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*  A geometric approach to problems in physics, many of which cannot be solved by any other methods

* Text is enriched with good examples and exercises at the end of every chapter

* Fine for a course or seminar directed at grad and adv. undergrad students interested in elliptic and hyperbolic differential equations, differential geometry, calculus of variations, quantum mechanics, and physics

Geometric Mechanics on Riemannian Manifolds: Applications to Partial Differential Equations

* Preface * Introductory Chapter * Laplace Operator on Riemannian Manifolds * Lagrangian Formalism on Riemannian Manifolds * Harmonic Maps from a Lagrangian Viewpoint * Conservation Theorems * Hamiltonian Formalism * Hamilton-Jacobi Theory * Minimal Hypersurfaces * Radially Symmetric Spaces * Fundamental Solutions for Heat Operators with Potentials * Fundamental Solutions for Elliptic Operators * Mechanical Curves * Bibliography * Index