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Author  Title  Accn#  Year  Item Type  Claims 
1 
Tristan Needham 
Visual differential geometry and forms: A Mathematical Drama in Five Acts 
026961 
2021 
Book 


1.
 
Title  Visual differential geometry and forms: A Mathematical Drama in Five Acts 
Author(s)  Tristan Needham 
Publication  USA, Princeton University Press, 2021. 
Description  PB : 584pp 
Abstract Note  An inviting, intuitive, and visual exploration of differential geometry and formsVisual Differential Geometry and Forms fulfills two principal goals. In the first four acts, Tristan Needham puts the geometry back into differential geometry. Using 235 handdrawn 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 GaussBonnet 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 nmanifold; 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 2forms; de Rham cohomology; differential geometry via Cartan’s method of moving frames; and the calculation of the Riemann tensor using curvature 2forms. 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. 
ISBN,Price  9780691203706 : $ 45.00 
Classification  1. 514.7 NEE
2. 514.77 NEE
3. 517.7 NEE

Keyword(s)  1. DIFFERENTIAL GEOMETRY
2. Forms
3. Geometry and Forms

Item Type  Book 
Circulation Data
Accession#  
Call#  Status  Issued To  Return Due On  Physical Location 
026961 


Issued 
AP05: Prakash Arumugasamy 
18/May/2024 

 