Visual differential geometry and forms: a mathematical drama in five acts
Publication details: Princeton Press University, 2021. New Jersey:Description: xxviii, 501p. : ill. ; pb. ; 25cmISBN:- 9780691203706
- 516.36 NEE
Item type | Current library | Collection | Call number | Copy number | Status | Date due | Barcode |
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Books | IIT Gandhinagar General Stacks | General | 516.36 NEE (Browse shelf(Opens below)) | 1 | Available | 030736 |
Browsing IIT Gandhinagar shelves, Shelving location: General Stacks, Collection: General Close shelf browser (Hides shelf browser)
516.36 CAR Differential geometry of curves and surfaces | 516.36 GRA Modern differential geometry of curves and surfaces with mathematica | 516.36 HEL Radon transform | 516.36 NEE Visual differential geometry and forms: a mathematical drama in five acts | 516.36 PRE Elementary differential geometry | 516.36 PRE Elementary differential geometry | 516.36 SHA Introductory course on differentiable manifolds |
Includes references and index
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
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