Sumários

Dynamic optimisation

27 Novembro 2012, 21:00 • Paulo Brito

Introduction: syllabus of the course, general presentation, references

Dynamic optimization in discrete time: calculus of variations

Nonlinear planra

23 Novembro 2012, 18:00 • GIANLUIGI DEL MAGNO

  1. More on phase portrait of general linear differential equations
  2. Planar nonlinear differential equations
  3. Stability 
  4. Local analysis of nonlinear differential equations
  5. Examples


Jordan Decomposition Theorem

20 Novembro 2012, 21:00 • GIANLUIGI DEL MAGNO


  1. Change of coordinates
  2. Jordan decomposition theorem
  3. Stability
  4. Phase portrait of general planar linear differential equations


Planar differential equations

16 Novembro 2012, 18:00 • GIANLUIGI DEL MAGNO

  1. General definitions
  2. Linear equations (with constant coefficients)
  3. Exponential matrix
  4. Computation of the exponential matrix for the Jordan Normal forms
  5. Phsse portrait of some linear equations


Scalar differential equations

13 Novembro 2012, 21:00 • GIANLUIGI DEL MAGNO

  1. Existence and uniquenss of solutions
  2. Equilibrium points and stability
  3. Phase portrait analysis
  4. Examples