Vladimir A. Zoric Book order

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.

This second edition of a very popular two-volume work presents a thorough first course in analysis, leading from real numbers to such advanced topics as differential forms on manifolds;

Based on a two-semester course aimed at illustrating various interactions of "pure mathematics" with other sciences, such as hydrodynamics, thermodynamics, statistical physics and information theory, this text unifies three general topics of analysis and physics, which are as follows: the dimensional analysis of physical quantities, which contains various applications including Kolmogorov's model for turbulence; functions of very large number of variables and the principle of concentration along with the non-linear law of large numbers, the geometric meaning of the Gauss and Maxwell distributions, and the Kotelnikov-Shannon theorem; and, finally, classical thermodynamics and contact geometry, which covers two main principles of thermodynamics in the language of differential forms, contact distributions, the Frobenius theorem and the Carnot-Caratheodory metric. It includes problems, historical remarks, and Zorich's popular article, "Mathematics as language and method."