Theory Programme
1. Prerequisites
2. Basic concepts
3. Cauchy problem on local domains: existence of solution
4. Unicity
5. Solution prolongability
6. Vectorial linear differential equations of first order.
7. Vectorial linear differential equations of first order, with constant coefficients.
8. Scalar differential equations of n-order.
9. Scalar differential equations of n-order and constant coefficients.
10. Continuity of the solution with respect to initial conditions and parameters.
11. Solution differenciability with respect to initial conditions initials and parameters.
12. Stability.
Practical Programme
1. Elementary methods for resolution of scalar equations. Detachable variable equations. Variable changes. Homogeneous equations. Equations reducible to homogeneous. Exact differential equations. Integrator factor. Resolution of a differential equation by means of obtaining an integrator factor in particular cases. First order linear equation. Bernouilli equation. Ricatti equation. Soluble equations in x. Soluble equations in y: Equation of Lagrange and Equation of Clairaut. Order reduction. Examples of equations without solutions that can be expressed by means of elementary functions. Study of the properties of the Cauchy problem solution without solving the respective equation.
2. Linear differential equations. Vectorial equatio
