At the end of the lectures, students should have acquired knowledge and understanding of the basic results of multivariable calculus, ordinary differential equations, curves in Euclidean n-dimensional spaces and of Peano-Jordan measure theory and integration.
Applying knowledge and understanding.
By means of the exercises students learn how to apply the theoretical knowledges to solve concrete problems, such as optimization problems. models from the applied sciences which lead to solving ordinary differential equation or to solving particular integrals for functions of several variables.
Students must be able to evaluate coherence and correctness of results obtained by themselves or by others.
Students must be able to communicate in a clear and precise way mathematical statements in the field of study, also in a context broader than mere calculus. Through the front lectures and the assistance of the teacher, the students acquire the specific and appropriate scientific vocabulary.
The student, who has attended the course, is able to deepen autonomously his/her knowledge of multivariate calculus, of the measure theory and integration for multivariate functions, starting from the basic and fundamental knowledges provided by the course. He/She will be also able to consult specialized textbooks, even outside the topics illustrated during the lectures. This to facilitate the entry in the labour market as well as a second-level study in a field which requires good mathematical skills.
The course schedules 4 hours of lectures per week plus other two hours per week for additional exercises.
The didactic activities consist lectures alternating with exercises. Both lectures and exercises will be delivered online via MS Teams. Students may attend lectures and exercises in streaming. They can also see the videos of the lectures starting from the web page of the course on Elly some days after its conclusion.
During the lectures, the topics of the course will be presented and discussed in a rigorous way. Much emphasis will be given to the application of the abstract results presented. To this aim, particular importance will be given to exercises, which are the most useful way to make students understand the relevance of the results presented in the theoretical lectures and to learn how they can be applied.