實分析導論

Introduction to Real Analysis

學期

109-1

學分

3 學分

當期課號

5418

永久課號

IAM5841

開課單位

應用數學系

授課教師

葉立明

校區

光復

類別

選修

上課時間表

* 根據陽明交大上課時間表所列

概述

本課程屬大學部與研究所程度的實分析課程,授課偏重於數學理論與分析方法的介紹,是高等微積分的一部分也是進入實變數函數論的基礎課程。

先修科目

calculus, linear algebra

教學方式

板書

評分方式

學期作業: 60 % 考試: 40%

週次計畫

週次	主題
第 0 週	Intrgeation of differential forms: vector analysis The Lebesque Theorem: set function
第 1 週	Some special functions: power series the exponetial and logarithmic functions the trigonometric functions
第 2 週	Some special functions: the algebraic completeness of the complex field Fourier series
第 3 週	Some special functions: The Gamma functions Functions of several variables: linear transformations
第 4 週	Functions of several variables: Differentiation The contraction principles
第 5 週	Functions of several variables: The inverse function Theorem The Implicit function Theorem
第 6 週	Functions of several variables: The Rank Theorem Determinants
第 7 週	Functions of several variables: derivatives of higher order differentiation of Integrals Intrgeation of differential forms: integration
第 8 週	Intrgeation of differential forms: primitive mapping partition of unity change of variables
第 9 週	Intrgeation of differential forms: differential forms simplexes and chains
第 10 週	Intrgeation of differential forms: Stokes' Theorem closed forms and exact forms
第 12 週	The Lebesque Theorem: construction of Lebesque measure measure spaces measurable functions
第 13 週	The Lebesque Theorem: simple functions integration
第 14 週	The Lebesque Theorem: comparison with Riemann integration integration of complex functions
第 15 週	The Lebesque Theorem: functions of class L^2
第 16 週	The Lebesque Theorem: functions of class L^p

教科書

Rudin, Walter Principles of mathematical analysis New York : McGraw-Hill, c1976

Office Hours