分析導論(二)
Introduction to Analysis (II)
學期
114-2
學分
4
學分
當期課號
516704
永久課號
SCMA10005
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 | |||
N 12:20–13:10 | 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、練習題共筆、助教演習課和圖書館諮詢討論
評分方式
共筆及報告，助教演習課、3次期中考和1次期末考
週次計畫
| 週次 | 主題 |
|---|---|
| 第 1 週 | the Riemann integral on the linethe fundamental theorem of calculusRiemann integration in several variablesRiemann integrabilitythe generalized mean value theorem and the second MVT for integralsiterated integrals and Fubini's theoremchange of variables for Riemann integrals in several variablesfunctions defined by integrals and the bounded convergence theoremimproper integrals of type Iimproper integrals of type II Cauchy principle value of improper integralsimproper integrals in R^kthe Lebesgue measure and Lebesque measurable setsthe Lebesgue integralarc lengthline integralsGreen's theoremsurface area and surface integralsvector derivativesGauss's divergence theorem and Green's formulaStoke's theoreminfinite series Taylor seriesseries with nonnegative terms I: the integral test and the comparison testsseries with nonnegative terms II& #x0D the ratio, root, and Raabe testsabsolute and conditional convergencealternative series, Dirichlet's test and Abel's testdouble series and products of seriessequences of functionsseries of functionsintegrals and derivatives of sequences and seriespower seriesdifferentiation and integration of power series and Abel's theoremthe Arzela-Ascoli theorem |
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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