Mathematics
A.Y. 2025/2026
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 linear algebra and of integral and differential calculus for real functions. Finally, there will be an introduction to differential equations.
Expected learning outcomes
The student will be able to master the tools of linear algebra and 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.
Attendance to theory and exercises classes is strongly recommended.
Attendance to theory and exercises classes is strongly recommended.
Teaching Resources
M. Bramanti, C.D. Pagani, S. Salsa: Matematica. Calcolo infinitesimale e algebra lineare.
Seconda edizione. Ed. Zanichelli, Bologna, 2004
Seconda edizione. Ed. Zanichelli, Bologna, 2004
Assessment methods and Criteria
The exam consists of a written and possibly an oral part, depending on the jury's decision.
The written exam aims at verifying the knowledge and understanding of the topics of the course, also in concrete situations, through the resolution of exercises and questions about the theory. Two midterm tests will be proposed: if passed, they will allow to avoid the written exam and the final grade will the be the rounded up average of the two grades. The evaluation of the written exam is subordinate to passing some exercises on the preliminary notions required for the course. The written exam is passed with a minimun grade of 18/30 and with a minimun threshold of points (decided and communicated by the jury) in the part about the theory.
The oral examination, when due, is accessible upon positive result in the written evaluation and consists in a discussion about topics of the course and/or about the written part. The subject of evaluation will be both the acquisition of the basics of the theory and the critical ability of dealing with new problems. Up to special cases, the outcome of the oral part modifies the grade of the written part (up or down).
The final grade will be out of thirty.
The written exam aims at verifying the knowledge and understanding of the topics of the course, also in concrete situations, through the resolution of exercises and questions about the theory. Two midterm tests will be proposed: if passed, they will allow to avoid the written exam and the final grade will the be the rounded up average of the two grades. The evaluation of the written exam is subordinate to passing some exercises on the preliminary notions required for the course. The written exam is passed with a minimun grade of 18/30 and with a minimun threshold of points (decided and communicated by the jury) in the part about the theory.
The oral examination, when due, is accessible upon positive result in the written evaluation and consists in a discussion about topics of the course and/or about the written part. The subject of evaluation will be both the acquisition of the basics of the theory and the critical ability of dealing with new problems. Up to special cases, the outcome of the oral part modifies the grade of the written part (up or down).
The final grade will be out of thirty.
MAT/03 - GEOMETRY - University credits: 12
Practicals: 32 hours
Lessons: 80 hours
Lessons: 80 hours
Professors:
Camere Chiara, Cavaterra Cecilia
Professor(s)
Reception:
appointment via email
Dipartimento di Matematica, Via Saldini 50 - ufficio n. 2060