COVID-19 UPDATES

  • Masks covering your nose and mouth are required for entry.
  • HOLIDAY ALERT: Online Orders will NOT be processed during our closure on November 25 & 26. We will process them as quickly as we can beginning on Saturday, November 27. A reminder: your order is not complete until you receive an email confirming that it is ready for pickup! Thank you! 

 

TOP 21 OF 2021

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

PLEASE READ BEFORE PLACING AN ORDER:

-Please do not come to the store until you get a confirmation email that your order is complete and ready for pickup!

-Please place orders for pre-order titles separately. If your pre-order is placed with other titles, please note that we will add additional shipping fees.

-Women & Children First is not responsible for lost or stolen packages.

Visual Differential Geometry and Forms: A Mathematical Drama in Five Acts Cover Image
$56.25
Unavailable

Description


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.

About the Author


Tristan Needham is professor of mathematics at the University of San Francisco. He is the author of Visual Complex Analysis.
Product Details
ISBN: 9780691203706
ISBN-10: 0691203709
Publisher: Princeton University Press
Publication Date: July 13th, 2021
Pages: 584
Language: English