INTRODUCTION TO DIFFERENTIAL GEOMETRY WITH APPLICATIONS TO NAVIER-STOKES DYNAMICS 0th Edition by Troy Story (PDF)

Description

Introduction to Differential Geometry with applications to Navier-Stokes Dynamics is an invaluable manuscript for anyone who wants to understand and use exterior calculus and differential geometry, the modern approach to calculus and geometry.Author Troy Story makes use of over thirty years of research experience to provide a smooth transition from conventional calculus to exterior calculus and differential geometry, assuming only a knowledge of conventional calculus. Introduction to Differential Geometry with applications to Navier-Stokes Dynamics includes the topics:Geometry, Exterior calculus,Homology and co-homology,Applications of differential geometry and exterior calculus to: Hamiltonian mechanics, geometric optics, irreversible thermodynamics, black hole dynamics, electromagnetism, classical string fields, and Navier-Stokes dynamics.

User’s Reviews

Editorial Reviews: About the Author Troy Story received his undergraduate degree from Morehouse College and his doctorate degree from the University of California at Berkeley (LBNL). He was a postdoctoral fellow and staff member at the UC Space Sciences Laboratory, and a postdoctoral fellow at Chalmers University of Technology (Sweden). His most notable publication prior to 2001 is the use of differential geometry to develop a mathematical model for irreversible thermodynamics (1988), one of four research manuscripts included in his previous book Dynamics on differential one-forms. The mathematical model for irreversible thermodynamics was generalized in 2002 , resulting in a unifying model embracing Hamiltonian mechanics, geometric optics, irreversible thermodynamics and the dynamics of black holes, electromagnetism, and classical strings. At the Mathematical Sciences Research Institute at Berkeley (2003), he applied the unified model to obtain a solution to the Navier-Stokes equation.

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

⭐Refering to this book as an introduction to anything is insane. Definitions occur rarely and invariably use terms which are themselves undefined. While it is reasonable for the author of a book on differentiable geometry to not define the derivative of real valued function of a single real variable, or a jacobian matrix, a notion such as a metric tensor should be fully defined.This book lacks any pretense of rigour (I do not recall seeing the word proof once!). This alone is not a damning feature but it is also lacking in tools to develop intuition as well. Do not expect to be able to prove or compute anything after reading this book. I got the e-book version and it is the worst 6 dollars I have ever spent.

⭐This book has the clearest and most direct introduction to differential geometry that I’ve seen, thus, I highly recommend it.One of the book’s highlights is chapter 2, which presents a discussion of exterior calculus assuming only a knowledge of conventional calculus. Unlike most books on this topic(exterior calculus), this book includes a definition of the exterior derivative rather than a few examples.Another highlight is the chapter on dynamics, where it is shown that many areas of dynamics can be described by differential one-forms, including Navier-Stokes dynamics for incompressible fluids.

⭐Beginning with a definiton of Euclidean geometry, this book presents a logical and rigorous introduction to differential geometry and exterior calculus. Rather than using the style of of writing theorems followed by proofs or sketches of proofs, the writer displays fundamental definitions followed by examples and a chapter on applications to dynamics. In contrast to one of the reviewers, my purchase of this book is an excellent investment.

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