What if you could actually see differential geometry rather than just memorizing formulas? Visual Differential Geometry and Forms transforms abstract mathematical concepts into tangible, visual understanding through 235 hand-drawn diagrams that make learning feel less like work and more like discovery.
The first four acts of this mathematical drama restore geometry to its rightful place in differential geometry. Needham deploys Newton's classical geometrical methods to provide stunning visual explanations of fundamental results that are typically presented in purely algebraic form. You'll discover four distinct geometrical proofs of the Global Gauss-Bonnet theorem, revealing the beautiful connection between local geometry and global topology.
Ever wondered how Einstein's field equations describe gravity as curved spacetime? This book makes it clear. You'll find geometrical treatments of the Riemann curvature tensor, Einstein's field equations with implications for gravitational waves and black holes, and much more—all explained through visual intuition rather than abstract notation.
The final act offers something truly unique: the first undergraduate introduction to differential forms that treats advanced topics in an intuitive, geometrical manner. You'll explore the unification of vector calculus theorems, Maxwell's equations reformulated using 2-forms, and even Cartan's method of moving frames—presented in a way that actually makes sense.
Requiring only basic calculus and geometry, this provocative rethinking of how differential geometry should be taught makes advanced mathematics accessible without sacrificing depth. Six of the seven chapters in the final act can be read independently, making it easy to jump to topics that interest you most.
This Kindle edition is presented in Print Replica Format, faithfully reproducing the author's hundreds of hand drawings exactly as intended—crisp, clear, and visually engaging. It's mathematics as you've never experienced it before.
