Differential Geometry and Its Applications (2nd Edition)

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9780130652461: Differential Geometry and Its Applications (2nd Edition)
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This book covers classical differential geometry with modern applications to a variety of disciplines including math and science. Surfaces, curvatures, geometry of curves, holonomy and the Gauss-Bonnet Theorem, minimal surfaces and complex variables, geodesics, least area surfaces of revolution, surfaces of Delaunay, and more. For mathematicians, scientists and other professionals wish to learn how classic differential theory applies to practical situations in math, science and industry.

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Book Description:

This book studies the differential geometry of surfaces and aims to help students make the transition from the standard university curriculum to a type of mathematics that is a unified whole, by mixing geometry, calculus, linear algebra, differential equations, complex variables, the calculus of variations, and notions from the sciences.

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Designed not just for the math major but for all students of science, this text provides an introduction to the basics of the calculus of variations and optimal control theory as well as differential geometry. It then applies these essential ideas to understand various phenomena, such as soap film formation and particle motion on surfaces.

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