實分析一

 

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課程概要: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. 

課程目標:To prepare the students for their future studies in modern analysis and probability. 

參考書目:1) G. B. Folland, Real Analysis; 2) S. L. Royden, Real Analysis; 3) S. Saks, Theory of Integral; 4) E. M. Stein & R. Shakarchi, Real Analysis. 

課程影音:
 

實分析一 臺大數學系 劉豐哲教授
實分析一:Introduction
實分析一:可加性
實分析:測度1
實分析:測度2
實分析:測度與積分1
實分析:測度與積分2
實分析:測度與積分3
實分析:賦距空間1
實分析:賦距空間2
實分析:Outer Measure1
實分析:Outer Measure2
實分析:Outer Measure3
實分析:Outer Measure4
實分析:Outer Measure5
實分析:複習 Caratheodory Measure
實分析:Caratheodory Measure2
實分析:Caratheodory Measure3
實分析:Caratheodory Measure4
實分析:Caratheodory Measure5
實分析:Riemann 與 Lebesgue 積分