Fundamentals of mathematics

A.Y. 2020/2021
Overall hours
MAT/01 MAT/02 MAT/03 MAT/04 MAT/05 MAT/06 MAT/07 MAT/08 MAT/09
Learning objectives
The aim of the course is to provide the basic mathematical tools for the applications of Mathematics to the other sciences (in particular, to Chemistry), focussing on the basic notions of integral and differential calculus for real functions.
Expected learning outcomes
The student will be able to master the tools of differential and integral calculus and to apply them to solving problems, particularly of a chemical nature.
Course syllabus and organization

Single session

Lesson period
First semester
The course will be fully online. Synchronous class sessions will be scheduled, in which every student will be invited to log in to a web conferencing system (if possible and in accordance with the other activities proposed to the students).
Videos with lessons and exercises collections, and any other file (slides or notes) will be made available at the official web space of this course, for an asynchronous use, till the end of the semester. Tutoring will be organized to create engagement and foster community, if possible by live.
The details of these meetings (lìplatform, links, password) will be available in the course web page of the Ariel platform, as well as the videos and every kind of material needed for the course.
The exams will be done by following the ways suggested on the web page of the university. The written exam will have the same structure as the one done in presence, possibly modified in time and number of exercises.
Course syllabus
Real and complex numbers. Sequences of real numbers. Differential calculus for real functions defined for one or more variables. Integral calculus for real functions defined on one variable. Elements of linear Aglebra: vectorial spaces, matrixes, linear functions and systems of linear equations. Resolution of linear differential equations of I and II order.
Prerequisites for admission
Elementary algebra and geometry; knowledge of trigonometry, exponential and logarithmic functions and their applications to equations and inequalities.
Teaching methods
Traditional lessons and exercises. Tutoring activities will be proposed, in room and on line, on exercises suggested by the teachers.
Teaching Resources
M. Bramanti, C.D. Pagani, S. Salsa:
Matematica. Calcolo infinitesimale e algebra lineare.
Seconda edizione. Ed. Zanichelli, Bologna, 2004

Exercises and teaching material will be provided on the web page of the course on the web portal Ariel.
Assessment methods and Criteria
The exam consists of a written and an oral part.
The written exam usually lasts 150 minutes. It aims to verify the knolwdege and understanding of the topics of the course in concrete situations, through the resolution of exercises. Two midterm tests will be proposed: if passed, they will allow to avoid the written exam.
A positive evaluation in the written part is required to attend the oral one. It consists of a colloquim where the knowledge of the main topics of the course will be avaluated, as well as the critical capability of discussing new concrete problems. A final mark will be given, up to 30/30.
MAT/01 - MATHEMATICAL LOGIC - University credits: 0
MAT/02 - ALGEBRA - University credits: 0
MAT/03 - GEOMETRY - University credits: 0
MAT/05 - MATHEMATICAL ANALYSIS - University credits: 0
MAT/06 - PROBABILITY AND STATISTICS - University credits: 0
MAT/07 - MATHEMATICAL PHYSICS - University credits: 0
MAT/08 - NUMERICAL ANALYSIS - University credits: 0
MAT/09 - OPERATIONS RESEARCH - University credits: 0
Practicals: 32 hours
Lessons: 56 hours