Ordinary Differential Equations
- Lectures: Mondays and Thursdays: 14:00-15:25, Room 114
- Tutorials: Thursdays: 11:35-11:30, Room 114
Course
Outline
- First order equations, Finding explicit solutions, Qualitative
analysis of first-order equations.
- Initial value problems, Existence and
uniqueness results.
- Linear ODEs, Solving systems of linear ODEs using matrix exponentials,
Asymptotic behaviour of solutions.
- Analysis of equilibrium points, Stability of equilibrium points,
Lyapunov’s theorems.
- Boundary value problems, Sturm-Liouville theory.
Texts
and References
- G. Teschl, Ordinary differential equations and dynamical systems,
Graduate Studies of Mathematics, vol. 140, American Mathematical
Society, 2012. An online edition is made available by the author in
his homepage. This will be our main text.
- M. E. Taylor, Introduction to differential equations,Second edition,
Pure Appl. Undergrad. Texts, 52 American Mathematical Society, 2022. Notes are made available by the author in his
homepage.
- W. Walter, Ordinary Differential Equations, Springer, 1998.
- M.W. Hirsch, S. Smale, and R.L. Devaney, Differential equations,
dynamical systems, and an introduction to chaos, 2nd edition,
Elsevier/Academic Press, 2004.
- E.A. Coddington and N. Levinson, Theory of Ordinary Differential
Equations, McGraw-Hill, 1955.
- G. Birkhoff, and G.C. Rota, Ordinary differential equations, 4th
edition, Wiley,1989.
Evaluation
Plan
- Final grade: Homework(20) + Mid-Semester Exam(30) + Final
Exam(50)
- To pass the course (DD), one needs to score at least 35% in the
course. The Final exam will cover the entire course.