微積分甲(二)課程綱要

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)

10.Parametric Equations and Polar Coordinates -- 2 hours
10.3 Polar Coordinates
10.4 Calculus in Polar Coordinates
11.Sequences, Series, and Power 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 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
12.◆Vectors and the Geometry of Space -- 1 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 Surfaces
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 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
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. 第一學期課程規劃 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。