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PDE. Lecture A1. Auxiliary Material for Derivation of PDE Models
Автор: Partial Education
Загружено: 2023-01-30
Просмотров: 391
Описание:
In this video we remind some facts from vector calculus, that are used in PDE courses. We start with the lemma stating that if integral over any subdomain of a continuous function vanishes, then the function is identically zero. Then we review the notion of parametrized surfaces, line and surface integrals as well as theorems of vector calculus.
1:22 Lemma, 1D case
5:32 Lemma, n-dimensional case
8:39 Parametrized surfaces
16:55 Line integrals
19:15 Integrals of scalar functions over a surface
21:00 Surface integrals of vector fields (fluxes).
24:18 Stokes' theorem
25:39 Green's theorem
27:06 Gauss' divergence theorem
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