Visual Differential Geometry and Forms

Name: Visual Differential Geometry and Forms
Brand: Princeton University Press
SKU: 9780691203706
Price: 1232 CZK
Availability: InStock

A Mathematical Drama in Five Acts

Autor: Tristan Needham

Jazyk:

Vazba: Brožovaná

Vydavatel: Princeton University Press

Dostupnost: Skladem u dodavatele

Odesíláme za 3-5 dnů

1 232 Kč

An inviting, intuitive, and visual exploration of differential geometry and formsVisual Differential...

Informace o knize

Autor

Tristan Needham

Jazyk

Angličtina

Vazba

Kniha - Brožovaná

Vydáno

2021

Stránek

584

EAN

9780691203706

ISBN

0691203709

Enbook ID

33320573

Vydavatel

Princeton University Press

Hmotnost

1006

Rozměry

178 x 178 x 33

Kompletní popis

An inviting, intuitive, and visual exploration of differential geometry and formsVisual Differential Geometry and Forms fulfills two principal goals. In the first four acts, Tristan Needham puts the geometry back into differential geometry. Using 235 hand-drawn diagrams, Needham deploys Newton’s geometrical methods to provide geometrical explanations of the classical results. In the fifth act, he offers the first undergraduate introduction to differential forms that treats advanced topics in an intuitive and geometrical manner. Unique features of the first four acts include: four distinct geometrical proofs of the fundamentally important Global Gauss-Bonnet theorem, providing a stunning link between local geometry and global topology; a simple, geometrical proof of Gauss’s famous Theorema Egregium; a complete geometrical treatment of the Riemann curvature tensor of an n-manifold; and a detailed geometrical treatment of Einstein’s field equation, describing gravity as curved spacetime (General Relativity), together with its implications for gravitational waves, black holes, and cosmology. The final act elucidates such topics as the unification of all the integral theorems of vector calculus; the elegant reformulation of Maxwell’s equations of electromagnetism in terms of 2-forms; de Rham cohomology; differential geometry via Cartan’s method of moving frames; and the calculation of the Riemann tensor using curvature 2-forms. Six of the seven chapters of Act V can be read completely independently from the rest of the book. Requiring only basic calculus and geometry, Visual Differential Geometry and Forms provocatively rethinks the way this important area of mathematics should be considered and taught.

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Visual Differential Geometry and Forms

A Mathematical Drama in Five Acts

Informace o knize

Kompletní popis

Mohlo by vás zajímat

Zákaznicí kteří koupili tuto knihu koupili také