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

A Mathematical Drama in Five Acts

Cover Art for 9780691203706, Visual Differential Geometry and Forms: A Mathematical Drama in Five Acts by Tristan Needham
ISBN: 9780691203706
Publisher: Princeton University Press
Published: 22 June, 2021
Format: Paperback
Language: English
Editions:
2 other editions of this product

Visual Differential Geometry and Forms fulfils 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.

Booko is reader-supported. When you buy through links on our site, we may earn an affiliate commission. Learn more

Shop Preferences

Customize which shops to display. You can include the following shops by logging in to change your settings.

Booko is reader-supported. When you buy through links on our site, we may earn an affiliate commission. Learn more

Historical Prices

Loading...
This graph is for informational purposes only. Occasionally pricing data is captured incorrectly, through bugs in Booko or the stores supplying data, which may distort the graph, providing undue hope that even lower prices sometimes appear.

Recently Updated