Applied Differential Geometry: A Modern Introduction by Vladimir G Ivancevic (PDF)

Description

This graduate-level monographic textbook treats applied differential geometry from a modern scientific perspective. Co-authored by the originator of the world’s leading human motion simulator — “Human Biodynamics Engine”, a complex, 264-DOF bio-mechanical system, modeled by differential-geometric tools — this is the first book that combines modern differential geometry with a wide spectrum of applications, from modern mechanics and physics, via nonlinear control, to biology and human sciences. The book is designed for a two-semester course, which gives mathematicians a variety of applications for their theory and physicists, as well as other scientists and engineers, a strong theory underlying their models.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This is a treasure trove of differential geometry. This isn’t Eisenhart or do Carmo but takes you from there to the great beyond and I mean to the Far Plane to use the parlance of D&D. I have had this book for some years and by far has been my “Landau” of Differential Geometry. However unlike Landau, everything is brought together ab initio, which means from the beginning. He makes a lot of references to his previous tome, Natural Biodynamics, which is probably the most fleshed out, “let’s consider everything affecting the system,” realistic physics book on the human body, from macro to micro scales.His style is very good in terms of building the machinery needed for the chapter and actually providing applications. This isn’t reduced to Quantum Field Theory or Relativity, which are in the book no doubt. He also does some novel applications for control theory, biodynamics (modeling the brain anyone?), crowd dynamics (using Wheeler’s geometrodynamics), Lie-derivative neural modeling, Econophysics, Path Integrals over Geometries, etc. Heck we even have some results from applying Witten’s Topological QFT, Penrose’s Twistors, Loop Quantum Gravity, and String Theory all in one book.The best part is everything is guided from start to finish, results are extremely well cited, and the Bibliography is a depository of knowledge from just about anything on Differential Geometry (40 pages). This book may need a second edition given how things have changed in nearly 10 years for the physics applications but the tools remain the same (and many you wouldn’t even imagine applying to the problems given). My main interest is in Fluid dynamics and although it does have some applications (index derivation of Navier Stokes, ABC Flow geometry), would like to see more at the level of Arnold’s Topological Methods in Hydrodynamics and maybe even an excursion in Fluid/Gravity dualism.Should you take one thing from this review and have not been able to find or read this book somewhere, it is this statement from the preface:”Compared to all differential–geometric books published so far, Applied Differential Geometry: A Modern Introduction has much wider variety of both physical and non–physical applications. After comprehensive reading of this book, a reader should be able to both read and write journal papers in such diverse fields as superstring & topological quantum field theory, nonlinear dynamics & control, robotics, biomechanics, neurodynamics, psychodynamics and socio–economical dynamics.”Good luck, we’re all counting on you.

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