Differential Geometry | Differential Geometry Lectures | Differential Geometry and Tensor Analysis

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In this video on differential geometry, you will first learn some of the important concepts. These concepts include curves, parametric curves, implicit functions, and others. You will also learn about Euclidean geometry, Euclid's fifth postulate, and the birth of axiomatic geometry. You will also learn how geometers have been trying to prove Euclid's fifth postulate. You will come to know the emergence of hyperbolic geometry and the ideas of Saccheri and Lambert.

00:00 - 03:36 - Core ideas of Differential Geometry
03:37 - 08:08 - Curves and their representations
08:09 - 11:41 - The need for parametric curves
11:42 - 15:41 - Vector valued functions in geometry
15:42 - 16:46 - Motion along parametric curves
16:47 - 22:03 - Transition to Differential Geometry
22:04 - 24:53 - Euclidean geometry
24:54 - 27:56 - Birth of Axiomatic geometry
27:57 - 32:06 - Beyond Euclidean geometry
32:07 - 33:57 - Mystery of Euclid's fifth axiom
33:58 - 35:56 - Many faces of the parallel axiom
35:57 - 38:44 - Hyperbolic geometry
38:45 - 42:02 - Emergence of Hyperbolic geometry
42:03 - 44:44 - Saccheri and Lambert's revolutionary ideas
44:45 - 48:01 - Johann Heinrich Lambert and a new geometry
48:02 - 52:20 - Beltrami's model of hyperbolic geometry
52:21 - 53:09 - Conclusion

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