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This is my video series about Manifolds where we start with topology, talk about differential forms and integration on manifolds, and end with the famous Stoke's theorem. I hope that it will help everyone who wants to learn about it.
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00:00 Introduction
00:20 Overview
02:24 Stoke's theorem as the goal
02:56 Metric Spaces
04:56 Definition Topology
07:29 Simple examples of topological spaces
09:07 Credits
#Manifolds
#Mathematics
#LearnMath
#calculus
I hope that this helps students, pupils and others. Have fun!
(This explanation fits to lectures for students in their first and second year of study: Mathematics for physicists, Mathematics for the natural science, Mathematics for engineers and so on)
Manifolds 1 | Introduction and Topology [dark version]
Теги
MathsMeasuresStudyingExplanationsLearningMathematicsMatriceseliminationJordannormal formmatricestransformation matrixmetricsspacesfunctionalopenboundaryclosedclosurelimitssequenceCauchycompletenessBanachHilbertBanach spacelpsequencesSchwarzorthogonalboundedcontinuousoperatorcontinuityRieszcompactsetHölderHoelderdualspacedual spaceHahn BanachspectrumeigenvalueeigenvectorresolventtopologyStokesGaußdifferential formsintegral