Tristan Needham Knihy

The book emphasizes the geometric foundations of differential geometry through 235 hand-drawn diagrams and Newton's methods. It presents four distinct geometrical proofs of the Global Gauss-Bonnet theorem, a straightforward proof of Gauss's Theorema Egregium, and a thorough examination of the Riemann curvature tensor. Additionally, it explores Einstein's field equation in the context of General Relativity. The final act introduces advanced topics like vector calculus integral theorems and Maxwell's equations reformulated with 2-forms, allowing readers to engage with its chapters independently.

FROM THE  Please do NOT buy this original 1997 edition!  I have created a new, greatly improved (and cheaper!) edition, which was published on February 28th, 2023:Visual Complex 25th Anniversary Edition (with a new Foreword by Roger Penrose)**************************************************************************************************This radical first course on complex analysis brings a beautiful and powerful subject to life by consistently using geometry (not calculation) as the means of explanation. Aimed at undergraduate students in mathematics, physics, and engineering, the book's intuitive explanations, lack of advanced prerequisites, and consciously user-friendly prose style will help students to master the subject more readily than was previously possible. The key to this is the book's use of new geometric arguments in place of the standard calculational ones. These geometric arguments are communicated with the aid of hundreds of diagrams of a standard seldom encountered in mathematical works. A new approach to a classical topic, this work will be of interest to students in mathematics, physics, and engineering, as well as to professionals in these fields.