in Polar Coordinates

  2. Parametric Equations and Polar Coordinates -- 2 hours
         11.1 Sequences
         11.2 Series
         11.3 The Integral Test and Estimates of Sums
         11.4 The Comparison Tests
         11.5 Alternating Series and Absolute Convergence
         11.6 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

  3. ◆ Vectors and the Geometry of Space
    ◆ 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 Surfaces

  4. ◆ Vector Functions
    ◆ 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

  5. Partial Derivatives -- 16 hours
         14.1 Functions of Several Variables
         14.2 Limits and Continuity
         14.3 Partial Derivatives
         14.4 Tangent Planes 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

  6. Multiple Integrals -- 11 hours
         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 (◆ The center of mass in Applications of Triple integrals)
         15.7 Triple Integrals in Cylindrical Coordinates
         15.8 Triple Integrals in Spherical Coordinates
         15.9 Change of Variables in Multiple Integrals

  7. Vector Calculus
    ◆ 16.1 Vector Fields
    ◆ 16.2 Line Integrals
    ◆ 16.3 The Fundamental Theorem for line integrals
    ◆ 16.4 Green’s Theorem
 
說明：
  1. 第二學期課程規劃 44小時，其餘時間由任課老師運用：演習課，考試，進度調整。
  2. 向量分析與常微分方程因時間因素省略，在二年級需有其他課程搭配。
  3. 課程內之定理與性質，強調在說明與講述其內容。
  4. 學期末有一次期末會考，題型為選擇、填空或計算/證明題；以鑑別基本觀念與計算能力為準。會考成績為微積分獎給獎依據。
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