• Differentiable Manifolds
    • Department of Mathematics
    • Credit. 3
    • MA401
    • Enroll
    • Fall , 2015
    • 2176
    • Course Description:
    • ( Exchange Programme )
    • Although the concept of “manifold” comes from geometry, it is used in many other areas of mathematics, such as dynamical systems, harmonic analysis, and differential topology. This course is an elementary introduction to the theory of differentiable manifolds. Topics to be covered include (but not limited to): topological manifolds, definition and examples of differentiable manifolds, submanifolds, vector fields on manifolds, basics of Lie groups and Lie algebra, tensor fields and exterior differentiation, basics of differential forms, integration on manifolds, manifolds with boundary and Stokes’s theorem.
    • Course Syllabus:
    • Students are expected to gain the basic knowledge of the fundamental theory of differentiable manifolds.
    • Schedule:
    • Topics/ Credit hours / Teaching methodology / Tasks / Intended learning outcomes / Assessment methods

      1.Introduction, I.1-I.3/3 Credit hours /lecture/homework
      2.I.4-I.5/3 Credit hours /lecture/homework
      3.Chapter II (only brief review of calculus)/3 Credit hours /lecture/homework
      4.III.1-III.2/3 Credit hours /lecture/homework
      5.III.3-III.7/3 Credit hours /lecture/homework
      6.III.8-III.9/3 Credit hours /lecture/homework
      7.IV.1-IV.4/3 Credit hours /lecture/homework
      8.IV.5-IV.6/3 Credit hours /lecture/homework
      9.IV.7-IV.9/3 Credit hours /lecture/homework
      10.V.1-V.2/3 Credit hours /lecture/homework
      11.V.3-V.6/3 Credit hours /lecture/homework
      12.V.7-V.8/3 Credit hours /lecture/homework
      13.VI.1-VI.4/3 Credit hours /lecture/homework
      14.VI.5/3 Credit hours /lecture/homework
      15.VI.6-VI.9/3 Credit hours /lecture/homework
      16.Wrap up, final review/3 Credit hours /lecture/homework/final
  • Reading list
  • Other Materials
  • Discussion
  • Homework download/submit
    • Rong Feng
    • Associate Professor
    • Read more
    • Male
    • E-mail:
    • frong@sjtu.edu.cn
    • Profile
    • I am currently a Special Researcher in the Department of Mathematics at Shanghai Jiao Tong University. I obtained my Ph.D. degree from University of Michigan in 2007. After completing a postdoc position at Syracuse University, I joined SJTU in 2009. My research interests are in Several Complex Variables, Complex Dynamics, Complex Geometry, etc.
  • Prerequisite Course:

    Mathematical Analysis, Linear Algebra, Point-Set Topology

  • Textbooks:

    “An Introduction to Differentiable Manifolds and Riemannian Geometry”, by William M. Boothby
  • Grading:

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