分析導論(二)
Introduction to Analysis (II)
學期
109-2
學分
4
學分
當期課號
1378
永久課號
DAM2104
開課單位
應用數學系
授課教師
李明佳
校區
光復
類別
必修
上課時間表
| 節 | 週二 | 週三 | 週四 |
|---|---|---|---|
3 10:10–11:00 | 分析導論(二) SA311 2 節連堂 | ||
4 11:10–12:00 | |||
5 13:20–14:10 | 分析導論(二) SA311 | ||
7 15:30–16:20 | 分析導論(二) SA311 2 節連堂 | ||
8 16:30–17:20 |
* 根據陽明交大上課時間表所列
概述
延續「分析導論(一)」的課程內容,詳見課程進度表。
先修科目
微積分、分析導論(一)
教學方式
教師上課、電子講義、助教演習課和圖書館諮詢討論
評分方式
助教演習課、2次期中考和1次期末考
週次計畫
| 週次 | 主題 |
|---|---|
| 第 18 週 | the Riemann integral on the line the fundamental theorem of calculus Riemann integration in several variables Riemann integrability the generalized mean value theorem and the second MVT for integrals iterated integrals and Fubini's theorem change of variables for Riemann integrals in several variables functions defined by integrals and the bounded convergence theorem improper integrals of type I improper integrals of type II Cauchy principle value of improper integrals improper integrals in R^k the Lebesgue measure and Lebesque measurable sets the Lebesgue integral arc length line integrals Green's theorem surface area and surface integrals vector derivatives Gauss's divergence theorem and Green's formula Stoke's theorem infinite series Taylor series series with nonnegative terms I: the integral test and the comparison tests series with nonnegative terms II; the ratio, root, and Raabe tests absolute and conditional convergence alternative series, Dirichlet's test and Abel's test double series and products of series sequences of functions series of functions integrals and derivatives of sequences and series power series differentiation and integration of power series and Abel's theorem the Arzela-Ascoli theorem |
教科書
Trench, William F., "Introduction to Real Analysis" (2013). Faculty Authored and Edited Books & CDs. 7. https://digitalcommons.trinity.edu/mono/7 Gernald B. Folland, Advanced Calculus, Prentice Hall, Upper Saddle River, NJ, 2002.
Office Hours
- 地點
- 科學一館337
- 時間
- 週三E&F
- 聯絡方式
- 分機:56463