Geometric Integration Theory is a comprehensive mathematical textbook written by Hassler Whitney, a renowned American mathematician. The book is part of the Princeton Mathematical Series and is the 21st book in the series. The book covers the theory of geometric integration, which is a branch of mathematics that deals with the integration of differential forms over manifolds. The book is divided into three parts. The first part introduces the foundational concepts of geometric integration, including the definition of manifolds, differential forms, and integration. The second part focuses on the theory of integration on manifolds, including the Stokes' theorem, the de Rham cohomology, and the Hodge theory. The third part covers the applications of geometric integration, including the theory of harmonic forms, the Poincar�� duality, and the Gauss-Bonnet theorem.The book is aimed at graduate students and researchers in mathematics and physics who are interested in the theory of geometric integration. It provides a rigorous and detailed treatment of the subject, with numerous examples and exercises to help readers understand the material. The book is highly regarded in the mathematical community and is considered a classic in the field of geometric integration.This scarce antiquarian book is a facsimile reprint of the old original and may contain some imperfections such as library marks and notations. Because we believe this work is culturally important, we have made it available as part of our commitment for protecting, preserving, and promoting the world's literature in affordable, high quality, modern editions, that are true to their original work.

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This treatment of geometric integration theory consists of an introduction to classical theory, a postulational approach to general theory, and a section on Lebesgue theory. Covers the theory of the Riemann integral; abstract integration theory; some relations between chains and functions; Lipschitz mappings; chains and additive set functions, more. 1957 edition.

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