Facoltà di Ingegneria - Guida degli insegnamenti (Syllabus)

Differential and integral calculus of real functions on one real variable. Matrix and vector algebra.

The aim of the course is that of providing further mathematical tools commonly employed in the engineering sciences, by means of introducing the basic elements of the differential and integral calculus for real functions of several variables and of the ordinary differential equations.

The many applications of the course topics in the applied sciences, for example in chemistry and in physics, will provide the student with the ability of modeling and solving practical engineering problems; they will also increase the ability of choosing independently the best solution techniques. The course will also provide the student with the ability to use mathematical laws in general scientific problems.

The expertise acquired in this course will be needed in order to study the material of later courses. Individual and collective problem-solving sessions will improve the ability to develop independent thought and learning capabilities. Oral presentations of the topics taught in the course, with the language proper of the basic disciplines of the degree course will help developing communication skills.

Ordinary differential equations. Vector functions. Differential calculs for real functions of more variables.Differential calculs for vector functions of more variables. Multiple integrals Vector fields. Power series and Fourier series.

The exam consists of a written test and a colloquium: - both tests will concern the topics of the current academic year; possible exceptions will be assessed on a case-by-case basis; - registration to the first written test is mandatory, and has to be done on line on the university platform Esse3 (the link is available on the teacher's web page); - the written test consists of a number of problems and questions concerning all topics treated during the course; this test will last two or three hours, and the student will not be permitted the use of any kind of material, not even a pocket calculator; - a minimum score of at least 18/30 in the written test is required for the admission to the oral test; - the list of the names of the students admitted to the oral test will be published by the teacher on his official web page; - the oral test will contain mainly theoretical questions, some of which may have to be formulated in written form, and may contain problems and exercises concerning course topics not covered in the written test or course topics in which the student may have shown weaknesses in the written test; - questions of general comprehension may be asked both in the written and in the oral test and may concern any of the course topics; - in the case of a successful written test, the student may sit for the oral test either in the same session or in the next available session, but not later; - in the case of a successful written test, but a not passing grade in the oral test, the student may try the oral test again in the next available session; in case of another failure, the student will have to sit for the whole exam again; - all written tests must be presented in readable form, with a negligible amount of corrections, which must anyway not mar the esthetics of the text; the exposition must be clear, fluent, well organized and consistent both in the mathematical and in the linguistic aspects; - honor code: each student pledges that the written tests are entirely his/her own work and that no input from other students or sources has been used; demeanors which are deemed unfair or not in line with these principles entail the failing of the exam.

In order to pass the exam, the student must demonstrate understanding of all the topics covered and concepts introduced during the course and published on line as Final program or Exam program at the end of the course, and to be able to use them in solving typical mathematical analysis problems.

The student must demonstrate to have acquired deep knowledge on the fundamental principles and techniques of mathematical analysis and on the solution of typical differential and integral calculus problems of real and vector valued functions, in one or more variables.

The highest grade of 30/30 will be given to those students which will have shown deep knowledge and perfect mastering of all the course topics and the ability of working with full independence both in solving the assigned problems and in the oral presentation. The lowest passing grade of 18/30 will be given to the students which will have shown sufficient knowledge and good mastering of all the course topics.

. Bramanti, C. D. Pagani, S. Salsa Anailisi Matematica 2, Ed. Zanichelli.

- Ingegneria Edile (Corso di Laurea Triennale (DM 270/04))

**Università Politecnica delle Marche**

P.zza Roma 22, 60121 Ancona

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