Differential geometry | What is differential geometry | Differential geometry msc mathematics

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Differential geometry is an important subject in M.Sc. mathematics. What is differential geometry? In this video, I have covered some of the basic and fundamental concepts of differential geometry. First, I have introduced the concept of curvature and how to calculate the curvature. Next, I have explained what is an Euclidean space. Further to that I have explained the concept of parameter and showed examples of parameterizing with a straight line and a helix. Are corners and cusps differentiable? That would be the topic for the next video.

00:00 - 01:25 - Objective of this video
01:26 - 02:13 - Topics covered
02:14 - 07:46 - What is a curvature?
07:47 - 11:26 - Euclidean space
11:27 - 13:14 - Why do we need to parameterize?
13:15 - 14:20 - Parameterization, technical definition
14:21 - 15:23 - Examples, straight line & Helix
15:24 - 16:03 - Example with tangent line
16:04 - 16:25 - Corners & cusps, are they differentiable?
16:26 - 18:14 - Topics for the next video

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My name is Shounak. I teach in a college. My subject of specialization is the general theory of relativity, tensor calculus, and topology. I also teach communicative English.
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