Mathematical Analysis II

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This second English edition of a popular two-volume work offers a comprehensive introduction to analysis, covering topics from real numbers to advanced concepts like differential forms on manifolds, asymptotic methods, and various transforms. It emphasizes a clear connection to the natural sciences and explores the essence of calculus concepts and theorems. The clarity of the exposition is complemented by a wealth of exercises, problems, and applications often overlooked in typical real analysis textbooks. The second edition includes new appendices—six in the first volume and five in the second—designed to benefit both students and teachers with diverse goals. These appendices include surveys that highlight important connections between analysis and other mathematical fields. The second volume presents classical analysis as part of a unified mathematical framework, illustrating its interactions with modern areas such as algebra, differential geometry, differential equations, complex analysis, and functional analysis. This work lays a strong foundation for advanced studies in any of these mathematical directions.