MAT 508E - Integration on Manifold

Course Objectives

1. To recall the basic definitions and theorems of manifold theory;
2. To introduce the orientations on manifolds;
3. To teach the concept of integration on n-dimensional real spaces;
4. To apply the concept of integration to chains and manifolds.

Course Description

Basic definitions: manifolds, charts, atlases, vector fields, tensors and forms. Orientation on manifolds. Inverse function theorem and implicit function theorem. Integration on n-dimensional real spaces. Integration on chains. Integration on manifolds.