This course first completes the theory of functions of one variable which was developed in Mathematical Analysis, presenting the basic concepts of numerical series, power series and Fourier series. The basic notions of the Laplace transform are also presented here. The course then presents basic topics in the mathematical analysis of functions of several variables. In particular, differential calculus in several variables, the theory of multiple integration, line, and surface integration.

Understanding of the subjects of the course and computational skill. Familiarity with the mathematical content of engineering disciplines.

The topics contained in the courses of Mathematical Analysis I and Linear Algebra and Geometry. In particular, limits, sequences, differential and integral calculus for functions of one variable, differential equations, linear algebra, geometry of curves.

Laplace transform.
Definition and convergence criteria for numerical series. Power series. Taylor series. Fourier series.
Review on vectors and elements of topology of R^n. Functions of several variables, vector fields. Limits and continuity. Partial and directional derivatives, Jacobian matrix. Differentiability, gradient and tangent plane. Second derivatives, Hessian matrix. Taylor polynomial. Critical points, free extrema.
Double and triple integrals, center of mass. Length of a curve and area of a graph. Line and surface integrals (graphs only), circulation and flux of a vector field.
Conservative vector fields. Green, Gauss and Stokes theorems.

Theoretical lessons: 50 hours. Exercise hours: 30 hours. Theoretical lessons are devoted to the presentation of the topics, with definitions, properties and the proofs which are believed to facilitate the learning process. Every theoretical aspect is associated with introductory examples. The exercise hours are devoted to the analysis and the methods required for solving exercises with the aim of preparing the student to the exam.

The following textbook covers the topics of the course:
- C. Canuto, A. Tabacco, "Mathematical Analysis II", Springer, 2014.

Other material will be availaible on the Portale della Didattica.

The goal of the exam is to test the knowledge of the candidate on the topics included in the official program of the course and to verify the computational and theoretical skills in solving problems. Marks range from 0 to 30 and the exam is succesful if the mark is at least 18.
The exam is written and consists of 7 exercises with closed answer and one exercise with open answer on the topics presented in the course. Questions cover also theoretical aspects.
The exam lasts two hours. During the exam it is forbidden to use notes, books, exercise sheets and pocket calculators.
There will be an oral exam only if required either by the teacher or by the student (in the last case only if the written exam’s grade is greater than or equal to 18/30).