國立清華大學數學系
變分法專題
Math 7100-00
(Fall
2006) Topics
on Calculus of Variations
General
Information
Hours and Days: W6W7W8 (i.e.
Classroom: 綜三 530
Instructor: 陳 國 璋
Office: 綜三 609
Office Hours: T5T6W4, or by appointments
Phone Number: (03) 5715131 Ext: 33067
Email: kchen@math.nthu.edu.tw
Prerequisite: Ordinary Differential Equations, Real Analysis
Reference:
Most
of the course materials are not available on books. A list of research papers
as suggested readings will be dispensed in class. Some other useful readings
are:
V.Arnold: Mathematical Methods of Classical Mechanics, Springer,
1989.
C.Siegel; J.Moser: Lectures on Celestial
Mechanics, Springer, 1971.
J.Jost; X.Li-Jost: Calculus of Variations,
A.Katok; B.Hasselblatt: Introduction to the
Modern Theory of Dynamical Systems,
K.Siburg: The Principle of Least Action in Geometry and Dynamics,
Springer, 2004.
Course
Description:
This course is research oriented; many research
problems will be suggested in classes. The course consists
of lectures on variational calculus with applications
to selected topics on Hamiltonian dynamical systems. We will emphasize
particularly on applications to the classical N-body problem. If time permits, we will
also discuss applications of variational calculus to monotone twist maps.
Those who intended to take this course should have some background on ordinary
differential equations and real analysis. Apart from that, I will try to make
this course as self-contained as possible; no prerequisite knowledge in
calculus of variations or dynamical systems is required.
Grading
Oral
presentation (40%) and Written report (60%).