A First Course In Differential Geometry Woodward
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A First Course in Differential Geometry
Author: Lyndon Woodward
language: en
Publisher: Cambridge University Press
Release Date: 2019
With detailed explanations and numerous examples, this textbook covers the differential geometry of surfaces in Euclidean space.
Visual Complex Analysis
This new 25th anniversary edition of Visual Complex Analysis introduces this powerful method combining complex numbers with ordinary calculus, and includes new introductory content and brand-new captions that fully explain the geometrical reasoning.
Visual Differential Geometry and Forms
Author: Tristan Needham
language: en
Publisher: Princeton University Press
Release Date: 2021-07-13
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.