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The Divergence Theorem and Sets of Finite Perimeter (Pure and Applied Mathematics: a Series of Monographs, Textbooks, and Lecture Notes, 303)

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The Divergence Theorem and Sets of Finite Perimeter (Pure and Applied Mathematics: a Series of Monographs, Textbooks, and Lecture Notes, 303)

4.85 52,283 ratings · 2,647 reviews
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Overview: This book is devoted to a detailed development of the divergence theorem. The framework is that of Lebesgue integration no generalized Riemann integrals of Henstock Kurzweil variety are involved.In Part I the divergence theorem is established by a combinatorial argument involving dyadic cubes. Only elementary properties of the Lebesgue integral and Hausdorff measures are used. The resulting integration by parts is sufficiently general for many applications. As an example, it is applied to removable singularities of Cauchy Riemann, Laplace, and minimal surface equations.The sets of finite perimeter are introduced in Part II. Both the geometric and analytic points of view are presented. The equivalence of these viewpoints is obtained via the functions of bounded variation. These functions are studied in a self-contained manner with no references to Sobolev s spaces. The coarea theorem provides a link between the sets of finite perimeter and functions of bounded variation.The general divergence theorem for bounded vector fields is proved in Part III. The proof consists of adapting the combinatorial argument of Part I to sets of finite perimeter. The unbounded vector fields and mean divergence are also discussed. The final chapter contains a characterization of the distributions that are equal to the flux of a continuous vector field.

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Published January 1, 2012
ISBN 14411324
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After spending years working in the corporate world, Washek F. Pfeffer finally decided to pursue a lifelong passion for writing. They currently reside in a quiet suburb where they spend most of their time outlining new stories, reading extensively, and occasionally attempting to bake.

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I was completely blown away. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I will undoubtedly revisit this masterpiece.
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Masterpiece from start to finish. The prose is exquisite. It’s accessible yet undeniably sophisticated. I will undoubtedly revisit this masterpiece.
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Masterpiece from start to finish. The author orchestrated a breathtaking finale. Truly a work of art. An absolute must-read for connoisseurs of the genre.
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I was completely blown away. I became deeply invested in the protagonist's journey. A masterclass in storytelling. A true literary gem.
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Masterpiece from start to finish. I became deeply invested in the protagonist's journey. A masterclass in storytelling. A true literary gem.
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Exceeded all my expectations. The author orchestrated a breathtaking finale. Truly a work of art. Worth every moment spent reading.
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