SYLLABUS AND NOTES

• Syllabus
• 1. Separable ODE
• 2. First-order linear ODE
• 3. Existence and uniqueness
• 4. First-order systems
• 5. Linear homogeneous systems
• 6. Exponential of a matrix
• 7. Exponentials: some examples
• 8. Homogeneous with constant coefficients
• 9. Method of undetermined coefficients
• 10. Variation of parameters
• 11. Reduction of order
• 12. Stability of linear systems
• 13. Lyapunov stability
• 14. Stability of nonlinear systems

FINAL EXAMS AND SOLUTIONS