Analysis on Manifolds

MA420 Spring 2001

Instructor: Gyo Taek Jin Office: 4404 Natural Science Bldg. Office hours: 10:30-11:30 am every Tuesday and Thursday Phone: 042-869-2724

Email: trefoil@kaist.ac.kr

Textbook: Differential Forms and Applications, Manfredo P. do Carmo, Springer-Verlag, 1994.

Lectures: 9:00–10:15 am every Tuesday and Thursday Room 3431 Natural Science Bldg.

Contents:

Chapter 1. Differential Forms in ℝ^{n} (2 weeks)

Chapter 2. Line Integrals (2 weeks)

Chapter 3. Differentiable Manifolds (2 weeks)

Chapter 4. Integration on Manifolds (3 weeks) §4.1. Integration of Differential Forms §4.2. Stokes Theorem §4.3. Poincaré’s Theorem

Chapter 5. Differential geometry of surfaces (3 weeks) §5.1. The Structure Equations of ℝ^{n} §5.2. Surfaces in ℝ^{3} §5.3. Intrinsic Geometry of Surfaces

Chapter 6. Gauss-Bonnet Theorem and Morse Theorem (2 weeks) §6.1. The Theorem of Gauss-Bonnet §6.2. The Theorem of Morse

Exams:

Midterm Exam (Chapters 1–3) Tuesday April 24, 9-11 am

Final Exam (Chapters 4–6) Tuesday June 19, 9-11 am

Grading: Homeworks 30%, Midterm exam 35%, Final exam 35%

Course URL: http://knot.kaist.ac.kr/~trefoil/courses/ma420/

(gtj2001/03/02)