Basics - Pre-Requisites

12 - General Relativity (Pre-requisites)

Lecture 01: How To Learn Mathematics for General Relativity

Lecture 02 : Einstein Field Equations Explained

Untitled presentation

Lecture 01: How To Learn Mathematics for General Relativity

How to learn General Theory of Relativity. How to understand the mathematics of General Relativity. Welcome to the first episode in this series of videos. In this first episode you will learn, what is General Relativity and how it is different from the flat Euclidean space. You will also come to know about the geometry of spacetime, which will help you to realize that you are entering into a world of geometry and the mathematics is more on the geometry of spacetime. This first episode, gives you a complete understanding on the need of calculus, especially partial differential equation, its importance and its role in General Relativity. You will come to know the major concepts that play a crucial role in understanding General Relativity as well as the best books on calculus that you can read. These books include both ordinary differential equations but mostly partial differential equations.

00:00 - 01:16 - Introduction

01:17 - 08:39 - What is General Relativity

08:40 - 13:32 - Curvature of spacetime

13:33 - 15:30 - Preparation for General Relativity

15:31 - 22:14 - Why you need Calculus to learn General Relativity

22:15 - 27:14 - Concepts of Calculus related to General Relativity

27:15 - 31:03 - Calculus books

31:04 - 36:26 - Partial differential equations book

36:27 - 37:36 - Need of calculus to learn Relativity

37:37 - 38:15 - Conclusion

00:00 - 01:21 - Introduction

01:22 - 06:07 - Recap of the earlier video

06:08 - 14:08 - Why do you need Linear Algebra

14:09 - 17:03 - Linear Algebra and General Relativity

17:04 - 22:33 - Elementary linear algebra by Anton Rorres

22:34 - 23:50 - Linear Algebra by Gilbert Strang

23:51 - 24:50 - Linear Algebra Done Right book review

24:51 - 26:06 - Schaum outline Linear Algebra

26:07 - 26:35 - Linear Algebra an introduction by Bronson Costa

26:36 - 27:42 - What is the sequence of reading the books

27:43 - 28:38 - Conclusion

00:00 - 01:20 - Introduction

01:21 - 04:48 - Recap of the earlier video

04:49 - 05:42 - Tensors and Linear Algebra

05:43 - 08:35 - Misconceptions about Tensors

08:36 - 13:35 - What is a Tensor

13:36 - 17:07 - Einstein field equations explained

17:08 - 21:15 - Origin of tensors

21:16 - 23:20 - Mathematics required for tensors

23:21 - 26:02 - Tensor transformation

26:03 - 27:28 - Tensor and General Relativity

27:29 - 30:29 - Stress energy momentum tensor

30:30 - 31:15 - Covariant derivative

31:16 - 32:52 - Ricci tensor and Ricci Scalar

32:52 - 35:00 - How tensors make your life easy

35:01 - 37:44 - Tensors and Covariant derivative

37:45 - 38:41 - Online resources for learning tensors

38:42 - 48:49 - Best book for Tensor Analysis

48:50 - 50:14 - In which order to read the books

50:15 - 51:03 - Conclusion

00:00 - 01:12 - Introduction

01:13 - 04:49 - A quick recap

04:50 - 06:39 - Flat spacetime and Curved spacetime

06:40 - 09:31 - Geometry of gravity

09:32 - 14:01 - Role of differential geometry in GR

14:02 - 29:25 - Why do we need Differential Geometry

29:26 - 35:44 - Manifolds and General Relativity

35:45 - 37:28 - Why you should learn Manifold

37:29 - 46:53 - Books on Manifold

46:54 - 50:22 - Best online lectures on Manifold

50:23 - 52:48 - Metric Tensor and General Relativity

52:49 - 53:45 - Geodesics and General Relativity

53:46 - 01:05:42 - Best books on Differential Geometry

01:05:43 - 01:06:31 - Conclusion

00:00 - 00:59 - Introduction

01:00 - 04:35 - Recap of the earlier video

04:36 - 08:22 - What is Non Euclidean Geometry

02:23 - 14:48 - Why you need to learn NE Geometry

14:49 - 23:05 - Euclidean and non Euclidean geometries

23:05 - 30:20 - Book on history of Geometry

30:21 - 35:26 - Book on foundation of NEGgeometry

35:27 - 38:24 - Book 3 Geometry Illuminated

38:25 - 36:06 - In which sequence you will read the books

36:07 - 39:50 - Conclusion

Lecture 02 : Einstein Field Equations Explained

Einstein field equations are a set of equations which are very important to General relativity. I have Einstein field equations have been explained in this video. First, I have discussed about the objective of the video and then the importance of Einstein's field equations. Further, I have demonstrated about the non-linear partial differential equations and the reason why they are called non-linear. I have also given illustrations about what is a field in physics and then why it is called a field equation. I have taken each and every component and explained Ricci scalar, Ricci tensor, metric tensor, stress-energy-momentum tensor and other aspects.