Ordinary Differential Equation is a basic language to describe physical world. For instances, population dynamics in biology, mechanics, electric circuits, chemical reactions, ..., are modeled in terms of single or systems of ordinary differential equations. This course is an entry level course. I plan to give an introduction to mathematical modelings of above systems and a standard theory of the ordinary differential equations. Its contents are useful for students in sciences and engineering.
Contents and schedule:
1.Introduction and First Order Differential Equations
2.Second Order Linear Euations (linear oscillators)
The First Exam
3 Linear systems with constant coefficients
4. The Laplace Transform
The second Exam
5. Nonlinear oscillators
6. Nonlinear systems in 2 dimensions
7. Existence and Uniwueness Theorem
The Third Exam