Relativity 107b: General Relativity Basics - Manifolds, Covariant Derivative, Geodesics

Full relativity playlist: https://www.youtube.com/playlist?list=PLJHszsWbB6hqlw73QjgZcFh4DrkQLSCQa Powerpoint slide files: https://github.com/eigenchris/MathNotes/tree/master/Relativity Leave me a tip: https://ko-fi.com/eigenchris You are free to continue watching to the next video, but if you feel you are getting confused, here are some other videos on geodesics and the covariant derivative: TC 15 - Geodesics + Christoffel Symbols on Sphere: https://www.youtube.com/watch?v=1CuTNveXJRc&list=PLJHszsWbB6hpk5h8lSfBkVrpjsqvUGTCx&index=17 TC 16 - Geodesics on Sphere example: https://www.youtube.com/watch?v=8sVDceI70HM&list=PLJHszsWbB6hpk5h8lSfBkVrpjsqvUGTCx&index=18 TC 17 - Flat Space Definition: https://www.youtube.com/watch?v=U5iMpOn5IHw&list=PLJHszsWbB6hpk5h8lSfBkVrpjsqvUGTCx&index=19 TC 17.5 - Component Definition: https://www.youtube.com/watch?v=8S_XOjd5Mec&list=PLJHszsWbB6hpk5h8lSfBkVrpjsqvUGTCx&index=20 TC 18 - Extrinsic Definition: https://www.youtube.com/watch?v=Af9JUiQtV1k&list=PLJHszsWbB6hpk5h8lSfBkVrpjsqvUGTCx&index=21 TC 19 - Intrinsic Definition: https://www.youtube.com/watch?v=EFKBp52LtDM&list=PLJHszsWbB6hpk5h8lSfBkVrpjsqvUGTCx&index=22 TC 20 - Abstract Definition: https://www.youtube.com/watch?v=cEEahoUUGyc&list=PLJHszsWbB6hpk5h8lSfBkVrpjsqvUGTCx&index=23 0:00 Introduction 1:35 Equivalence Principle and Manifolds 6:15 Extrinsic vs Intrinsic views of Manifolds 10:29 Tangent Vectors on Manifolds 16:20 Covariant Derivative Notation 22:10 Levi Civita Connection 28:58 Geodesics 33:44 Summary