Programme Intensive Reminder (for Analysis on Manifolds)

Announcements:
  • The final meeting, on Friday 18/9 has been rescheduled to the morning.
  • The material for all subjects of the first two lectures can be found in the lecture notes [1],[2],[3] and in the books by S. Lang and F. Warner.

    • Fall semester 2009

     
  • Meeting 1: Thursday 10 September, 13:00 -16:00 Wentgebouw, room OC 109
  • Teacher: Erik van den Ban
  • Manifolds, smooth maps, examples
  • tangent vectors, vector fields, vector bundles.

  • Meeting 2: Friday 11 September, 10:00 - 13:00 Buys Ballot Lab, 513
  • Teacher: Erik van den Ban
  • Inverse function theorem, immersions, submersions
  • several characterizations of submanifolds

  • Meeting 3: Monday 14 September, 10:00- 13:00, BBL 415
  • Teacher: Marius Crainic
  • differential forms, de Rham cohomology
  • integration, densities

  • Meeting 4: Wednesday 16 September, 10:00 - 13:00 Minnaert, 208
  • Teacher: Marius Crainic
  • Banach spaces, Hilbert spaces, ex: L^2
  • Compact operators, Fredholm operators

  • Meeting 5: Friday 18 September, 10:00 - 13:00, Buys Ballot, 513
  • Teacher: Marius Crainic
  • Locally convex vector spaces, Schwartz space
  • Fourier transform.

    • Literature

    The following literature will be available in the mathematics library, just for consultance, not for take out.

  • Lang, Serge. Differential Manifolds. Addison-Wesley Publishing Company, 1972.
  • Warner, Frank W. Foundations of differentiable manifolds and Lie groups.
    Corrected reprint of the 1971 edition. Graduate Texts in Mathematics, 94. Springer-Verlag, New York-Berlin, 1983. ix+272 pp. ISBN: 0-387-90894-3
  • F. Treves, "Topological vector spaces, distributions and kernels", Academic Press, New York-London 1967 xvi+624 pp.
  • L. Schwarz, "Functional Analysis", Courant Institute of Mathematical Sciences, 1964
  • Ho"rmander, Lars. The analysis of linear partial differential operators. I. Distribution theory and Fourier analysis.
    Reprint of the second (1990) edition. Classics in Mathematics. Springer-Verlag, Berlin, 2003. x+440 pp. ISBN: 3-540-00662-1 35-02
  • Ho"rmander, Lars. Linear partial differential operators.
    Springer Verlag, Berlin-New York, 1976. vii+285 pp. 35-XX (46FXX)

    • Suggested lecture notes

  • [1] Prerequisites from differential geometry (E.P. van den Ban)
  • [2] Lie derivatives, tensors and forms (E.P. van den Ban)
  • [3]