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MATHEMATICS II

ADA AMENDOLA MATHEMATICS II

0612100002
DEPARTMENT OF CIVIL ENGINEERING
EQF6
BSC DEGREE IN CIVIL ENGINEERING
2024/2025

OBBLIGATORIO
YEAR OF COURSE 1
YEAR OF DIDACTIC SYSTEM 2022
SPRING SEMESTER
CFUHOURSACTIVITY
990LESSONS
ADA AMENDOLA T Curriculum
Objectives
EXPECTED LEARNING OUTCOMES AND SKILLS TO BE ACQUIRED:
ACQUISITION OF TOOLS AND METHODS TO DESCRIBE, EVALUATE AND INTERPRET VARIABILITY IN THE FIELD
EXPERIMENTAL, ENVIRONMENTAL AND INDUSTRIAL FOR THE PURPOSE OF MAKING DECISIONS IN A CONTROLLED RISK REGIME, WITH
APPLICATIONS TO THE DESIGN, MANAGEMENT OF SERVICES AND TERRITORY PLANNING; ACQUISITION OF METHODS E
TOOLS TO PLAN THE COLLECTION OF DATA IN ORDER TO ALLOW OBJECTIVE ANALYSIS OF THE PROBLEM TREATED;
ACQUISITION OF METHODS AND TOOLS TO ANALYZE THE EFFECT OF DIFFERENT FACTORS ON A PHENOMENON
OF INTEREST AND MAKE QUANTITATIVE COMPARISONS BETWEEN THEM; ACQUISITION OF METHODS AND TOOLS FOR CONSTRUCTING E
SUBJECT INTERPRETATIVE MODELS OF A PHYSICAL OR TECHNOLOGICAL PHENOMENON TO EXPERIMENTAL VERIFICATION.
KNOWLEDGE AND UNDERSTANDING:
UNDERSTANDING THE DESCRIPTION OF NON-DETERMINISTIC PHENOMENA BASED ON PROBABILITY THEORY.
UNDERSTANDING THE DESCRIPTION OF THE VARIABILITY OF A PHENOMENON THROUGH RANDOM VARIABLES, THEIR TRANSFORMATIONS AND THEIR PROBABILITY MODELS. UNDERSTANDING THE BASIC ELEMENTS OF INDUCTIVE REASONING AND THE BASIC ELEMENTS OF DESCRIPTIVE STATISTICS AND INFERENTIAL STATISTICS.
UNDERSTANDING THE ANALYSIS AND DESCRIPTION OF A PHENOMENON USING LINEAR REGRESSION MODELS.
UNDERSTANDING OF THE BASIC ELEMENTS FOR RELIABILITY ANALYSIS AND RISK ANALYSIS AND OF THE ELEMENTS OF EXTREME VALUE THEORY.
ABILITY TO APPLY KNOWLEDGE AND UNDERSTANDING:
ABILITY TO ANALYZE NON-DETERMINISTIC PHENOMENA. ABILITY TO ESTIMATE UNKNOWN QUANTITIES OF A PHENOMENON ON A STATISTICAL BASIS. ABILITY TO CARRY OUT HYPOTHESIS TESTING ON A STATISTICAL BASIS. ABILITY TO SET SIMPLE DESIGN PROBLEMS ON A PROBABILISTIC BASIS. ABILITY TO CARRY OUT RELIABILITY ASSESSMENTS OF SYSTEMS AND STRUCTURES.
ABILITY TO ANALYZE EXTREME PHENOMENA AND ESTIMATE THEIR RETURN PERIODS.
INDEPENDENT JUDGMENTS:
BEING ABLE TO IDENTIFY THE MOST APPROPRIATE METHODS FOR ANALYZING A NON-DETERMINISTIC PHENOMENON. KNOWING HOW TO CHOOSE THE MOST APPROPRIATE STATISTICAL PROCEDURE TO ESTIMATE UNKNOWN QUANTITIES AND/OR VERIFY ALTERNATIVE HYPOTHESES BETWEEN THEMSELVES.
KNOWING HOW TO CRITICALLY ANALYZE THE RESULTS PROVIDED BY STATISTICAL PROCESSING SOFTWARE.
COMMUNICATION SKILLS:
BEING ABLE TO EXPOSE BOTH ORALLY AND IN WRITING A TOPIC RELATED TO THE PROBABILISTIC EVALUATION OF A RANDOM PHENOMENON.
KNOWING HOW TO EXPOSE THE TOPICS OF STATISTICAL DATA ANALYSIS IN A CORRECT AND COMPLETE MANNER.
LEARNING ABILITY:
BEING ABLE TO APPLY THE KNOWLEDGE ACQUIRED TO CONTEXTS DIFFERENT THAN THOSE PRESENTED DURING THE COURSE.
KNOWING HOW TO USE DIFFERENT SOURCES TO EXPLAIN THE METHODOLOGIES INTRODUCED IN THE COURSE.
Prerequisites
TEACHING MATHEMATICS I IS PREPARATORY FOR TEACHING.
IN PARTICULAR, KNOWLEDGE RELATING TO BASIC MATHEMATICAL ANALYSIS IS REQUIRED, WITH PARTICULAR REFERENCE TO:
ALGEBRAIC EQUATIONS AND INEQUATIONS, STUDY OF THE GRAPH OF A FUNCTION OF A REAL VARIABLE, NUMERICAL SEQUENCES AND SERIES, LIMITS OF A FUNCTION, CONTINUITY AND DERIVABILITY OF A FUNCTION, FUNDAMENTAL THEOREMS OF DIFFERENTIAL AND INTEGRAL CALCULUS.
Contents
SEQUENCES OF FUNCTIONS (4 HOURS)
PUNCTUAL AND UNIFORM CONVERGENCE. MAIN THEOREMS (CONTINUITY OF THE LIMIT, TRANSITION TO THE LIMIT UNDER THE SIGN OF INTEGRAL AND DERIVATIVE). UNIFORM CAUCHY CRITERION
(LESSONS 4 HOURS; EXERCISES 0 HOURS)

