课程简介
This course introduces the main ideas of real analysis, focusing on the structure and
completeness of the real numbers, including supremum, infimum, and the notions of lim sup and
lim inf as foundations for convergence. We study the topology of Rn, covering continuity,
uniform continuity, and compactness, with particular attention to the Heine–Borel theorem, and
revisit key ideas from calculus such as integration in a more rigorous setting through the
Riemann integral and the Fundamental Theorem of Calculus, including improper integrals. The
course also examines sequences and series of functions with an emphasis on uniform
convergence, and concludes with an introduction to Fourier series.
