中文摘要：

基于黎曼流形及次黎曼流形在控制论、动力系统、规范场论等领域中的广泛应用的事实，本文拟对作为研究生课程的《微分流形及其应用》给出研习该课程的一般方法和思路．作为一个应用，用微分流形的语式给出Hamilton—Jacobi—Equations表示式．

英文摘要：

The studies of differential manifolds and their applications are motivated to the active fields with applications of Riemanian manifolds and Sub-Riemannian manifolds in Control Theory, Dynamics Theory, Gauge Fields, etc. We here investigate the ideas and approaches of differential manifolds as a course for postgraduates, and give out the thought of trains with studying this subject. As a conclusion, we also obtain the well known Hamilton-Jacobi-Equations in differential manifold languages.