Single Variable Real Analysis

An advanced single-variable course taught at UCR as Cálculo en una Variable 2, giving a rigorous, real-analysis-style treatment of the calculus of real-valued functions of one real variable. The notes follow Dr. Pedro Méndez Hernández’s lectures and cover sequences and series of real numbers, the Riemann integral, improper integrals, and sequences and series of functions. Topics include the convergence of sequences and Cauchy criteria, \(\limsup\) and \(\liminf\), convergence tests for numerical series, the construction and properties of the Riemann integral and its applications, improper integrals, pointwise and uniform convergence of function sequences, power series, and Taylor expansions.

These are personal notes I took as a student. They were written in Spanish and translated into English; both versions are available and you can switch between them at any point. They are shared as-is, may contain errors, and are not affiliated with the instructor.