Academic Year 2022-2023

CALCULUS 2

Teachers

Paolo Baiti
Marco Pasini
Alessandro Armando Vigliano
Course Year
2
Unit Credits
12
Teaching Period
Annuity
Course Type
Characterizing
Prerequisites. Inalienable prerequisites: foundations of Mathematical Analysis 1 and Linear Algebra.
Teaching Methods. The course includes: lectures and exercises.
Verification of Learning. Exercises, homeworks and teamwork. The final exam will consist in a written test, suitable for checking the ability of the student in applying methods and tools, and an oral test, mainly theoretical, with the aim to verify the knowledge and understanding of the concepts taught during the course. As an alternative to the written test, at the end of each didactic period a partial written test is provided; passing both partial tests is equivalent to passing the written test itself.
Objectives
The course will provide the basic knowledge of Mathematical Analysis 2, such as metric and normed spaces, function series and Fourier series, differential calculus for real functions of several variables, ordinary differential equations, Lebesgue measure and Lebesgue integration theory, parametric curves and surfaces, differential forms.

The student will have to know the foundations of Mathematical Analysis 2, in particular the basic concepts of metric and normed spaces, function series and Fourier series, differential calculus for real functions of several variables, ordinary differential equations, Lebesgue measure and Lebesgue integration theory, parametric curves and surfaces, differential forms. He/she will manage to apply the fundamental theorems of Mathematical Analysis 2 in abstract and applied frameworks as well as to choose the suitable analytical methods in order to solve the assignments or problems found in the bibliography.

The student will be able to present, in writing as well as orally, the topics learnt during the course and to write autonomously a correct mathematical proof. He/she will learn to study independently and achieve the ability to deepen the lesson theory also by consulting the texts available in the bibliography.

Contents
Metric, normed and Hilbert spaces. Limits and continuous functions. Compact spaces, connected spaces. Function series and Fourier series. Differential calculus for real functions of several variables. Free and constrained optimization. Implicit function theorem, inverse function theorem. Ordinary differential equations. Lebesgue measure and Lebesgue integration theory, parametric curves and surfaces, differential forms. More issues about Fourier series
Texts
Teacher lecture notes.

E.Giusti, Analisi Matematica 2 or N.Fusco, P.Marcellini, G.Sbordone, Analisi Matematica due.