| Lectures and exercises |
hours |
| Topics |
Specific contents |
|
| Foundations of functional analysis |
Metric spaces; contractions and fixed point theorems, their use in numerical analysis. Normed spaces and Banach spaces. Hilbert spaces. Fourier series. Norm of operators. |
10
|
| Differential equations |
Introduction to systems of differential equations. Numerical methods for ordinary differential equations and systems. Fundamentals of transforms |
8
|
| Complements of Analysis |
Links with linear algebra; Dini’s theorem on implicit functions and its applications, use of Lagrange multipliers. Convex functions and Kuhn-Tucker theorem. Envelopes. |
8
|
| Integration in many variables |
Measure. Integration with respect to a measure. Reduction methods. Change of variables |
6
|
| Integration on Varieties |
Geometric measures. Integration with respect to geometric measures. Oriented integrals of work and of flow and related theorems |
8
|
| Total hours for lectures and exercises |
40 |
| for exercises only |
10 |
|
Further educational activities
|
hours
|
| Labs |
10 |
| Tutorials / Seminars |
|
| Workshops |
|
| Guided tours |
|
| |
|
| Total hours for further educational activities |
10 |
| Total hours |
50
|