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.