ВВЕДЕНИЕ В ВАРИАЦИОННЫЙ АНАЛИЗ ЗА 21 МИНУТУ!

#math #maths #mathematics #mathanalysis #variationalanalysis #variations #variation #function #functionalanalysis #shiz Chapters: 00:00 Intro 00:10 1. Extrema 01:12 Leibniz's 1684 work 02:02 Where is extrema theory applied? 04:09 2. Generalization 04:18 Comparison of classical and variational analysis 05:18 Examples of functionals for optimization 05:40 Analogy of analogies 06:18 3. Differentiation of functionals 07:18 Typical function spaces for variance analysis 07:55 Fréchet is direction-independent 08:25 Action of variance Derivative in terms of the skew field or brackets 08:50 4. Necessary Condition for an Extremum 10:09 Du Bois-Reymond Lemma 11:15 5. Alternative Derivation via Finite-Dimensional Approximations 12:00 Acceleration on Generalized Functions 13:10 The Geometric Meaning of Local Variation 13:37 6. The Brachistochrone Problem 15:30 Euler/Leibniz Solution 17:10 Solution Using Variational Calculus Methods 17:30 Conditional Extremum 18:50 Theorem for Isoparametric Problems 19:03 Dido's Problem 19:58 8. Problems 20:30 A Little About Optimal Control 21:10 Bye! tg: t.me/FluxiaMonada You can support the author financially here: donationalerts.com/r/don_rumata_01 Music by Vincent Rubinetti Download the music on Bandcamp: https://vincerubinetti.bandcamp.com Stream the music on Spotify: https://open.spotify.com/artist/2SRhE...