Understanding of the subjects of the course and computational skills in applying the mathematical tools presented in the course. Familiarity with the mathematical content 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.

Laplace transform. Review on vectors and elements of topology of the n-dimensional Euclidean space. 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, circulation and flux of a vector field. Conservative vector fields. Green, Gauss and Stokes theorems. Definition and convergence criteria for numerical series. Power series. Fourier series.

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 notes of the course will be made available on the web portal. The teacher of the course will suggest some textbooks among the following during the lectures: - T. Apostol, "Calcolo, volume terzo (Analisi 2)", Bollati Boringhieri. - M. Bramanti, C.D. Pagani, S. Salsa, “Analisi matematica 2”, Zanichelli. - C. Canuto, A. Tabacco, "Analisi Matematica II", Springer. - S. Salsa, A. Squellati, “Esercizi di Analisi matematica 2”, Zanichelli. - S. Lancelotti, “Esercizi e quiz di Analisi Matematica II”, Celid. - D. Bazzanella, P. Boieri, L. Caire, A. Tabacco, Serie di funzioni e trasformate, CLUT. Further material will be made avalaible on the web portal.

Lecture notes; Text book; Exercises; Exercise with solutions ;

You can take this exam before attending the course

Exam: Written test; Compulsory oral exam;

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 consists of a written part and an optional oral part. The written part and consists of 7 exercises with closed answer and one exercise with open answer on the topics presented in the course, with the aim of ascertaining the level of comprehension of the topics of 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 written exam lasts two hours. Marks are given according to the following rules. Closed answer exercises: 3 points if correct, 0 points if blank, -1 point if wrong. Open answer exercise: 9 points. An additional point is reserved to notational clarity and rigour in the exposition and allows the student 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 together with the date in which the students can see their tests and ask for explanations. Student 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.

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.