Chemical Sciences

FRANCESCA DE MARCHIS
ANDREA DAVINI

The main purpose of the course is to give the student a good knowledge of the basic theory of Differential and Integral Calculus of Functions of several variables, as well as of Linear Algebra.

Specific objectives :

Knowledge and understanding: at the end of the course the student will have learned the basic theory to study functions of several variables both with scalar or vector values. Moreover he/she will be able to study simple linear maps between vector spaces.

Applications : at the end of the course the student will be able to solve simple problems which require the use of the differential and integral calculus . In particular he /she will be able to find extremals of functions of several variables and also determine the potential of a vector field. Moreover he/she will have the ability to solve linear systems.

Critical abilities: the student will have the basic knowledge to understand the mathematical tools necessary to study Chemistry and Physics and the way to derive some formulas used in these fields.

Communication skills: the student will have the ability to expose the topics studied in written and in oral form.

Learning skills: the course will improve the logical abilities and of learning of various scientific disciplines.

The students will learn the basic notions of Linear Algebra and Differential Calculus for functions of severable variables. They will be able to use them in problems related to other sciences.

Differential calculus and integrals for functions of one variable

Linear Algebra : Vector spaces and linear maps - Matrices - Eigenvalues and eigenvectors - Linear systems - Quadratic forms.
Functions of several variables : Limit and continuity - Partial and directional derivatives and differentiability- Higher derivatives , Taylor formula - Local and global maxima or minima.
Vector valued functions : Regular curves and their length - Integral on curves - Vector fields and their integral on curves - Conservative vector fields.
Integral for functions of several variables : Integrals on planar domains, triple integrals- Recduction and change of variables formulas - Gauss Green and Divergence theorems.

- Bramanti M., Pagani C.D., Salsa S.: Matematica - Calcolo Infinitesimale e Algebra Lineare - Zanichelli

The classes will be given using a blackboard

It is advisable to take the classes

The evaluation is based on a written and oral exam. The last one can be granted depending on the result of the written part. The written exam can be substituted by two intermediate partial exams given after the first half of the course and after the end of the course.

Some exercises should be solved including full details . There will be also some multiple choice questions.

• • Books: Bramanti M., Pagani C.D., Salsa S.: Matematica - Calcolo Infinitesimale e Algebra Lineare - Zanichelli