Sciences
Subject: MATHEMATICS II (A.A. 2024/2025)
degree course in CHEMISTRY
Course year  2 

CFU  6 
Teaching units 
Unit Matematica II
Mathematics, Information Technology and Physics (lesson)

Exam type  oral 
Evaluation  final vote 
Teaching language  Italiano 
Overview
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.
Admission requirements
 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.
Course contents
 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.
 Eigenfunctions.
 Hints on the Schroedinger equation.
 Minima and maxima for two variables functions
Teaching methods
 Lectures in the classroom, with illustration of the content chapters by means of a blackboard.
Assessment methods
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 prerequisite. 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 indepth analysis of some topics treated during the course. The final score is expressed by averaging the evaluations received in the written and oral tests.
Learning outcomes
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
COMMUNICATIVE ABILITY
 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.
LEARNING SKILLS
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.
Readings
http://morespace.unimore.it/danielefunaro/provasottopagina/
Testi suggeriti:
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