Lecture Notes for Math 524
Dr. Michael Y. Li
October 17, 2011
These notes are based on the lecture notes of Professor James S. Muldowney, the books of Hale,
Copple, Coddington and Levinson, and Perko. They are for the use of students in my graduate
ODE cl
-While the Lie derivative is an intrinsic notion depending only on the
differentiable structure, a connection is an additional piece of geometric
structure.
-A geometric meaning of giving a connection on a manifold is that it allows
us to talk of parallel
-So for an orthonormal frame field, the E1(p), . . . , En(p) form
anorthonormal basis of the tangent space TMp at each point p in the
domain of definition of the frame field. The dual basis of the cotangent
space then provides a family of linear different
-Suppose that M is a semi-Riemannian manifold, meaning that we are
given a smoothly varying non-degenerate scalar product h , ix on each
tangent space TMx Given two vector fields X and Y , we let hX, Y i denote
the function
hX, Y i(x) := hX(x), Y (x)ix .
Lecture Notes for Math 524
Dr. Michael Y. Li
December 7, 2004
These notes are based on the lecture notes of Professor James S. Muldowney, the books of Hale,
Copple, Coddington and Levinson, and Perko. They are for the use of students in my graduate
ODE cl
Lecture Notes for Math 524
Dr. Michael Y. Li
March 30, 2005
These notes are based on the lecture notes of Professor James S. Muldowney, the books of Hale,
Copple, Coddington and Levinson, and Perko. They are for the use of students in my graduate
ODE clas
Lecture Notes for Math 524
Dr. Michael Y. Li
September 8, 2014
These notes are based on the lecture notes of Professor James S. Muldowney, the books of Hale,
Copple, Coddington and Levinson, and Perko. They are for the use of students in my graduate
ODE c
Lecture Notes for Math 524
Dr. Michael Y. Li
October 27, 2004
These notes are based on the lecture notes of Professor James S. Muldowney, the books of Hale,
Copple, Coddington and Levinson, and Perko. They are for the use of students in my graduate
ODE cl
-Suppose that, during an epidemic, you know the rate at which new cases
of a disease are appearing and you want to predict the how many new
cases there will be at some future time.
-The problem is to find a function F whose derivative is a known function