Mathematics II

A.Y. 2020/2021
Overall hours
MAT/01 MAT/02 MAT/05
Learning objectives
The aim of the course is to supply the students with some mathematical tools necessary to the comprehension of mathematical models in the physical , geological and economical fields.
Expected learning outcomes
Tools of differential and integral calculus for functions of two variables. Basics in statistics.
Course syllabus and organization

Single session

Lesson period
First semester
The lectures and exercises and the material related to the course will be made available to the students on ARIEL.
The remote lessons and exercises will be synchronous on the Microsoft Teams platform.
Course syllabus
Differential calculus for real and vector functions of vector variables: limits, continuity, directional derivatives, differentiability. Free and constrained extrema.
Conservative fields.
Double integrals: definition and calculus via iterated integrations.
Ordinary differential equations. Integration of some types of differential equations of first order. Linear ordinary differential equations of order 2.
Descriptive statistics. Statistical data and their representation. Index of position and dispersion. Box-plot.
Prerequisites for admission
Differential and integral calculus for real functions of a real variable.
Basic knowledge of Analytical Geometry and Linear Algebra.
Teaching methods
Attendance mode: strongly recommended
Mode of delivery: lectures and exercise classes.
Teaching Resources
Reference book: Calcolo. Funzioni di più variabili.
James Stewart.
Assessment methods and Criteria
The exam consists of a written and an oral part, both of them mandatory. The written part aims at verifying the capacity of solving exercises and the knowledge of main topics presented during the classes. The duration of the written exam will be proportional to the number of exercises and questions assigned, also taking into account the nature and complexity of the exercises themselves (however, the duration will not exceed three hours). The written test can be replaced by two ongoing tests. The oral exam can be taken only if the written component has been successfully passed. The oral part consists of an oral examination that focuses mainly on theoretical topics of the course and on the written exam. The complete final examination is passed if all the two parts (written and oral) are successfully passed. Final marks are given using the numerical range 0-30, and will be communicated immediately after the oral examination.
MAT/01 - MATHEMATICAL LOGIC - University credits: 0
MAT/02 - ALGEBRA - University credits: 0
MAT/05 - MATHEMATICAL ANALYSIS - University credits: 0
Practicals: 36 hours
Lessons: 24 hours
Professor: Terraneo Elide