1. Introduction to Ordinary Differential Equations (ODEs) of first order. Separable differential equations.
2. Homogeneous ODEs, linear and exact equations – Euler integrating factor, variable transformations.
3. Problems – Applications of first-order differential equations.
4. Higher-order differential equations – Reduction of order – Applications.
5. Linear differential equations – The vector space of solutions, solving linear ODEs with constant coefficients – Exercises.
6. Applications to oscillators (solutions of damped oscillations and resonance) – Problems.
7. Systems of 2×2 linear differential equations with constant coefficients – General solution.
8. Exercises on systems of 2×2 linear differential equations with constant coefficients – Linear systems of higher dimension.
9. Introduction to nonlinear systems – Phase space, integrals, and flow lines.
10. Introduction to Partial Differential Equations (PDEs) – General solution of first-order linear PDEs.
11. Particular solutions of first-order linear PDEs – Special forms of homogeneous higher-order linear PDEs.
12. Problems involving second-order PDEs. Higher-order nonhomogeneous linear PDEs.