99621 - Mathematical Analysis T-2

Learning outcomes

Through the course the student learns the basic results as well as the basic tools of advanced calculus. At the end of the course, he/she masters the notions of partial derivatives, differentiability and integrability for functions of several real variables. He/She will be able to apply this knowledge to the study of many problems posed by pure and applied sciences.

Course contents

Introduction to functions in several variables: topology of R^n, euclidean scalar product, differential calculus, extrema of a function: min, max and saddle points, the tangent plane.

Riemann integral of a function: definition, integration on normal domains.

Curves in R^n, line integrals: the work of a vector field; closed and exact differential forms. Conservative vector fields.

Ordinary differential equations: linear differential equations of first and second order; the corresponding Cauchy problem.

Readings/Bibliography

S.Lang "Calculus of several variables" Springer Verlag (III edition)

C.Canuto-A.Tabacco "Mathematical Analysis II" Springer

Teaching methods

Theory and exercises

Assessment methods

The exam aims to verify the achievement of the following educational objectives:

• Knowledge of the basic concepts of mathematical analysis covered during lectures.
• Ability to use these tools to solve exercises and problems.

The exam consists of a written test focused on the types of exercises discussed in class and on some questions about the main theoretical aspects covered during the course.

During the, the use of books, notes, calculators, smartphone, smartwatch or computing devices is not allowed.

There will be three exam sessions:

• Summer (3 dates: June and July),
• Autumn (1 dates: September),
• Winter (2 dates: January and February).

Teaching tools

Blackboard, video and pc

Office hours

See the website of Marco Mughetti