At the end of the course, the student will master the methods and techniques of mathematical analysis, with particular reference to differential and integral calculus in multiple real variables. They will also know the fundamentals and methods for solving elementary ordinary differential equations and the concept of Fourier series expansion.In order to understand the potential and limitations of the aforementioned tools, the student will also have a full awareness of their theoretical foundations and will be able to express them with adequate language proficiency.
Differential and integral calculus in one variable. Geometry and linear algebra.
The teaching is composed by lectures, exercises and tutoring. In all three activities the student is encouraged to participate with suggestions and proposals.
The exam aims to verify the student's achievement of the course's educational objectives. In particular:
The exam includes both a practical and a theoretical test, both of which are mandatory.
The practical test is written and consists of solving 4 to 6 exercises, each with a specified score announced at the beginning of the test. Il will also be requested to answer to 3/4 theoretical questions in order to evaluate knowledge of definitions, examples, theorem statements, and proofs. Consideration is given to the relevance of the answers to the questions, the ability to summarize, and the proper use of language.
Linear systems.
Functions of several variables: limits and continuity.
Differential calculus for functions of several variables.
Differential calculus on curves and surfaces.
Multiple integration. Integrals on curves and surfaces.
Series and trigonometric series.
Differential equations and Cauchy problems.
All the materials of the course will be posted on the Moodle web page of the course. The students will be invited to join this page in order to receive all the announcements about the course during the semester.
