
Course unit
INSTITUTIONS OF MATHEMATICS
PSP4063395, A.A. 2018/19
Information concerning the students who enrolled in A.Y. 2016/17
ECTS: details
Type 
ScientificDisciplinary Sector 
Credits allocated 
Educational activities in elective or integrative disciplines 
MAT/07 
Mathematical Physics 
9.0 
Course unit organization
Period 
First semester 
Year 
3rd Year 
Teaching method 
frontal 
Type of hours 
Credits 
Teaching hours 
Hours of Individual study 
Shifts 
Lecture 
9.0 
63 
162.0 
No turn 
Examination board
Board 
From 
To 
Members of the board 
5 20181 
01/10/2018 
30/09/2019 
ZANZOTTO
GIOVANNI
(Presidente)
CIATTI
PAOLO
(Membro Effettivo)

Prerequisites:

First and second degree equations and inequalities; analytic geometry on the plane; main trigonometric relations; properties of powers and logarithms. 
Target skills and knowledge:

The course provides the basic knowledge of differential calculus, and introduces some fundamental concepts of linear algebra with some of its main applications. The acquisition of theoretical, methodological, and applicative skills in these basic areas of mathematics is a necessary first step in understanding the fundamental results of most contemporary sciences, which increasingly use mathematics as a basic method of investigation and as universal language for understanding and communicating its results. 
Examination methods:

Written exam with open questions. An oral examination is also possible. The written exam (duration two hours, containing one or two theoretical questions plus 45 exercises, each involving a few specific questions) aims to verify that the expected learning outcomes are actually acquired by the students. The optional oral test focuses first on the discussion of the salient points of the solutions to the written test proposed by the student. This leads to a more indepth discussion of some of the topics covered in the course. 
Assessment criteria:

Evaluation based on the result of the written exam (theoretical questions and exercises) and the oral questions (discussion of the written exam and theoretical questions). 
Course unit contents:

Recollections on the prerequisites for the course. Real functions of a real variable. Definition of limit. Theorems and operations on limits. Sequences. Continuous functions: definition and main theorems. Composite function limit; fundamental limits. Derivative. Operations with derivatives. Theorems of Rolle, Lagrange, L'Hopital. Relative and absolute maxima and minima. Concavity and convexity; flexes; asymptotes. Study of functions and graph. Simple constrained optimization problems. Differential; primitives of a function. Notes on the indefinite and definite integral, and on the fundamental theorem of integral calculus. Linear algebra: vector spaces, vectors, generators, bases, dimension, direct sum. Matrices; rank and determinant. Systems of linear equations; Rouche'Capelli theorem and the space of solutions to a linear system. Linear systems and applications; eigenvalues and eigenvectors. 
Planned learning activities and teaching methods:

Class lectures: presentation of the topics listed above, with demonstration of some theorems; various examples. Ample space is given to the exercises to complement the theoretical lessons, even with the direct participation of the students. A main point of the presentation of the material is highlighting of the applicative aspects of the proposed theoretical knowledge. 
Additional notes about suggested reading:

The textbook of the course is supplemented by handout material available at the library. 
Textbooks (and optional supplementary readings) 

A. Guerraggio, Matematica per le scienze. Torino: Pearson, 2012. Testo consigliato.

G. Artico, 333 esercizi svolti. Padova: Libreria Progetto, 2003. Eserciziario.

A. Bichara, A. Del Fra, Geometria. Bologna: Progetto Leonardo, 2005. Testo aggiuntivo.

Innovative teaching methods: Teaching and learning strategies
 Problem based learning
 Questioning
 Problem solving
 Peer feedback
 Active quizzes for Concept Verification Tests and class discussions
 Students peer review
Sustainable Development Goals (SDGs)

