Last friday (21/4) I started ¡­

Last friday (21/4) I started the lecture showing that the version of Stokes Theorem that you (probably) know from the vector calculus (where M is a smooth surface with boundary in three space) can be derived from the general version of Stokes Theorem given in this course. I then gave some applications of Stokes Theorem (5.4.2, 5.4.3 and 5.4.4 in Barden and Thomas). Then I started on 6.1 and defined de Rham cohomology for a manifold, and I proved Prop 6.1.2., formulated Theorem 6.1.3 and then jumped back to section 5.5 which I need for the proof of 6.1.3. I proved 5.5.1 and I will start on 5.5.2 today,and then finish section 5.5, 6.2 and (hopefully) 6.3.