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Visual Differential Geometry and Forms: A Mathematical Drama in Five Acts by Tristan Needham (Paperback, 2021)

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Visual Differential Geometry and Forms: A Mathematical Drama in Five Acts

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An inviting, intuitive, and visualexploration of differential geometry and forms Visual 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.

Product Identifiers

Publisher
Princeton University Press
ISBN-13
9780691203706
eBay Product ID (ePID)
23049054913

Product Key Features

Author
Tristan Needham
Publication Name
Visual Differential Geometry and Forms: a Mathematical Drama in Five Acts
Format
Paperback
Language
English
Subject
Mathematics, Physics
Publication Year
2021
Type
Textbook
Number of Pages
584 Pages

Dimensions

Item Height
254mm
Item Width
178mm

Additional Product Features

Title_Author
Tristan Needham
Country/Region of Manufacture
United States

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5 out of 5 stars
by petrmiencil11 Sep, 2022
Amazing text, fun to read!
Great intro into differential geometry, fully recommended!
Verified purchase: Yes | Condition: New
5 out of 5 stars
by cjmaud104 Mar, 2022
Great new book on differential geometry.
Refreshing style with great explanations.
Verified purchase: Yes | Condition: New

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