# Fisica | GEOMETRY

## Fisica GEOMETRY

 0512600008 DIPARTIMENTO DI FISICA "E.R. CAIANIELLO" PHYSICS 2015/2016

 OBBLIGATORIO YEAR OF COURSE 1 YEAR OF DIDACTIC SYSTEM 2010 ANNUALE
SSD CFU HOURS ACTIVITY TYPE OF ACTIVITY MAT/03 9 72 LESSONS BASIC COMPULSORY SUBJECTS
 GIOVANNI SPARANO T ANNAMARIA MIRANDA
Objectives
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.

KNOWLEDGE AND UNDERSTANDING:
THE COURSE AIMS TO PROVIDE THE FIRST TOOLS OF LINEAR ALGEBRA NECESSARY FOR THE STUDY OF PHYSICS IN GENERAL AND AFFINE AND EUCLIDEAN GEOMETRY.

APPLYING KNOWLEDGE AND UNDERSTANDING:
THE COURSE FURTHER AIMS TO ENABLE STUDENTS TO USE THE RELATED CALCULATION TOOLS. 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.

COMMUNICATION SKILLS:
THE COURSE WILL FACILITATE THE STUDENT'S ABILITY TO PRESENT IN A CLEAR AND RIGOROUS WAY THE ACQUIRED KNOWLEDGE.

MAKING JUDGEMENTS:
THE STUDENTS ARE GUIDED TO LEARN IN A CRITICAL AND RESPONSIBLE WAY EVERYTHING THAT IS EXPLAINED TO THEM AND ENRICH THEIR JUDGMENT THROUGH THE STUDY OF THE SUGGESTED TEACHING MATERIAL.

LEARNING SKILLS:
THE COURSE WILL TEND TO INTRODUCE THE STUDENT, BESIDES THE SPECIFIC TOPICS TREATED, TO THE MATHEMATICAL THINKING AND, AS A CONSEQUENCE, TO DEVELOP THOSE LEARNING SKILLS NECESSARY TO DEAL WITH THE SUBSEQUENT STUDIES.
Prerequisites
IT IS REQUIRED A 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 MONITORING AND EVALUATION OF THE LEVEL OF LEARNING BY THE STUDENT WILL OCCUR THROUGH A FINAL EXAM CONSISTING OF A WRITTEN EXAM FOLLOWED BY AN ORAL EXAMINATION. TO BE ADMITTED TO THE ORAL EXAMINATION, THE STUDENT MUST HAVE OBTAINED A SUFFICIENT EVALUATION FOR THE WRITTEN EXAM.
Texts
R. ESPOSITO, A. RUSSO, LEZIONI DI GEOMETRIA, PARTE PRIMA, LIGUORI.
E. SERNESI, GEOMETRIA 1, BOLLATI BORINGHIERI.
S. LIPSCHUTZ, ALGEBRA LINEARE MCGRAW-HILL.
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