Basic Analysis I: Introduction to Real Analysis, Volume I

Livro digital

Título:
Basic Analysis I: Introduction to Real Analysis, Volume I

Autor:
Jiří Lebl

Categoria:
Tecnologia > Geral

Doador:
Raffaello D. N.

Sinopse:
Real analysis becomes manageable when abstraction grows from familiar ground. Jiří Lebl begins with sets and real numbers, then develops sequences and series, continuous functions, derivatives, and the Riemann integral before moving to sequences of functions and metric spaces. The progression culminates in fixed-point ideas and Picard’s existence-and-uniqueness theorem, showing how the earlier techniques converge in a substantial result. The text balances a concrete study of the real line with a path toward more advanced mathematics. Readers meet Cauchy sequences, Bolzano–Weierstrass, uniform continuity, Taylor’s theorem, improper integrals, pointwise and uniform convergence, completeness, compactness, and continuous maps on metric spaces. Hundreds of exercises and carefully chosen figures turn proof techniques into active practice rather than passive recognition. Designed for undergraduates with a first course in proofs, this volume can support either a measured introduction or a faster route toward graduate study. Its strength is the combination of rigor, flexibility, and visual explanation: definitions are motivated, theorems are connected, and optional detours let instructors and independent readers choose their depth without losing the central narrative of analysis.