SERIES OF FUNCTIONS (4 HOURS)
PUNCTUAL, UNIFORM, TOTAL CONVERGENCE. POWER SERIES. MAIN THEOREMS (CAUCHY-HADAMARD, D'ALEMBERT, INTEGRATION AND DERIVATION BY SERIES)
(LESSONS 3 HOURS; EXERCISES 1 HOUR)

FUNCTIONS OF MULTIPLE VARIABLES (12 PM)
LIMITS AND CONTINUITY. PARTIAL AND DIRECTIONAL DERIVATIVES. MAIN THEOREMS (SCHWARZ, TOTAL DIFFERENTIAL, DERIVATION OF COMPOSITE FUNCTIONS). GRADIENT. DIFFERENTIABILITY. RELATIVE MAXIMUM AND MINIMUM
(LESSONS 9 HOURS; EXERCISES 3 HOURS)

ORDINARY DIFFERENTIAL EQUATIONS (2 PM)
PARTICULAR INTEGRAL AND GENERAL INTEGRAL. THE CAUCHY PROBLEM. THEOREMS OF EXISTENCE AND LOCAL AND GLOBAL UNIQUENESS. MAIN FIRST ORDER DIFFERENTIAL EQUATIONS. LINEAR DIFFERENTIAL EQUATIONS WITH CONSTANT COEFFICIENTS OF ORDER N HOMOGENEOUS AND NON-HOMOGENEOUS
(LESSONS 9 HOURS; EXERCISES 5 HOURS)

INTEGRALS OF FUNCTIONS OF MULTIPLE VARIABLES (2 PM)
PROPERTY. APPLICATION TO AREAS AND VOLUMES. REDUCTION FORMULAS. CHANGE OF VARIABLES
(LESSONS 9 HOURS; EXERCISES 5 HOURS)

CURVES AND CURVILINEAR INTEGRALS (6 HOURS)
REGULAR CURVES. LENGTH OF A CURVE. CURVILINEAR INTEGRAL OF A FUNCTION
(LESSONS 4 HOURS; EXERCISES 2 HOURS)


DIFFERENTIAL FORMS (10 AM)
VECTOR FIELDS. CURVILINEAR INTEGRAL OF A LINEAR DIFFERENTIAL FORM. CLOSED AND EXACT FORMS. ACCURACY CRITERIA
(LESSONS 7 HOURS; EXERCISES 3 HOURS)

