Advanced Calculus of a Single Variable

Focusing on a rigorous exploration of single variable calculus, this advanced undergraduate textbook emphasizes a deeper understanding of fundamental concepts. It covers limits with a focus on epsilon-delta definitions, differentiates between pointwise and uniform continuity, and provides rigorous proofs for L'Hôpital's rule. Additionally, it delves into the Riemann integral, including improper integrals and relevant tests. Designed for a one-semester course, it reflects years of classroom experience, aiming to elevate students' comprehension of calculus beyond introductory levels.