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課程資訊

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Calculus(II)

   

用書:Calculus(Early Transcendentals), James Stewart, 8th 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)

 
10.
Parametric Equations and Polar Coordinates -- 4 hours
  10.3 Polar Coordinates
  10.4 Areas and Lengths in Polar Coordinates
   
11.

Infinite Sequences and Series -- 15 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
  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
   
12.

◆Vectors and the Geometry of Space -- 3 hours

  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
   
13.

Vector Functions -- 3 hours

  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
   
14.

Partial Derivatives -- 16 hours

  14.1 Functions of Several Variables
  14.2 Limits and Continuity
  14.3 Partial Derivatives
  14.4 Tangent Plans and Differentials 
  14.5 The Chain Rule
  14.6 Directional Derivatives and the Gradient Vector
  14.7 Maximum and Minimum Values
  14.8 Lagrange Multipliers
   
15.

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
  15.7 Triple Integrals in Cylindrical Coordinates
  15.8 Triple Integrals in Spherical Coordinates
  15.9 Change of Variables in Multiple Integrals
   
16.
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 52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,強調其說明與講述內容。
4.
每學期各有一次期末會考,題型為選擇及填充題;以鑑別基本觀念與計算能力為準。
此次考試成績為微積分獎給獎依據。
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