Mathematical Analysis 3

The course aims to complete the basic Knowledge of Mathematical Analysis for the students of the three-year degree in Physics. In
particular the course will provide the student with the knowledge and the mastery of the following concepts, widely used in Physics:
·implicit functions and constrained maxima and minima;
·differential forms, exact and closed forms;
·Lebesgue theory for functions of several variables;
·surfaces and surface integral;
·Gauss-Green formulas, divergence and Stokes theorem.

At the end of the course the students will have acquired the following knowledge and skills.
1. Knowledge and understanding of the following subjects:
·implicit functions;
·constrained maxima and minima;
·differential forms, exact and closed forms;
·Lebesgue theory for functions of several variables;
·surfaces and surface integral;
·Gauss-Green formulas, divergence and Stokes theorem.
2. Ability to present and discuss in a critical way the concepts studied;
3. Ability to solve problems by using the results and the tools, they have learnt.
In particular they will be able
·to study implicit functions
·to minimize functions of several variables with constraints
· to calculate integrals in several variables;
·to understand whether a differential form is exact and to determine a primitive;
·to apply the divergence and Stokes theorems in the plane and in the space
4. Ability to use the tools they have studied in different framework.