By Francis Borceux

This publication offers the classical thought of curves within the aircraft and three-d house, and the classical idea of surfaces in three-d house. It will pay specific recognition to the ancient improvement of the idea and the initial methods that aid modern geometrical notions. It incorporates a bankruptcy that lists a truly large scope of airplane curves and their houses. The publication ways the brink of algebraic topology, offering an built-in presentation absolutely available 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 variety of differentiable services, not only these produced from polynomials. through the 18th century, Euler utilized those rules to set up what's nonetheless at the present time the classical concept of such a lot basic curves and surfaces, mostly utilized in engineering. input this interesting global via extraordinary theorems and a large offer of unusual examples. succeed in the doorways of algebraic topology via researching simply how an integer (= the Euler-Poincaré features) linked to a floor supplies loads of fascinating info at the form of the skin. And penetrate the exciting global of Riemannian geometry, the geometry that underlies the speculation of relativity.

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

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