Differential Geometry: Lecture 4 part 1: curves and velocity

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Here we introduce the idea of a curve as a mapping, briefly discuss the need for regularity and show how the velocity acts on functions when we view tangent vectors as derivations.
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How is this space-filling curve constructed?

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Really why this music ? she give me head ache i can not even listing ? the explain fantastic but the music it is noise my ear

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