MA 5210, Spring 04

Differentiable Manifolds
Lecturer: J. Wu
Tutors: J. Wu,
Office: S14, 04-07, Faculty of Science, Lower Kent Ridge Road.
Office Hours: By making appointment through e-mail.
e-mail: matwuj@nus.edu.sg
Phone: 6874-4940.
Text Books:
  1. Lang, Serge, Introduction to differentiable manifolds, Imprint New York , Interscience Publishers [1962]
  2. Victor Guillemin and Alan Pollack, Differential Topology, Prentice Hall, Inc, Englewood Cliffs, New Jersey [1974].
  3. Conlon, Lawrence, Differentiable manifolds : a first course / Lawrence Conlon, Birkh8auser , [1993].
  4. Milnor, J.W., Topology from the differentiable viewpoint, The University Press of Virginia, Charlottesville, 1990.
  5. Jänich, Klaus. Vector analysis / Klaus Jänich ; translated by Leslie Kay. Imprint New York : Springer, [c2001].
Topics
  1. Tangent Spaces, Vector Fields in Rn and the Inverse Mapping Theorem
  2. Topological Manifolds, Differentiable Manifolds, Diffeomorphisms, Immersions, Submersions and Submanifolds

    Examples of Manifolds

  3. Fibre Bundles and Vector Bundles
  4. Tangent Bundles and Vector Fields
  5. Cotangent Bundles and Tensor Fields, Tensor Algebras and Exterior Algebras, Orientation of Manifolds, Integration on Manifolds
  6. Stokes' Theorem, DeRham Cohomology
Lectures: Wed 10-12 S13-05-03; Sat 10-12 S13-05-03.
  • Everybody must attend all lectures and should arrive on time. In case you missed the class due to sick, then you should submit your MC to me. If you missed some classes without sufficient reasons, you might get negative credit to your grade from the course.
    • Exams
  • Final Exam:
    • Tutorials
  • Homework 1
  • Solutions , provided by Yeo Sze Ling
  • Homework 2
  • Homework 3
  • Homework 4
  • Solutions , provided by Sun Qiang
  • Homework 5
  • Solutions , provided by Lim Meng Fai
  • Homework 6
  • Solutions , provided by Tan Tony
    • Feedback on matters related to the course will be welcome. Please send it to
    matwuj@nus.edu.sg