Ordinary Differential Equations
Jinn-Liang Liu
Fall 1997
http://www.math.nctu.edu.tw/~jinnliu
Exam 3:
1. Hirsch & Smale (p. 198) Problem 3.
2. Hirsch & Smale (p. 199) Problem 7.
3. Beltrami (p. 58) Exercise 3.4.5.
4. Beltrami (p. 59) Exercise 3.4.8.
5. Beltrami (p. 79) Exercise 4.5.9.
6. Beltrami (p. 79) Exercise 4.5.10.
Textbooks
-
E. Beltrami (B), Mathematics for Dynamic Modeling, 1987,
Academic Press, Inc.
-
M. W. Hirsch and S. Smale (HS), Differential
Equations, Dynamical Systems and Linear Algebra, 1974, Academic
Press, Inc.
Syllabus
Models
Newton's Laws of Motion
The Struggle for Life
Conservation of Mass
The Pumping Heart
Mathematics
Existence, Uniqueness, Stability, Linearity, Nonlinearity
Equilibria, Limit Cycles, Bifurcation, Attractors, Chaos
Eigenvalues, Phase Plane, Liapunov Functions
Fundamental (Local and Global) Theorems of ODEs
Liapunov's Theorem, Poincare-Bendixon Theorem
Exams
Exam 1: 10/22/97, Exam 2: 12/3/97, Exam 3: 1/7/97
Grading Policy
Exam 1: 30%, Exam 2: 30%, Exam 3: 40%
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