Differential geometry | Differential geometry lecture video | Differential geometry msc mathematics

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Differential geometry is a challenging subject. In this differential geometry lecture video I have explained the basic concepts of differential geometry, the Msc mathematics part and how it is related to General theory of relativity. I have covered the basic concepts, including manifold, open balls, open sets, smooth surfaces, charts, transition map and other things. I have also related these concepts to General theor of relativity and how differential geometry helps to measure the curvature of spacetime.

00:00 - 01:16 - Introduction
01:17 - 02:36 - Topics
02:37 - 09:11 - What is a manifold?
09:12 - 10:55 - What is an ambient space
10:56 - 16:39 - Manifold, Charts & Atlas
16:40 - 17:42 - Defining a space
17:43 - 18:00 - Magnitude (Norm)
18:01 - 21:39 - What are open sets
21:40 - 24:26 - What is an open ball
24:27 - 25:49 - What is an open disk
25:50 - 27:24 - Parameterizing a line
27:25 - 31:37 - Smooth paths & smooth surfaces
31:38 - 33:27 - Smooth surface
33:28 - 34:54 - Smooth path
34:55 - 35:39 - Examples of parameter
35:40 - 39:37 - What is a chart?
39:38 - 48:46 - Investigating curved space time
48:47 - 50:46 - Summary

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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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[nothing_is_real_]

Wow. Much needed topic. Thank you so much for high quality tutorials.

[Prof_Hazra_IIT]

Absolutely brilliant. Heartiest wishes. Please make another video on this topic considering these topics: Lie Group-Lie algebra correspondence, how to write a geometric lagrangian and how to solve differential equations on smooth Manifolds.

[drlalitsingh]

Sir,
It would be better, if there would be a series of entire general theory of relativity.

[p.kalyanachakravarty]

Hello Sir!
At 4:14 it has been mentioned that “Manifold is a topological space that locally resembles a Euclidean space”.
Sir then why do we need these new concepts if we can manage with Euclidean geometry?

[p.kalyanachakravarty]

Sir at 11:51 in the section of “what is a manifold ? “you have drawn arrows to top, bottom, right and left on the circular arcs. Sir how did you find these directions on each arc and why is y taken to be positive ?

[p.kalyanachakravarty]

Hello Sir!
How is the subject of Topology related to Differential Geometry ?

[p.kalyanachakravarty]

Sir I have been trying since yesterday night to give reply to the message you posted last night but I am unable to do so and I am not able to figure out the reason for that. Please see..