- Understanding of the subjects of the course and computational skills in applying the mathematical tools presented in the course. - Familiarity with the mathematical contents of engineering disciplines. - Ability in building a logical sequence of arguments using the tools introduced in the course.

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.

- 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 (15 hrs). - 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 (25 hrs). - Definition and convergence criteria for numerical series. Power series. Fourier series (20 hrs).

Theoretical lessons: 40 hours. Exercises: 20 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 of the methods required to solve exercises with the aim of preparing the student to the exam.

All the topics of the course can be found for instance in the following textbook: - C. Canuto, A. Tabacco, "Mathematical Analysis II", Springer, 2015. Exercises and exams of previous years are available on the Home Page of the course in the Teaching Portal. Other possible material will be suggested in class and made available through the Teaching Portal.

Exercises;

You can take this exam before attending the course

Exam: Written test; Optional oral exam;

The goal of the exam is to test the knowledge of the students on the topics included in the official program of the course and to verify their computational and theoretical skills in solving problems. Marks range from 0 to 30 and the exam is successful if the mark is at least 18/30. The exam consists of a written part and an optional oral part. The written part consists of 7 exercises with closed answer and 1 exercise with open answer on the topics presented in the course. The aim of the exam is to certify the Expected Learning Outcomes (see above). Questions cover both computational and theoretical aspects, to evaluate the ability in building a logical sequence of arguments using the tools introduced in the course. The exam lasts 100 minutes. Marks are given according to the following rules. Each exercise with closed answer assigns: 3 points if correct, 0 points if blank, -1 point if wrong. The exercise with open answer assigns a maximum of 9 points, that can be less depending on the presence and significance of mistakes. 1 additional point is reserved to the notational clarity and the rigour of the exposition and it allows to obtain a cum Laude mark. During the exam it is forbidden to use notes, books, exercise sheets and pocket calculators. The test results will be posted on the teaching portal. Both students and the teacher can request an optional oral part that can alter both in the positive and in the negative the mark obtained in the written part. The optional oral part can only be requested in the same exam session of the written part. Students can request the optional oral part only if the mark they obtained in the written part is at least 18/30. The optional oral part concerns mainly the theoretical aspects of the course as definitions, statements of propositions and theorems and related proofs, and it requires a thorough knowledge of the whole matter.

In addition to the message sent by the online system, students with disabilities or Specific Learning Disorders (SLD) are invited to directly inform the professor in charge of the course about the special arrangements for the exam that have been agreed with the Special Needs Unit. The professor has to be informed at least one week before the beginning of the examination session in order to provide students with the most suitable arrangements for each specific type of exam.