分析導論榮譽班(二)

Introduction to Analysis (II), Honor Class

學期

110-2

學分

4 學分

當期課號

1358

永久課號

DAM2106

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	分析導論榮譽班(二) SA215 2 節連堂
4 11:10–12:00	分析導論榮譽班(二) SA215 2 節連堂
5 13:20–14:10		分析導論榮譽班(二) SA215
7 15:30–16:20			分析導論榮譽班(二) SA215 2 節連堂
8 16:30–17:20			分析導論榮譽班(二) SA215 2 節連堂

* 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

Terence Tao, Analysis I, II, 3rd edition, 2016, Springer ebooks 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