Lyoubomira SOFTOVA PALAGACHEVA | DIFFERENTIAL EQUATIONS
Lyoubomira SOFTOVA PALAGACHEVA DIFFERENTIAL EQUATIONS
cod. 0512300025
DIFFERENTIAL EQUATIONS
| 0512300025 | |
| DIPARTIMENTO DI MATEMATICA | |
| EQF6 | |
| MATHEMATICS | |
| 2021/2022 |
| 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 AND AUTONOMOUS SYSTEMS. 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 LESSONS) 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 LESSONS + 2H EXERCISES) CAUCHY PROBLEM AND DEPENDENCE OF THE SOLUTION FROM THE INITIAL DATA. GRONWALL LEMMA. (2H LESSONS) HIGHER ORDER EQUATIONS RESOLVABLE THROUGH SUBSTITUTIONS. LINEAR EQUATIONS WITH VARIABLE COEFFICIENTS. EULER EQUATION. (6H LESSONS + 2H EXERCISES) FIRST-ORDER EQUATION SYSTEMS. LINEAR SYSTEMS, EXISTENCE AND UNIQUENESS THEOREMS. FUNDAMENTAL MATRIX. EIGENVALUES AND EIGENVECTORS. (6H LESSONS + 2H EXERCISES) AUTONOMOUS SYSTEMS. STABILITY AND BALANCE POINTS. LINEARIZATION OF NONLINEAR SYSTEMS. MATHEMATICAL MODELS. (6H LESSONS + 4H EXERCISES) BOUNDARY PROBLEMS, GREEN FUNCTION. THE STURM-LIOUVILLE PROBLEM. (2H LESSONS + 2H EXERCISES) LAPLACE TRANSFORM AND ANTITRANSFORM. APPLICATION TO DIFFERENTIAL EQUATIONS. (4H LESSONS + 2H EXERCISES) |
| Teaching Methods | |
|---|---|
| FRONTAL LESSON PRACTICE LESSON |
| Verification of learning | |
|---|---|
| THE LEARNING VERIFICATION TAKES PLACE THROUGH 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 V.ARNOLD, ORDINARY DIFFERENTIAL EQUATIONS, SPRINGER-VERLAG, 1992 |
| More Information | |
|---|---|
| LSOFTOVA@UNISA.IT LBSOFTOVA@YAHOO.COM |
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