# Unit MATHEMATICS I

Course
Mechanical engineering
Study-unit Code
GP004936
Curriculum
In all curricula
Teacher
Anna Salvadori
Teachers
• Anna Salvadori
Hours
• 108 ore - Anna Salvadori
CFU
12
Course Regulation
Coorte 2023
Offered
2023/24
Learning activities
Base
Area
Matematica, informatica e statistica
Academic discipline
MAT/05
Type of study-unit
Obbligatorio (Required)
Type of learning activities
Attività formativa monodisciplinare
Language of instruction
Italiano
Contents
Basic course of Calculus (one variable) with elements of Numerical Calculus
Reference texts
P.Brandi - A.Salvadori, Prima di iniziare, Aguaplano Officina del Libro (2015) - [basic knowlwdge]

P.Brandi - A. Salvadori, Percorsi di Matematica, 2 volumi, Aguaplano-Officina del libro, Passignano s.T. (PG), (2015) (textbook
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
Prerequisites
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.
Teaching methods
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
Other information
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
For information on support services for students with disabilities and / or SLD
visit the page http://www.unipg.it/disabilita-e-dsa
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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