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 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.
✔ Author(s): Tristan Needham
✔ Title: Visual Differential Geometry and Forms: A Mathematical Drama in Five Acts
✔ Rating : 4.7 out of 5 base on (295 reviews)
✔ ISBN-10: 0691203709
✔ ISBN-13: 9780691203706
✔ Language: English
✔ Format ebook: PDF, EPUB, Kindle, Audio, HTML and MOBI
✔ Device compatibles: Android, iOS, PC and Amazon Kindle
Readers' opinions about Visual Differential Geometry and Forms by Tristan Needham
Sarah Franklin
The world-building in this book was simply phenomenal. I was transported to a different realm and felt like I was part of the characters' journey. The attention to detail made it all so immersive.
Laura Hill
The author's writing style is so captivating; I couldn't put the book down. Every sentence was beautifully crafted, and the descriptions painted vivid images in my mind. A true literary gem.
Violet Tyler
The author's ability to evoke a wide range of emotions through their words is truly remarkable. I felt like I was on an emotional rollercoaster throughout the entire book.
![Ultimate Apocrypha Collection [Volume I: Old Testament]: A Complete Collection Of The Apocrypha, Pseudepigrapha & Deuterocanonical Books of the Bible thumb](https://i1.wp.com/us.shortlinks.top/1544216491_500.jpg)
