There exists a sequence of rectangles, Ri, i = 0, ..., N + 1 such that R0 = Q0, RN+1 = Q and Int Ri -intersect- Int Ri+1 is non-empty. (Figure by Prof. Victor Guillemin.)
This course continues from Analysis I (18.100B
), in the direction of manifolds and global analysis. The first half of the course covers multivariable calculus. The rest of the course covers the theory of differential forms in n-dimensional vector spaces and manifolds.