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.