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

Tristan Needham

ISBN 10: 0691203709 / ISBN 13: 9780691203706

Published by Princeton University Press Jul 2021, 2021

About this Item

Neuware - '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'.

Seller Inventory # 9780691203706

Bibliographic Details

• Title: Visual Differential Geometry and Forms : A Mathematical Drama in Five Acts
• Publisher: Princeton University Press Jul 2021
• Publication Date: 2021
• Language: English
• ISBN 10: 0691203709
• ISBN 13: 9780691203706
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 252W x 175H x 29D millimeters 252 millimeters width by 175 millimeters height by 29 millimeters depth
• Weight: 905 grams

About this title

Synopsis

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About the Author

Tristan Needham is professor of mathematics at the University of San Francisco. He is the author of Visual Complex Analysis.