章節

週次

課程進度

  

11. Infinite Sequences and Series

第一週

(2/22~2/26)

11.1 Sequences

11.2 Series

11.3 The Integral Test and Estimates of Sums

  

第二週

(3/1~3/5)

11.4 The Comparison Tests

11.5 Alternating Series

11.6 Absolute Convergence and the Ratio and Root Tests

  

第三週

(3/8~3/12)

11.7 Strategy for Testing Series

11.8 Power Series

11.9 Representations of Functions as Power Series

  

第四週

(3/15~3/19)

11.10 Taylor and Maclaurin Series

11.11 Applications of Taylor Polynomials

緩衝時間

  

13. Vector Functions

  

第五週

(3/22~3/26)

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

第六週

(3/29~4/2)

14.1 Functions of Several Variables

14.2 Limits and Continuity

14.3 Partial Derivatives

  

第七週

(4/5~4/9)　

14.4 Tangent Planes and Linear Approximations

14.5 The Chain Rule                 

4/5(一)～4/7(三)放假

  

第八週

(4/12~4/16)　

14.6 Directional Derivatives and the Gradient Vector

14.7 Maximum and Minimum Values

14.8 Lagrange Multipliers

  

15. Multiple Integrals

第九週

(4/19~4/23)

緩衝時間

15.1 Double Integrals over Rectangles

15.2 Iterated Integrals

  

期中考4/24（六）9：00～11：30

考試範圍：11.1～14.8（英文命題）

  

第十週

(4/26~4/30)

15.3 Double Integrals over General Regions

15.4 Double Integrals in Polar Coordinates

  

第十一週

(5/3~5/7)

15.5 Applications of Double Integrals

15.6 Triple Integrals

15.7 Triple Integrals in Cylindrical Coordinates

  

第十二週

(5/10~5/14)

15.8 Triple Integrals in Spherical Coordinates

15.9 Change of Variables in Multiple Integrals

  

16. Vector Calculus

第十三週

(5/17~5/21)

緩衝時間

16.1 Vector Fields

16.2 Line Integrals

  

第十四週

(5/24~5/28)

16.3 The Fundamental Theorem for Line Integrals

16.4 Green’s Theorem

  

第十五週

(5/31~6/4)

16.5 Curl and Divergence

16.6 Parametric Surfaces and Their Areas

16.7 Surface Integrals                     

 

第十六週

(6/7~6/11)

16.8 Stokes’ Theorem

16.9 The Divergence Theorem  

 

第十七週

(6/14~6/18)

16.10 Summary

緩衝時間                                 

6/16(三)放假

  

期末考6/19（六）9：00～11：30

考試範圍：15.1～16.10（英文命題）