Lyoubomira SOFTOVA PALAGACHEVA | DIFFERENTIAL EQUATIONS
Lyoubomira SOFTOVA PALAGACHEVA DIFFERENTIAL EQUATIONS
cod. 0512300025
DIFFERENTIAL EQUATIONS
| 0512300025 | |
| DEPARTMENT OF MATHEMATICS | |
| EQF6 | |
| MATHEMATICS | |
| 2024/2025 |
| YEAR OF COURSE 3 | |
| YEAR OF DIDACTIC SYSTEM 2018 | |
| AUTUMN SEMESTER |
| SSD | CFU | HOURS | ACTIVITY | |
|---|---|---|---|---|
| MAT/05 | 6 | 48 | LESSONS |
| Exam | Date | Session | |
|---|---|---|---|
| EQUAZIONI DIFFERERNZIALI | 21/01/2025 - 09:00 | SESSIONE ORDINARIA | |
| EQUAZIONI DIFFERERNZIALI | 21/01/2025 - 09:00 | SESSIONE DI RECUPERO | |
| EQUAZIONI DIFFERERNZIALI | 06/02/2025 - 09:00 | SESSIONE ORDINARIA | |
| EQUAZIONI DIFFERERNZIALI | 06/02/2025 - 09:00 | SESSIONE DI RECUPERO | |
| EQUAZIONI DIFFERERNZIALI | 21/02/2025 - 09:00 | SESSIONE ORDINARIA | |
| EQUAZIONI DIFFERERNZIALI | 21/02/2025 - 09:00 | SESSIONE DI RECUPERO |
| Objectives | |
|---|---|
| THE MAIN GOAL OF THE COURSE IS TO INTRODUCE THE STUDENTS TO THE THEORY OF ORDINARY DIFFERENTIAL EQUATIONS, SYSTEMS OF ORDINARY DIFFERENTIAL EQUATIONS AND VARIOUS PROBLEMS WITH INITIAL DATA AND DATA ON THE BORDER. THERE ARE PRESENTED DIFFERENT METHODS FOR SOLVING FIRST ORDER AND HIGHER ORDER DIFFERENTIAL EQUATIONS, THE STURM-LIOUVILLE PROBLEM, THE LAPLACE TRASFORM AND APPLICATIONS. |
| Prerequisites | |
|---|---|
| BASIC PROPERTIES OF FUNCTIONS OF A REAL VARIABLE: CONTINUITY, DIFFERENTIABILITY, INTEGRATION. LINEAR DIFFERENTIAL EQUATIONS WITH CONSTANT COEFFICIENTS |
| Contents | |
|---|---|
| DIRECTIONAL FIELDS, ISOCLINES AND INTEGRAL CURVES. (2H LECTURES) FIRST-ORDER EQUATIONS RESOLVABLE THROUGH SUBSTITUTIONS, BERNOULLI EQUATION, RICCATI EQUATION, HOMOGENEOUS EQUATIONS AND EXACT DIFFERENTIAL EQUATIONS. EQUATIONS NON-RESOLVABLE WITH RESPECT TO THE DERIVATIVE. (6H LECTURES) CAUCHY PROBLEM AND DEPENDENCE OF THE SOLUTION FROM THE INITIAL DATA AND PARAMETERS. GRONWALL LEMMA. (2H LECTURES) HIGHER ORDER EQUATIONS RESOLVABLE THROUGH SUBSTITUTIONS. LINEAR EQUATIONS WITH VARIABLE COEFFICIENTS. EULER EQUATION. (8H LECTURES) FIRST-ORDER EQUATION SYSTEMS. LINEAR SYSTEMS, EXISTENCE AND UNIQUENESS THEOREMS. FUNDAMENTAL MATRIX. EIGENVALUES AND EIGENVECTORS. (8H LECTURES) AUTONOMOUS SYSTEMS. STABILITY AND BALANCE POINTS. LINEARIZATION OF NONLINEAR SYSTEMS. MATHEMATICAL MODELS. (8H LECTURES) BOUNDARY PROBLEMS, GREEN FUNCTION. THE STURM-LIOUVILLE PROBLEM. SOME APPLICATIONS TO PDE. (6H LECTURES) LAPLACE TRANSFORM AND ANTITRANSFORM. APPLICATION TO DIFFERENTIAL EQUATIONS. (6H LECTURES) MATHEMATICAL MODELS (2H-LEZIONI). |
| Teaching Methods | |
|---|---|
| FRONTAL LECTURES (48H). |
| Verification of learning | |
|---|---|
| THE VERIFICATION OF LEARNING TAKES PLACE THROUGH THE DISCUSSION OF A TERM PAPER THAT FOCUSES ON A THEORETICAL TOPIC AND ON MATHEMATICAL MODELS CONCERNING THE MAIN APPLICATIONS OF THE TREATED ARGUMENTS. BOTH THE EXPOSURE AND THE LEVEL OF DETAIL OF THE ASSIGNED TOPIC AS WELL AS THE RIGOR AND METHODOLOGY OF CARRYING OUT THE EXERCISES WILL BE EVALUATED. THE MINIMUM GRADE OF 18/30 IS ASSIGNED WHEN THE THEORETICAL KNOWLEDGE IS SCARCE AND THE DEVELOPMENT OF THE PROBLEMS IS PARTIAL. THE MAXIMUM VOTE 30/30 IS ASSIGNED IF THE STUDENT DEMONSTRATES MASTERY OF ALL THE TOPICS TREATED IN THE COURSE. LODE IS AWARDED WHEN BOTH THE PRESENTATION AND THE ABILITY TO APPLY THEORETICAL KNOWLEDGE TO CREATE MATHEMATICAL MODELS BY DESCRIBING GEOMETRIC, PHYSICAL OR MECHANICAL PROBLEMS ARE EXCELLENT. AN ORAL EXAM AND INCLUDES A WRITTEN EXAM, TO INTEGRATE THE ORAL EXAM. IN PARTICULAR, ON THE BASIS OF METHODOLOGIES, INSTRUMENTS AND CONTENT GIVEN DURING THE LESSONS, THE STUDENT MUST DEMONSTRATE THAT HE IS ABLE TO UNDERSTAND THE PROBLEM, FIND THE CORRECT MATHEMATICAL-QUANTITATIVE INTERPRETATION, RECOGNIZE THE APPROPRIATE METHOD, UNDERSTAND THE ANSWERS DEDUCED BY THE METHOD AND ITS INFERENCES. |
| Texts | |
|---|---|
| C.PAGANI, S. SALSA, ANALISI MATEMATICA 2, ZANICHELLI, 2016 A. AMBROSETTI, APPUNTI SULLE EQUAZIONI DIFFERENZIALI ORDINARIE, SPRINGER-VERLAG 2012 P.L. KORMAN, LECTURES ON DIFFERENTIAL EQUATIONS, AMS/MAA TEXTBOOKS, VOL. 54, 2019 |
| More Information | |
|---|---|
| LSOFTOVA@UNISA.IT LBSOFTOVA@YAHOO.COM |
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