- Docente: Pier Luigi Papini
- Credits: 9
- Language: Italian
- Moduli: Pier Luigi Papini (Modulo 1) Pier Luigi Papini (Modulo 2)
- Teaching Mode: Traditional lectures (Modulo 1) Traditional lectures (Modulo 2)
- Campus: Bologna
- Corso: First cycle degree programme (L) in Civil Engineering (cod. 0919)
Learning outcomes
At the end, after passing the final exam, the student should know basic notions concerning functions of more variables (properties, differentiability, maxima and minima), curves, potentials, multiple integrals, their meaning; solving some simple types of differental equations. Moreover, the student should know elementary probability, with special emphasis on some continuous distributions (like uniforn and normal).
Course contents
Real functions of n real variables; continuity; derivatives; differentiation. Taylors formula.
Maxima and minima, free and constrained (Lagrange multipliers).
Curves; regular curves; length. Integrals along a curve.
Differential forms; primitives.
Differential equations: 1st order equations; separation of variables.
Linear differential equations of order n: solution set. Case of constant coefficients.
Multiple integrals; reduction. Measure. Applications.
Elements of probability theory (discrete and continuous case). Mean value, variance.
Some particular distributions.
Readings/Bibliography
Reference book: M. Bertsch, R. Dal Passo, L. Giacomelli - Elementi di Analisi Matematica, ed. McGraw Hill (2007).
Notes concerning probability will be distributed.
Teaching methods
During the course theory will always be integrated by exercises.
Assessment methods
Final exam will consist of a written proof, followed by a short oral proof.
Office hours
See the website of Pier Luigi Papini