This comprehensive textbook on multivariable calculus serves as a sequel to a one-variable calculus text. It connects concepts between the two, covers unique topics like monotonicity and convexity, and emphasizes geometric approaches. Each chapter includes detailed proofs, examples, exercises, and a section of notes for further exploration.
This textbook offers a comprehensive introduction to single-variable calculus, highlighting geometric definitions and analytic characterizations. It includes numerous examples, exercises, and a "Notes and Comments" section. The second edition features significant revisions, new chapters, and appendices, making it suitable for rigorous undergraduate courses.
Focusing on the interplay between algebraic and metric structures, this introduction to functional analysis appeals to mathematicians, scientists, and engineers alike. It emphasizes practical applicability while presenting foundational concepts. Notably, it features Zabreiko's theorem, which asserts that every countably subadditive seminorm on a Banach space is continuous, leading to several significant theorems in the field. This unique perspective enhances the understanding of functional analysis for a diverse audience.