Read e-book online A Differential Approach to Geometry: Geometric Trilogy III: PDF

By Francis Borceux

This publication provides the classical conception of curves within the aircraft and 3-dimensional area, and the classical concept of surfaces in 3-dimensional house. It can pay specific realization to the historic improvement of the idea and the initial methods that help modern geometrical notions. It contains a bankruptcy that lists a really vast scope of aircraft curves and their houses. The booklet ways the brink of algebraic topology, delivering an built-in presentation totally obtainable to undergraduate-level students.

At the tip of the seventeenth century, Newton and Leibniz built differential calculus, hence making to be had the very wide selection of differentiable features, not only these constituted of polynomials. in the course of the 18th century, Euler utilized those principles to set up what's nonetheless this day the classical idea of so much common curves and surfaces, principally utilized in engineering. input this interesting global via striking theorems and a large offer of bizarre examples. achieve the doorways of algebraic topology through gaining knowledge of simply how an integer (= the Euler-Poincaré features) linked to a floor delivers loads of attention-grabbing info at the form of the outside. And penetrate the exciting international of Riemannian geometry, the geometry that underlies the idea of relativity.

The publication is of curiosity to all those that train classical differential geometry as much as fairly a complicated point. The bankruptcy on Riemannian geometry is of significant curiosity to those that need to “intuitively” introduce scholars to the hugely technical nature of this department of arithmetic, particularly while getting ready scholars for classes on relativity.

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A Differential Approach to Geometry: Geometric Trilogy III: 3 by Francis Borceux

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