The course “Topics in differential geometry” introduces basic and important objects which are widely used in mathematics and physics : vector fields and differential forms. Firstly, we propose a geometric point of view on differential equations using the langage of vector fields, their integral curves and their flows. Secondly, we define differential forms and the exterior differentiation of such forms. Many formulas used in physics (Gauss- Green-Riemann-Ostrogradski-Stokes) are naturally expressed and unified in those terms and will illustrate the course.
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Pour les étudiants du diplôme Bachelor of Science de l'Ecole polytechniqueLe rattrapage est autorisé (Note de rattrapage conservée)
- Crédits ECTS acquis : 4 ECTS