# Computer science | MATHEMATICAL ANALYSIS

## Computer science MATHEMATICAL ANALYSIS

 0512100001 DIPARTIMENTO DI INFORMATICA COMPUTER SCIENCE 2013/2014

 OBBLIGATORIO YEAR OF COURSE 1 YEAR OF DIDACTIC SYSTEM 2008 SECONDO SEMESTRE
SSD CFU HOURS ACTIVITY TYPE OF ACTIVITY MAT/05 8 64 LESSONS BASIC COMPULSORY SUBJECTS MAT/05 4 32 EXERCISES BASIC COMPULSORY SUBJECTS

 PATRIZIA DI GIRONIMO T
Objectives
THE COURSE AIMS TO GIVE:

-KNOWLEDGE AND UNDERSTANDING OF THE BASIC CONCEPTS OF MATHEMATICS OF CONTINUOUS AND TO GET THE STUDENT USED TO A STRICT WAY OF THINKING THANKS TO DEMONSTRATIONS
-APPLYING KNOWLEDGE AND UNDERSTANDING
THE COURSE HAS THE OBJECTIVE TO MAKE THE STUDENT ABLE TO EQUATE THE THEORETICAL KNOWLEDGE ACQUIRED AND KNOW HOW TO SOLVE SIMPLE EXERCISES. IN PARTICULAR, THE STUDENT MUST BE ABLE TO SOLVE EXERCISES RELATED TO THE STUDY OF THE FUNCTIONS OF A REAL VARIABLE: CALCULATION OF LIMITS OF FUNCTIONS, CALCULATION OF DERIVATIVES, STUDY AND COMPARISON OF THE GRAPH OF A FUNCTION FROM ITS ALGEBRAIC EXPRESSION CALCULATION OF INTEGRAL.

-COMMUNICATION SKILLS
MORE PARTICULARLY AT THE END OF THE COURSE THE STUDENT WILL BE ABLE TO EXPOSE CLEARLY AND STRICTLY DEFINITIONS, PROBLEMS AND THEOREMS CONCERNING THE CONTENTS OF THE COURSE.

-MAKING JUDGEMENTS
STUDENTS ARE GUIDED TO LEARN IN A CRITICAL AND A RESPONSIBLE WAY EVERYTHING WHICH IS TAUGHT THEM DURING THE COURSE AND TO DEVELOP THEIR JUDGEMENT SKILLS THANKS TO THE STUDY OF THE MATERIAL PROVIDED BY THE TEACHER.
Prerequisites
KNOWLEDGE OF HIGH SCHOOL LEVEL OF MATHEMATICS IS REQUIRED. IN PARTICULAR, ELEMENTARY ALGEBRA, METHODS OF SOLVING OF EQUATIONS AND INEQUALITIES OF FIRST AND SECOND GRADE AND SOME ELEMENTS OF TRIGONOMETRY.
Contents
-SET THEORY
-THE REAL NUMBER
-THE REAL FUNCTIONS
-SEQUENCE OF REAL NUMBER
-LIMITS OF FUNCTIONS
-DERIVATES
-THE RIEMANN INTEGRAL
-TAYLOR'S FORMULA
-NUMERICAL SERIES
-FUNCTIONS OF SEVERAL VARIABLES
Teaching Methods
THE COURSE PROVIDES A PART OF THEORETICAL LESSONS AND A PART OF PRACTICAL ONES; THE FORMER ARE AIMED TO LEARNING THE BASICS OF MATHEMATICS OF CONTINUOUS AND DEMONSTRATION OF THE DIFFERENT USED TECHNIQUES, THE LATTER HELP TO ILLUSTRATE HOW THE THEORETICAL KNOWLEDGE ACQUIRED CAN BE USED IN ORDER TO SOLVE PROBLEMS.
Verification of learning
WITH A WRITTEN TEST FOLLOWED BY AN ORAL ONE, THE LEVEL OF KNOWLEDGE OF THE STUDENT WILL BE TESTED
Texts