SURFACES AND SURFACE INTEGRALS (4 HOURS)
AREA OF A SURFACE AND SURFACE INTEGRALS. DIVERGENCE THEOREM. STOKES FORMULA
(LESSONS 3 HOURS; EXERCISES 1 HOUR)

LINEAR ALGEBRA (4 PM)
VECTORS AND MATRIXES. ELEMENTARY OPERATIONS. LINEARLY INDEPENDENT AND LINEARLY DEPENDENT VECTORS. SYSTEMS OF LINEAR EQUATIONS. EIGENVALUES AND EIGENVECTORS
(LESSONS 9 HOURS; EXERCISES 7 HOURS)

ANALYTICAL GEOMETRY (6 HOURS)
LINES AND PLANES IN R^2 AND R^3
(LESSONS 3 HOURS; EXERCISES 3 HOURS)
Teaching Methods
THE COURSE INCLUDES THEORETICAL LESSONS, DURING WHICH THE TOPICS OF THE COURSE WILL BE PRESENTED THROUGH LECTURES (60 HOURS) AND CLASSROOM EXERCISES (30 HOURS), DURING WHICH THE MAIN TOOLS NECESSARY FOR THE RESOLUTION OF EXERCISES RELATED TO THE CONTENTS OF THE 'TEACHING.
ATTENDANCE IS MANDATORY
Verification of learning
THE EXAM CONSISTS OF A WRITTEN TEST AND AN ORAL TEST.

THE WRITTEN TEST HAS A DURATION OF 2:30 HOURS AND CONSISTS OF THE SOLUTION OF SIX EXERCISES ON THE FOLLOWING TOPICS:
- EXTREME OF FUNCTIONS OF TWO VARIABLES,
- ORDINARY DIFFERENTIAL EQUATIONS,
- DIFFERENTIAL FORMS IN R^2,
- INTEGRALS OF FUNCTIONS OF TWO VARIABLES ON A DOMAIN OF R^2,
- EIGENVALUES AND EIGENVECTORS OF LINEAR TRANSFORMATIONS IN R^3,
- ANALYTICAL GEOMETRY IN SPACE.

THE ASSESSMENT OF THE TEST VARIES FROM THE MINIMUM INDICATED BY BAND "E" TO THE MAXIMUM INDICATED BY BAND "A". TO BE ADMITTED TO THE ORAL IT IS NECESSARY TO SUFFICIENTLY PERFORM AT LEAST TWO EXERCISES OUT OF THE FIRST FOUR AND AT LEAST ONE OF THE NEXT TWO. OVERALL TO BE ADMITTED YOU MUST HAVE A RATING AT LEAST EQUAL TO BAND "D".

THE ORAL INTERVIEW LASTS ABOUT 20 MINUTES AND EVALUATES THE KNOWLEDGE ACQUIRED.

THE ORAL EXAM LASTS ABOUT 20 MINUTES AND IS AIMED TO ASSESS THE KNOWLEDGE OF THE COURSE TOPICS AND COVERS THE DEFINITIONS, THEOREMS AND THEIR PROOFS AND OCCASIONALLY THE SOLUTION OF SIMPLE EXERCISES.

IN THE FINAL ASSESSMENT, EXPRESSED IN THIRTIETHS, THE EVALUATION OF THE WRITTEN TEST WEIGHS FOR 40%, WHILE THE INTERVIEW WEIGHS FOR THE REMAINING 60%.
PRAISE IS AWARDED IF BOTH THE WRITTEN TEST AND THE ORAL TEST ARE PASSED WITH BRILLIANTS.
Texts
THEORY
- N. FUSCO, P. MARCELLINI, C. SBORDONE, “ELEMENTS OF MATHEMATICAL ANALYSIS 2”, LIGUORI EDITORE
- COURSE NOTES

EXERCISES
- P. MARCELLINI - C. SBORDONE, “MATHEMATICS EXERCISES VOL. 2ND FIRST AND SECOND PART“, LIGUORI EDITORE
More Information
THE TEACHING IS PROVIDED IN PRESENCE WITH MANDATORY FREQUENCY. THE LANGUAGE OF TEACHING IS ITALIAN.
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