Course Language:

English

Course Objectives:

To teach the theory of exterior differential forms and integration on smooth manifolds.

Course Content:

Functions on Euclidean spaces. Differentiation. Inverse and implicit function theorems. Integration. Partitions of unity. Sard's theorem. Multilinear functions, tensors, fields and differential forms. Poincare lemma. Chains and integration over chains. Stokes' theorem. Differentiable manifolds. Fields and forms on manifolds. Orientation and volume. Applications.

Course Methodology:

1: Lecture, 2: Problem Solving, 3:Question-answer, 4: Homework

Course Evaluation Methods:

A: Written examination, B: Homework