Yves Talpaert

Differtial Geometry with Application to Mechanics and Physics

Lecture 1 Manifolds

Lecture 2 Tangent Vector Space

Lecture 3 Tangent Bundle

Lecture 4 Cotangent Bundle

Lecture 5 Exterior Differential Forms

Lecture 6 Lie derivatives Lie groups

Lecture 7 Intagration of Forms

Lecture 8 Riemannian Geometry

Lecture 9 Lagrange and Hamilton Mechanics

Lecture 10 Symplectic Geometry--Hamilton Gacobi Mechanics