Differential geometry lecture | What is differential geometry | History of differential geometry

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This is an introduction to differential geometry. What is differential geometry? This is a very common question. I have discussed in details about differential geometry along with the history of differential geometry.

00:00 - 00:51 - Introduction
00:51- 02:24 - What is differential geometry:
02:24 - 04:53 - Branches of differential geometry
04:53 - 05:50 - The objective of this program
05:50 - 07:50 - What is a smooth manifold:
07:51 - 09:07 - What is smoothness?
09:09 - 11:08 - What do we need abstractness?
11:09 - 12:59 - Which one should I study first: Topology or differential geometry
13:00 - 13:58 - Why do we apply calculus to differential geometry
13:59 - 19:43 - Why should I learn differential geometry
19:44 - 21:22 - Is Differential Geometry Difficult
21:23 - 31:44 - History of differential geometry
31:44 - 35:52 - Who discovered non-Euclidean geometry?
35:52 - 40:45 - Gauss' contribution to differential geometry-
40:46 - 46:35 - Riemann's contribution to differential geometry-
46:36 - 49:22 - Elwin Bruno Christoffel
49:23 - 54:41 - Ricci Curbastro
54:42 - 57:25 - Luigi Bianchi-
57:26 - 1:08:30 - Modern Differential Geometry
01:08:30 - 01:12:22 - Conclusion

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My name is Shounak. I teach in a college.

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[GeodesicBruh]

I can feel the passion you have for the subject as well as teaching.

A thing that not many professors have sadly. Thank you for these great videos.

Thank you a lot for helping the physicists and mathematicians of the future

[ramazen]

Excellent introduction to Differential Geometry. Thank you. I wish similar explanations and backgrounds are given for all the topics in mathematics.

[RahulSharmaSingularity]

This a detailed yet excellent explanation on starting their route to Differential Geo and GR ! Awesome and keep going ! Much love from Canada

[dilrubayeasmin]

Before studying over the Differential geometry i wanted to know, why I've to study it? What I'm going to learn from it? That's why, I've come here, but really I'm the lucky one who have found this video..🙂

Just want to say thank u sir from the bottom of my heart.

[thabolikotsi]

Thank you I'm doing General Relativity second semester and might study Differential Geometry next year

[waynerl]

re visualize abstract spaces:
metrics of curvature of a real metric ( space) ..clearly represented as imaginary...
ARE Imaginary quantities.

Thus creating an opportunity for a cyclic variable!!

[waynerl]

Physics is a finitary subset of mathematics.
Singularities are to be Removed.