Università degli Studi di Perugia

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Study-unit MATHEMATICS I

Course name Mechanical engineering
Study-unit Code GP004936
Location PERUGIA
Curriculum Comune a tutti i curricula
Lecturer Anna Salvadori
Lecturers
  • Anna Salvadori - Didattica Ufficiale
Hours
  • 123 Hours - Didattica Ufficiale - Anna Salvadori
CFU 12
Course Regulation Coorte 2017
Supplied 2017/18
Supplied other course regulation
Learning activities Base
Area Matematica, informatica e statistica
Sector MAT/05
Type of study-unit Obbligatorio (Required)
Type of learning activities Attività formativa monodisciplinare
Language of instruction Italian
Contents Basic course of Calculus (one variable) with elements of Numerical Calculus
Reference texts P.Brandi - A. Salvadori, Percorsi di Matematica, 2 volums, Aguaplano-Officina del libro, Passignano s.T. (PG), (2015)
P.Brandi - A.Salvadori, Prima di iniziare, Aguaplano-Officina del libro, Passignano s.T. (PG), (2011)
Educational objectives Matematica 1 is a basic course of Calculus (one variable) with elements of Numerical Calculus.
Together with Matematica 2 has the task to provide the mathematical skills needed to face the studies of Mechanical Engineering.
The main objective of the course is to provide basic knowledge in the following areas:
- Differential and integral calculus for functions of one variable
- Polynomial approximation
- Approximate solution of equations (both numerical and differential)
- Data fitting
- Numerical integration
- Mathematical modeling with basic tools (both discrete and continuous models).

The main skills is to understand the fundamental role of calculus in the modeling of phenomena and / or real situations. In particular, the students will become familiar with the two key concepts of optimization and balance and their applications in various fields, mainly of industrial engineering.
Prerequisites Mathematics 1 is a challenging and intensive course (12 CFU - thirteen weeks).
In order to follow the lessons in a profitable way, it is essential to have a good preparation on the basic knowledge (see list below). Basic knowledge. Algebra of polynomials.
Elements of analytic geometry on the plane. Elements of goniometry and trigonometry.
Elementary functions and their inverse or partial inverse. Transformations of a function (translation and rescaling) and effect on the graph. Elementary equations and inequalities.
Teaching methods The course is organized as follows:
- Classroom lectures on all topics of the course
- Exercises in the classroom with student involvement
- Two written exercises in the classroom to simulate the written exam.
Learning verification modality The exam includes a written test and an oral interview.
The written exam is divided into two consecutive stages A and B.
Phase A - 2 hours
type: resolution of (three or four) problems; the use of textbooks, manuals, graphic-symbolic calculator (strictly off-line) is allowed;
objective: to assess the knowledge and the skills of application type.
It will be particularly appreciated not only the correctness of the calculation procedures, but also the quality of the arguments used to support the anwer.
Phase B - 1 hour
type: some open questions, is not allowed the use of any support;
verification of knowledge and argumentative demonstration.

Interview - 20-30 minutes
objective: assessing the communication skills of the student.
Timing: the date of the written tests are fixed; that of the interview can be agreed with the teacher
Extended program Iterative processes. Sequences. Limit. Derivative. Riemann integral. Applications of differentiation an integration theory: qualitative study of a function, optimization problems. Series. Polynomial approximation. Ordinary differential equations of first order. Linear differential equations of higher order. Elements of numerical analysis.
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