The course aims to recall some basic notions on linear algebra and functions of several variables; moreover, it aims to give some essential knowledge on unconstrained and equality/inequality constrained optimization and an introduction to differential equations and systems of differential equations.
Module 1 (prof. L. Pellegrini)
Fundamental notions
A refresh on linear algebra.
Vector spaces and subspaces.
Systems of linear equations.
Linear transformations.
Functions of several variables
Calculus of functions of several variables.
Quadratic forms and definite matrices.
Convex functions and generalized convexity.
Optimization
Unconstrained optimization.
Constrained optimization with equality constraints.
Lagrangian function and optimality conditions.
Constrained optimization with inequality constraints.
Kuhn-Tucker theorem.
Constraints Qualification.
Module 2 (prof. A. Peretti)
Differential equations
A refresh on indefinite integrals and integration techniques.
Ordinary differential equations. Some general aspects.
Linear 1st order differential equations.
Separable differential equations.
Linear 2nd order differential equations. The non homogeneous case.
Systems of differential equations.
Solution of a system through diagonalization.
| Reference books | |||||
| Author | Title | Publisher | Year | ISBN | Note |
| R.K. SUNDARAM | A first course in Optimization Theory | Cambridge ; New York : Cambridge University Press | 1996 | 978-0-521-49770-1 | |
| C.P. SIMON, L.E. BLUME | Mathematics for Economists | New York, London: Norton & Company Press, Cambridge | 1994 | 0-393-95733-0 | |
Written and oral exam
