Fundamentals of Mathematics
A.Y. 2023/2024
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.
Lesson period: First semester
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
Single course
This course can be attended as a single course.
Course syllabus and organization
Single session
Responsible
Lesson period
First semester
Course syllabus
Real and complex numbers. Vectors and matrices. Linear systems and Gauss method. Elementary geometry in the plane and in the space. Abstract vector spaces, linear maps, eigenvalues and eigenvectors. Sequences of real numbers. Differential calculus for real functions defined for one or more variables. Integral calculus for real functions defined on one variable. Resolution of linear differential equations of I and II order.
Prerequisites for admission
Rational and irrational equations and inequalities, and systems. Elementary algebra and geometry; knowledge of trigonometry, exponential and logarithmic functions and their applications to equations and inequalities. Basic notions of analytic geometry and applications: lines and conics.
Teaching methods
Traditional lessons and exercises. Tutoring activities will be proposed 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
Matematica. Calcolo infinitesimale e algebra lineare.
Seconda edizione. Ed. Zanichelli, Bologna, 2004
Assessment methods and Criteria
The exam consists of a written and possibly an oral part.
The written exam aims at verifying 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, if this is needed according to the teachers. It consists of an interview where the knowledge of the main topics of the course will be evaluated, as well as the critical capability of discussing new concrete problems. A final mark will be given, up to 30/30.
The written exam aims at verifying 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, if this is needed according to the teachers. It consists of an interview where the knowledge of the main topics of the course will be evaluated, 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
MAT/02 - ALGEBRA
MAT/03 - GEOMETRY
MAT/04 - MATHEMATICS EDUCATION AND HISTORY OF MATHEMATICS
MAT/05 - MATHEMATICAL ANALYSIS
MAT/06 - PROBABILITY AND STATISTICS
MAT/07 - MATHEMATICAL PHYSICS
MAT/08 - NUMERICAL ANALYSIS
MAT/09 - OPERATIONS RESEARCH
MAT/02 - ALGEBRA
MAT/03 - GEOMETRY
MAT/04 - MATHEMATICS EDUCATION AND HISTORY OF MATHEMATICS
MAT/05 - MATHEMATICAL ANALYSIS
MAT/06 - PROBABILITY AND STATISTICS
MAT/07 - MATHEMATICAL PHYSICS
MAT/08 - NUMERICAL ANALYSIS
MAT/09 - OPERATIONS RESEARCH
Practicals: 32 hours
Lessons: 56 hours
Lessons: 56 hours
Professors:
Camere Chiara, Cozzi Matteo
Educational website(s)
Professor(s)