Mathematical analysis 2

Viac o knihe

This second English edition of a popular two-volume work offers a comprehensive first course in analysis, progressing from real numbers to advanced topics like differential forms on manifolds, asymptotic methods, and various transforms. The course is distinguished by its clear focus on the natural sciences and an informal exploration of the fundamental concepts and theorems of calculus. It combines clarity of exposition with a rich array of exercises, problems, and applications to areas often overlooked in traditional real analysis textbooks. A key enhancement in this edition is the inclusion of appendices in both volumes—six in the first and five in the second—designed to assist students in mathematics and physics, as well as teachers with varying objectives. These appendices cover diverse topics, including surveys that draw important conceptual connections between analysis and other mathematical fields. The second volume presents classical analysis as part of a unified mathematics framework, illustrating its interactions with modern areas such as algebra, differential geometry, differential equations, complex analysis, and functional analysis, thus providing a solid foundation for advanced study in these disciplines.