Download E-books Geometric Integration Theory (Dover Books on Mathematics) PDF

By Hassler Whitney

Geared towards upper-level undergraduates and graduate scholars, this remedy of geometric integration idea contains 3 components: an creation to classical concept, a postulational method of normal thought, and a last part that maintains the overall research with Lebesgue theory.
The introductory bankruptcy exhibits how the best hypotheses bring about the employment of simple instruments. the hole 3rd of the remedy, an exam of classical concept, results in the speculation of the Riemann quintessential and contains a learn of soft (i.e., differentiable) manifolds. the second one half, on common conception, explores summary integration conception, a few family members among chains and features, normal homes of chains and cochains, and chains and cochains in open units. The 3rd and ultimate part surveys Lebesgue thought when it comes to flat cochains and differential kinds, Lipschitz mappings, and chains and additive set features. Appendixes on vector and linear areas, geometric and topological preliminaries, and analytical preliminaries, in addition to indexes of symbols and phrases, finish the text.

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