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實分析

數學系 劉豐哲

課程簡介

中文課程名稱:實分析
英文課程名稱:Real Analysis
授課教師:劉豐哲
學分數:3學分
開課單位:數學系
建立日期:2016 年 9 月

課程概述

A brief review of what covered in Real Analysis I, especially differentiation of functions of a real variable, functions of bounded variation and absolutely continuous functions, will be made first. Product measures, change of variables formula for integrals in Euclidean space, polar coordinates with application to potential integrals, basic principles of linear analysis and Hilbert space constitute the first part of the course content. The second part includes further study of L^p spaces, Fourier integral and Sobolev spaces with application to regularity of weak solutions of partial differential equations, and elements of probability theory.