Math 396, Winter 2010. Honors Analysis II
NOTE. All homework and midterm solutions have been temporarily removed. They will be
returned to this website once I am done teaching the Math 395/396 sequence in 2010-2011.

My office is 4859 East Hall, and my office hours are Tuesdays, 5pm-6pm; Wednesdays, 2pm-4pm; and by appointment.
The class meets on Mondays, Tuesdays, Wednesdays and Fridays, 11am-12pm, in room 205 of the David M. Dennison Building.

Syllabus in PDF
Final grade policies in PDF
Final Exam

The final exam in PDF
Midterm

Take-home midterm in PDF
Midterm solutions in PDF
Homeworks

Homework 1 (due Friday, January 15, at the beginning of class) in PDF
Solutions to Homework 1 in PDF
Homework 2 (due Friday, January 22, at the beginning of class) in PDF
Solutions to Homework 2 in PDF
Homework 3 (due Friday, January 29, at the beginning of class) in PDF
Solutions to Homework 3 in PDF
Homework 4 (due Friday, February 5, at the beginning of class) in PDF
Homework 5 (due Friday, February 12, at the beginning of class) in PDF
Homework 6 (due Friday, February 19, at the beginning of class) in PDF
Solutions to Homework 6 in PDF
Homework 7 (due Friday, February 26, at the beginning of class) in PDF
Solutions to Homework 7 in PDF
Homework 8 (due Friday, March 19, at the beginning of class) in PDF
Homework 9 (due Friday, March 26, at the beginning of class) in PDF
Homework 10 (due Friday, April 9, at the beginning of class) in PDF
Homework 11 (due Tuesday, April 20, at the beginning of class) in PDF





Lecture summaries (arranged by week)
  1. Introduction to manifolds (week of January 4)
    Notes on the definition of a manifold in PDF
     
  2. Manifolds and tangent spaces (week of January 11)
    • Notes on atlases and the second (equivalent) definition of a smooth manifold in PDF
    • Notes on tangent spaces to smooth manifolds in PDF
       
  3. Introduction to submanifolds of smooth manifolds (week of January 18)
    See below for lecture notes on submanifolds
     
  4. The Hopf fibration (week of January 25)
    Notes on the Hopf fibration in PDF
     
  5. Immersed submanifolds of smooth manifolds (week of February 1)
    Notes on submanifolds in PDF
     
  6. Vector fields and their flows (week of February 8)
     
  7. Introduction to differential forms and integration (week of February 15)
    • The Fundamental Theorem of Calculus as a special case of Stokes' Theorem
    • Differential forms on the line and on the plane
    • Green's theorem in the plane: an ad hoc approach
     
  8. Orientable manifolds and differential forms (week of February 22)
    • Orientable and oriented manifolds in PDF
    • Differential forms on smooth manifolds in PDF
       
  9. Spring break (week of March 1)
     
  10. Differential forms; manifolds with boundary; Stokes' theorem (week of March 8)
    • Manifolds with boundary and Stokes' theorem in PDF
       
  11. De Rham cohomology of manifolds (week of March 15)
    Notes on de Rham cohomology in PDF
    (Appearing here by courtesy of Viknesh Krishnan)
     
  12. The fundamental group and the first de Rham cohomology of a manifold (week of March 21)
    See the notes on de Rham cohomology (above).
     
  13. Introduction to surfaces (week of March 28)
  14. Smooth surfaces and Riemann surfaces (week of April 5)
  15. Riemann surfaces and Riemannian manifolds (week of April 12)
    The current version of the notes on surfaces can be found here