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

• Visual Differential Geometry and Forms: A Mathematical Drama in Five Acts
• Tristan Needham
• Page: 584
• Format: pdf, ePub, mobi, fb2
• ISBN: 9780691203706
• Publisher: Princeton University Press

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e-Books collections Visual Differential Geometry and Forms: A Mathematical Drama in Five Acts 9780691203706 by Tristan Needham in English

An inviting, intuitive, and visual exploration 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.

Visual Differential Geometry and Forms - Mathematics
Jul 13, 2021 — Visual Differential Geometry and Forms fulfills two principal goals. In the first four acts, Tristan Needham puts the geometry back into Euclidean and NonEuclidean Geometry: 3Exercises for Act II: 83Exercises for Prologue and Act I: 24ACT III: 90
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Visual Differential Geometry and Forms: A Mathematical Drama in Five In the first four acts, Tristan Needham puts the geometry back into 
Visual Differential Geometry and Forms: A Mathematical Drama in
Visual Differential Geometry and Forms: A Mathematical Drama in Five Acts (Hardcover) In the first four acts, Tristan Needham puts the geometry back into 
Visual Differential Geometry and Forms: A Mathematical
AbeBooks.com: Visual Differential Geometry and Forms: A Mathematical Drama in Five Acts: 584 pages. 10.00x7.00x1.10 inches. In Stock.
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