# Fisica | GEOMETRY

## Fisica GEOMETRY

 0512600008 DIPARTIMENTO DI FISICA "E.R. CAIANIELLO" EQF6 PHYSICS 2018/2019

 OBBLIGATORIO YEAR OF COURSE 1 YEAR OF DIDACTIC SYSTEM 2017 SECONDO SEMESTRE
SSD CFU HOURS ACTIVITY TYPE OF ACTIVITY MAT/03 9 72 LESSONS SUPPLEMENTARY COMPULSORY SUBJECTS
 GIOVANNI SPARANO T ANTONIO DE NICOLA
Objectives
THE AIM OF THE COURSE IS TO INTRODUCE STUDENTS TO THE THEORY OF VECTOR SPACES AND TO THE THEORY OF AFFINE AND EUCLIDEAN GEOMETRY.

KNOWLEDGE AND UNDERSTANDING:
THE COURSE AIMS TO PROVIDE THE FUNDAMENTAL TOOLS OF LINEAR ALGEBRA WHICH, BESIDES THEIR GENERAL USEFULNESS IN THE STUDY OF PHYSICS, ARE ESSENTIAL FOR THE STUDY OF AFFINE GEOMETRY. WITH THE USE OF THESE TOOLS THE STUDENTS WILL BE INTRODUCED TO THE STUDY OF AFFINE AND EUCLIDEAN SPACES, AFFINE AND ISOMETRIC MAPS, AND CONIC SECTIONS.

APPLYING KNOWLEDGE AND UNDERSTANDING:
THE COURSE AIMS TO ENABLE STUDENTS TO USE THE CALCULATION TOOLS RELATED TO THE ABOVE MENTIONED TOPICS. IN PARTICULAR, THE STUDENT WILL KNOW HOW TO OPERATE WITH MATRICES, SOLVING SYSTEMS OF LINEAR EQUATIONS AND DEALING WITH ISSUES RELATED TO VECTOR SPACES, LINEAR APPLICATIONS AND THEIR PHYSICAL APPLICATIONS.
Prerequisites
IT IS REQUIRED THAT STUDENTS HAVE A GOOD KNOWLEDGE OF THE BASIC TOPICS IN MATHEMATICS COVERED IN HIGH SCHOOL.
Contents
1. VECTOR SPACES

2. MATRICES, DETERMINANTS AND SYSTEMS OF LINEAR EQUATIONS

3. LINEAR MAPS

4. LINEAR AND BILINEAR FORMS

5. EUCLIDEAN VECTOR SPACES

6. THE PROBLEM OF DIAGONALIZATION

7. HERMITIAN FORMS

8. AFFINE AND EUCLIDEAN AFFINE SPACES

9. EUCLIDEAN CONIC SECTIONS
Teaching Methods
72 HOURS OF LECTURES DIVIDED BETWEEN THEORETICAL LESSONS AND EXERCISES
Verification of learning
THE EXAM IS AIMED TO EVALUATE KNOWLEDGE AND UNDERSTANDING OF THE CONCEPTS PRESENTED IN CLASS AND THE ABILITY TO APPLY SUCH KNOWLEDGE TO THE SOLUTION OF SIMPLE PROBLEMS.
THE EXAMINATION IS DIVIDED INTO A SELECTIVE WRITTEN EXAM AND AN ORAL EXAM. THE WRITTEN EXAM CONSISTS OF SOME EXERCISES. THE ORAL EXAM EVALUATES THE ACQUIRED KNOWLEDGE OF LINEAR ALGEBRA, THE THEORY OF AFFINE SPACES AND EUCLIDEAN CONICS.
THE FINAL EVALUATION IS EXPRESSED BY A VOTE FROM 0 TO 30. THE WRITTEN EXAM IF PASSED GIVES ACCESS TO THE ORAL EXAM WHICH DETERMINES THE FINAL VOTE IN FULL. PASSING THE WRITTEN EXAM IN ONE OF THE SESSIONS WILL EXONERATE FROM THE WRITTEN EXAM UNTIL SEPTEMBER.
Texts
R. ESPOSITO, A. RUSSO, "LEZIONI DI GEOMETRIA, PARTE PRIMA", LIGUORI.
E. SERNESI, "GEOMETRIA 1", BOLLATI BORINGHIERI.
S. LIPSCHUTZ, "ALGEBRA LINEARE", MCGRAW-HILL.