I.Contents：
1. Introductions: Some basic Mathematical models,Historical remarks;
2. First order differential equations: Method of integrating factors, Separable equations,Autonomous equations,etc.;
3. Second order linear equarions:Equations with constant coefficients, Wronskian,Complex roots of the characteristic equations, Mechanical and electrical vibrations,etc.;
4. Higher order linear equations;
5. Series solutions of second order linear equations ;
6. Laplace transform ;
7. Systems of first order linear equations.
II.Course prerequisite：
Freshman Calculus
III.Reference material ( textbook(s) )：
Text book: W. E. Boyce and R.C. Diprima, `Elementary Differential Equations and Boundary Value Problems`, 8 th ed. ,Wiley 2005.
IV.Grading scheme：
Home work 10%, Midterm Exam40%,Final Exam 50%.