Introduction to Differential Geometry with applications to Navier-Stokes Dynamics

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.

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.