|SCIENTIFIC DISCIPLINARY SECTOR||MAT/05|
Prerequisites (for future units)
Basic topics in calculus of severable variables are treated. The course is split into two semesters. The first part is devoted to differential calculus, integration theory in two (or several) variables and function series. The second part deals with integration along curves and surfaces, Gauss and Stokes' theorems and their consequences, and an introduction to systems of differential equations. SMID students need to take only part I (first semester - 8 credits). Both semesters are mandatory for Physics students.
Students will become acquainted with the most important topics in several (real) variables and how they are used in practice. We only present proofs that illustrate fundamental principles and are free of technicalities.
Applications to Physics and Probability are emphasised.
At the end of the first semester, students will be able to manipulate functions of several variables and solve basic optimization problems. Moreover they will be at their ease with mean and conditional expectation.
Physics students will be able to apply vector calculus: use double, triple and line integrals in applications, including Green's Theorem, Stokes' Theorem and Divergence Theorem.
First year calculus (derivatives and integrals for functions of a single variable, sequences and numerical series). Vector spaces, eigevalues and eigenvectors are frequently used.
Both theory and exercises are presented by the teacher. The first semester consists of 12 weeks with four hours of theory and two hours of exercises per week. The second semester consists of 12 weeks with three hours of theory and two hours of exercises per week.
Sequences and series
Differential geometry of curves and surfaces.
Serge Lang - Calculus of Several Variables, Third Edition, Undergraduate Texts in Mathematics, Springer, 1987.
Office hours: Questions during or at the end of lectures are welcome. Meetings will be organized upon email request.
Office hours: Weekly office hours will be communicated. Meetings upon email requests will also be considered.
FRANCESCA ASTENGO (President)
FILIPPO DE MARI CASARETO DAL VERME (President Substitute)
Classes will start according to the academic calendar.
All class schedules are posted on the EasyAcademy portal.
Written and oral exam
The written examination consists in solving some exercises on the topics of the course. It is approved with grade at least 15/30.
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