Facoltà di Ingegneria - Guida degli insegnamenti (Syllabus)

Algebric calculus and analytic geometry

The aim of the course is that of providing (together with the course of Calculus 2) the basic mathematical tools needed in the planning, designing and building processes related to the degree course topics. In particular, the course offers the basic knowledge of the differential and integral calculus for real functions of one variable with a number of applications.

The main classical results of analysis will be introduced, in order to develop the students ability to use mathematical methods towards collecting, interpreting and organizing with the correct methodology the data related to the structural and functional aspects of a project; the theoretical notions will be accompanied by numerous applications. This path will lead the student to achieving the capability of: 1. analizing problems; 2. detecting the methods of solution; 3. choosing the best solving technique.

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.

Elements of set theory. The set of real numbers and its properties. Complex numbers. Numerical sequences and definition of limit. Numerical series and their behavior. Functions of one variable: elementary functions. Limit of function. Continuous functions and their properties. Differential calculus for functions of one variable. Graph of function. Taylor polynomial. Taylor series. Complex exponential. Integral calculus for functions of one variable. Riemann's integral. Improper integral and convergence criteria. Sequences and series of functions: pointwise and uniform convergence. Power series and Fourier series.

The exam consists of a written and an oral test: - the tests will concern the topics covered during the course offered in the same academic year; - the registration to the first written test is mandatory, and has to be done on line on the university web page; - the written test consists of a number of problems and questions (from five to ten, according to difficulty) concerning all topics treated during the course; this test will last two hours; the student will not be permitted the use of any kind of electronic device, not even a pocket calculator; - a minimum score of at least 16/30 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 web page; - the oral test will contain mainly theoretical questions, some of which may be formulated in written form and contain 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; - in case of a successful written test, the student may sit for the oral test either in the same session or the next available session, not later; - in case of a successful written test, but a non-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 have to be correctly and fluently written, well organized, easily readable and with a negligible presence of corrections which must anyway not mar the esthetics of the text; - 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 a good understanding of all topics and concepts covered during the course, and which will be 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 calculus problems.

Assignement of a numerical score in the range 0-30.

The final score will be given by the teacher on the basis of the score of the written test and of the level of knowledge and comprehension of the topics covered during the course.

M. Bramanti, C. D. Pagani, S. Salsa: Analisi Matematica 1 S. Salsa, A. Squellati Esercizi di Matematica, vol. 1, Zanichelli. M. Bertsch, R. Dal Passo, L. Giacomelli, Analisi Matematica, McGraw-Hill

- Ingegneria Edile-Architettura (Corso di Laurea Magistrale con Riconoscimento Europeo (DM 270/04))

**Università Politecnica delle Marche**

P.zza Roma 22, 60121 Ancona

Tel (+39) 071.220.1, Fax (+39) 071.220.2324

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