Geometric Mechanics on Riemannian Manifolds: Applications to Partial Differential EquationsDifferential geometry techniques have very useful and important applications in partial differential equations and quantum mechanics. This work presents a purely geometric treatment of problems in physics involving quantum harmonic oscillators, quartic oscillators, minimal surfaces, and Schrdinger's, Einstein's and Newton's equations. Geometric Mechanics on Riemannian Manifolds is a fine text for a course or seminar directed at graduate and advanced