27213 - Mathematical Analysis 2

Course contents

Differential calculus for functions of several real variables. Taylor's formula. Local maxima and minima. Local invertibility and implicit functions. Constrained extrema.

Sequences and series of functions: punctual and uniform convergence. Power series. Convergence criteria.

Path integrals. Vector fields, potentials.

Elements of measure theory and Lebesgue's integration in R^n. Passage to the limit under the integral sign, reduction and change of variables theorems.

Local existence and extendability of the solutions of Cauchy problems for ordinary differential equations; solution methods for equations of a particular type. Linear equations and systems: general integral, resolution of equations and systems with constant coefficients.

Readings/Bibliography

Notes of the teachers will be available on Insegnamenti Online.

To study in depth the topics of the course, students can consult:

E. Lanconelli: Lezioni di Analisi Matematica 2, prima parte, ed. Pitagora

N. Fusco, P. Marcellini, C. Sbordone: Analisi Matematica due, ed. Liguori

G.C. Barozzi, G. Dore, E. Obrecht: Elementi di Analisi Matematica, vol. 2, ed. Zanichelli

Textbooks about exercises:

M. Bramanti, Esercitazioni di Analisi Matematica 2, ed. Esculapio

P. Marcellini, C. Sbordone: Esercitazioni di Analisi Matematica due, parte I e parte II, ed. Zanichelli

Teaching methods

Lectures and exercises in the classroom.

Assessment methods

The examination consists of a preliminary written test and an oral one.

The written test consists of six exercises related to the arguments of the course. In order to participate to the written test the student must register at least three days before the test through AlmaEsami.

The written test remains valid for the oral exam in the same examination period.

The oral test follows the written test; it mainly concerns the theoretical aspects of the course. The student must show to know the concepts explained during the course (in particular definitions, theorems and their proofs) and how to connect them.

In the period between the first and second cycle the student can take a partial examination on the topics of the first module of the course. The rules of partial examination are the same as for the total examination.

The student who have passed the examination relative to the first module can take the examination relative to the second module within July. After this date the first partial examination is canceled.

Office hours

See the website of Giovanni Dore

See the website of Giovanni Cupini