| Educational guide School of Engineering |
english |
| Degree in Mathematical and Physical Engineering (2021) |
 Subjects |
| DIFFERENTIAL EQUATIONS I |
| Contents |
| IDENTIFYING DATA | 2023_24 |
| Subject | DIFFERENTIAL EQUATIONS I | Code | 17274006 | |||||
| Study programme |
|
Cycle | 1st | |||||
| Descriptors | Credits | Type | Year | Period | ||||
| 6 | Basic Course | First | 2Q |
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| Competences | Learning outcomes | Contents |
| Planning | Methodologies | Personalized attention |
| Assessment | Sources of information | Recommendations |
| Topic | Sub-topic |
| First-order ordinary differential equations | a. Definitions and terminology b. Intial value problem: theorems of existence and uniqueness c. Resolution of first-order ODEs d. Numerical methods for ODEs |
| Linear differential equations | a. First-order linear systems, and higher-order linear ODEs b. Linear dependency: the Wornskian c. Resolution of homogeneous equations d. Resolution of inhomogeneous equations e. Laplace transform |
| Qualitative theory of ordinary differential equations | a. Autonomous systems b. Phase space, phase plane, and phase portrait c. Fixed points and periodic orbits d. Stability: direct Lyapunov method e. Linearization: Hartman-Grobman theorem f. Alpha and omega limit sets: Poincaré–Bendixson theorem |
| Partial differential equations | a. Definitions and main PDEs in physics b. Boundary problem c. Resolution by separation of variables |
