Subject: MATHEMATICS II (A.A. 2024/2025)
Unit Matematica II
Mathematics, Information Technology and Physics (lesson)
The aim of the class is to introduce the differential and integral calculus for real functions of several variables
and to approach the solution of some standard differential problems.
- Differential calculus for real functions of real variables.
- Integral calculus for real functions of one real variable.
- First order linear differential equations.
- Preliminary notions of linear algebra.
- Elements of linear algebra.
- Linear systems.
- Eigenvalues and eigenvectors.
- First order (systems of) linear or nonlinear differential equations.
- Vector fields, integral along curves and potentials.
- Irrotational fields.
- Multiple integrals.
- Hints on the Schroedinger equation.
- Minima and maxima for two variables functions
- Lectures in the classroom, with illustration of the content chapters by means of a blackboard.
Examination: written and oral exam. The candidate must demonstrate a thorough knowledge of the course content, including frontal lessons and classroom activities.The verification is integral with respect to the course's content; it is also verified the student's ability to relate specific subject content with the knowledge listed as pre-requisite. The written exam lasts 2 hours in average. The oral exam consists in the correction of some of the exercises carried out in the written test and in the in-depth analysis of some topics treated during the course. The final score is expressed by averaging the evaluations received in the written and oral tests.
KNOWLEDGE AND COMPREHENSION
- knowledge of the basic techniques for the analysis of functions of multiple variables and the solution of
some standard differential problems.
CAPACITY TO APPLY KNOWLEDGE
- solve elementary mathematical problems choosing and applying the most suited mathematical technique;
CAPABILITY TO JUDGE
- Capability to individuate among different algorithms for the solution of a given mathematical problem according to the peculiarities and the structure of the data at disposal
- Discussion in classroom and preparation of final exam give the student communication capabilities and relational skills to argument the obtained results or discuss results presented by others.
Through the overall course activities the student:
- acquires capability to deepen using bibliography the acquired knowledge;
- is capable of retriving a suitable procedure by the analysis of appropriate sources on the web or reference textbooks.
L. Amerio – Analisi Matematica – Vol. 1 – UTET
C.D. Pagani, S. Salsa – Analisi Matematica – Vol. 2 – Masson
T.M. Apostol – Calcolo – Vol. 3 – Boringhieri
M. Bramanti, C.D. Pagani, S. Salsa – Matematica, Calcolo Infinitesimale e Algebra Lineare – Zanichelli
R. Eisberg, R. Resnick – Quantum Physics – Second edition – J. Wiley & Sons