Lyoubomira SOFTOVA PALAGACHEVA | DIFFERENTIAL EQUATIONS
Lyoubomira SOFTOVA PALAGACHEVA DIFFERENTIAL EQUATIONS
cod. 0512300025
DIFFERENTIAL EQUATIONS
| 0512300025 | |
| DEPARTMENT OF MATHEMATICS | |
| EQF6 | |
| MATHEMATICS | |
| 2023/2024 |
| YEAR OF COURSE 3 | |
| YEAR OF DIDACTIC SYSTEM 2018 | |
| AUTUMN SEMESTER |
| SSD | CFU | HOURS | ACTIVITY | |
|---|---|---|---|---|
| MAT/05 | 6 | 48 | LESSONS |
| 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 OR DATA ON THE BORDER. THERE ARE PRESENTED DIFFERENT METHODS FOR SOLVING FIRST ORDER AND HIGHER ORDER DIFFERENTIAL EQUATIONS. THE QUALITATIVE STUDY OF AUTONOMOUS SYSTEMS OF THE FIRST ORDER IS ALSO PRESENTED. |
| 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. (8H 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. (4H LECTURES) LAPLACE TRANSFORM AND ANTITRANSFORM. APPLICATION TO DIFFERENTIAL EQUATIONS. (6H LECTURES) MATHEMATICAL MODELS (2H-LEZIONI). |
| Teaching Methods | |
|---|---|
| FRONTAL LECTURES |
| Verification of learning | |
|---|---|
| THE EXAM CONSISTS IN THE DISCUSSION OF A THESYS THAT FOCUSES ON A THEORY TOPIC AND AN APPLICATION PART THAT DEMONSTRATES THE STUDENT'S ABILITY TO CREATE AND SOLVE MATHEMATICAL MODELS THROUGH DIFFERENTIAL EQUATIONS. BOTH THE EXPOSURE AND LEVEL OF IN-DEPTH OF THE ASSIGNED TOPIC AS WELL AS THE RIGOROUSITY AND METHODOLOGY OF CARRYING OUT THE MATHEMATICAL MODELS WILL BE EVALUATED. THE MINIMUM MARK OF 18/30 IS ASSIGNED WHEN THEORETICAL KNOWLEDGE IS POOR AND THE WORKING OF THE PROBLEMS IS PARTIAL. THE MAXIMUM MARK OF 30/30 IS ASSIGNED IF THE STUDENT DEMONSTRATES MASTERY OF ALL THE TOPICS COVERED IN THE COURSE. LODE IS AWARDED WHEN BOTH THE PRESENTATION AND THE ABILITY TO APPLY THEORETICAL KNOWLEDGE TO CREATE MATHEMATICAL MODELS DESCRIBING GEOMETRIC, PHYSICAL OR MECHANICAL PROBLEMS IS EXCELLENT. |
| Texts | |
|---|---|
| A. AMBROSETTI, APPUNTI SULLE EQUAZIONI DIFFERENZIALI ORDINARIE, SPRINGER-VERLAG 2012 V.ARNOLD, ORDINARY DIFFERENTIAL EQUATIONS, SPRINGER-VERLAG, 1992 P.L. KORMAN, LECTURES ON DIFFERENTIAL EQUATIONS, AMS/MAA TEXTBOOKS, VOL. 54, 2019 C.PAGANI, S. SALSA, ANALISI MATEMATICA 2, ZANICHELLI, 2016 |
| More Information | |
|---|---|
| LSOFTOVA@UNISA.IT LBSOFTOVA@YAHOO.COM |
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