20/1: I defined smooth manifolds, ¡­

20/1: I defined smooth manifolds, gave examples of such manifolds and defined and gave examples of smooth maps between smooth manifolds. The lecture covered more or less the material in the textbook up to 1.3.

27/1: I reviewed the Inverse Fuction Theorem, proved the Submersion and Implicit Function Theorem (1.3.1, 1.3.2 and 1.3.3). I defined a smooth submanifold of smooth manifold and showed that the inverse image of a regular value (for some smooth map) is a smooth submanifold. I gave examples of smooth submanifolds of Euclidean spaces of this kind. The lecture covered the material of section 1.3 in the textbook up to 1.3.10 (which will be the starting point of the next lecture).