Symplectic geometry & classical mechanics, Lecture 1

For winter semester 2017-18 I am giving a course on symplectic geometry and classical mechanics. This course is intended for anyone with a familiarity with classical mechanics and basic differential geometry. Problem sheets will be made available on my blog (https://tjoresearchnotes.wordpress.com/), however solutions will not be distributed. Here in the first lecture, I introduce the basic definitions for locally euclidean spaces and manifolds.