微積分甲(二)
Calculus A (II)
學期
113-2
學分
4
學分
當期課號
564018
永久課號
GECS10002
開課單位
微積分教學小組
授課教師
王賜聖
校區
光復
類別
必修
上課時間表
| 節 | 週一 | 週四 |
|---|---|---|
3 10:10–11:00 | 微積分甲(二) SC204 2 節連堂 | |
4 11:10–12:00 | ||
7 15:30–16:20 | 微積分甲(二) SC204 2 節連堂 | |
8 16:30–17:20 |
* 根據陽明交大上課時間表所列
先修科目
微積分甲(一)
教學方式
其餘補充事項,會在第一次上課時與修課同學們說明清楚。
評分方式
1.學期作業、考試、評量: (1) 小考和作業佔學期總成績30%。 (2) 第一次期中考佔學期總成績 20%,第二次期中考佔學期總成績20%,考試範圍與時間將另行公佈。 (3) 陽明交通大學期末微積分會考,成績佔學期總成績30%。
課程大綱
- Ch10. Parametric Equations and Polar Coordinates
- Ch11. Sequences, Series, and Power Series
- Ch12.◆ Vectors and the Geometry of Space (◆為選教)
- Ch13. Vector Functions (◆為選教部分)
- Ch14. Partial Derivatives
- Ch15. Multiple Integrals (◆部分為選教)
- Ch16. ◆ Vector Calculus (◆部分為選教)
週次計畫
| 週次 | 主題 |
|---|---|
| 第 1 週 | Chapter 6 Applications of Integration -Polar Coordinates Review: Vectors and the Geometry of Space -Vectors, The Dot Product, The Cross Product Chapter 7 Vector Functions -Limits and Continuity |
| 第 2 週 | Chapter 7 Vector Functions -Space Curves -Derivatives and Integrals of Vector Functions -Arc Length Chapter 8 Partial Derivatives -Functions of Several Variables -Limits and Continuity |
| 第 3 週 | Chapter 8 Partial Derivatives -Limits and Continuity -Differentiability and Partial Derivatives -Tangent Plane and Linear Approximation |
| 第 4 週 | Chapter 8 Partial Derivatives -The Chain Rule -Implicit Differentiation -Directional Derivatives and the Gradient Vector -The maximum/minimum rate of change |
| 第 5 週 | Chapter 8 Partial Derivatives -Tangent Planes to Level Curves/Surfaces -Local Maximum and Minimum Values -Absolute Maximum and Minimum Values -Lagrange Multipliers |
| 第 6 週 | Chapter 8 Partial Derivatives -Lagrange Multiplier Method Chapter 9 Multiple Integrals -Double Integrals over Rectangles -Review |
| 第 7 週 | Midterm Exam |
| 第 8 週 | Chapter 9 Multiple Integrals -Double Integrals over Rectangles -Double Integrals over General Regions -Double Integrals in Polar Coordinates |
| 第 9 週 | Chapter 9 Multiple Integrals -Surface Area -Triple Integrals -Triple Integrals in Cylindrical Coordinates |
| 第 10 週 | Chapter 9 Multiple Integrals -Triple Integrals in Spherical Coordinates -Change of Variables in Multiple Integrals Chapter 10 Sequences, Series, and Power Series -Sequences |
| 第 11 週 | Chapter 10 Sequences, Series, and Power Series -Sequences -Series -The Integral Test |
| 第 12 週 | Chapter 10 Sequences, Series, and Power Series -Comparison Tests -Alternating Series and Absolute Convergence |
| 第 13 週 | Midterm Exam Chapter 10 Sequences, Series, and Power Series -The Ratio and Root Tests -Strategy for Testing Series -Power Series |
| 第 14 週 | Chapter 10 Sequences, Series, and Power Series -Power Series -Representation of Functions as Power Series -Taylor Series and Maclaurin Series |
| 第 15 週 | Chapter 10 Sequences, Series, and Power Series -Taylor Series and Maclaurin Series -Proofs of Taylor's Inequality, Interval of Convergence, Differentiation of Power Series and The Binomial Series |
| 第 16 週 | Review |
教科書
Calculus(Early Transcendentals), James Stewart, 9th Edition
Office Hours
- 聯絡方式
- 老師的e-mail:sswangtw@nycu.edu.tw