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Currently Playing: Relativity 105c: Acceleration - The Jacobian (changing basis in curvilinear Rindler coordinates)

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 Previous videos on the Jacobian from my Tensor Calculus series: TC2 - Polar Coordinates : https://www.youtube.com/watch?v=rr5qEb_kT6c&list=PLJHszsWbB6hpk5h8lSfBkVrpjsqvUGTCx&index=3&t=212s TC3 - Jacobian : https://www.youtube.com/watch?v=OMCguyCnTQk&list=PLJHszsWbB6hpk5h8lSfBkVrpjsqvUGTCx&index=4&t=378s TC4 - Tangent Vectors : https://www.youtube.com/watch?v=9yOb9gHnLUk&list=PLJHszsWbB6hpk5h8lSfBkVrpjsqvUGTCx&index=5&t=6s TC5 - Vector Transformation Rules : https://www.youtube.com/watch?v=zKuyaQ4JRs8&list=PLJHszsWbB6hpk5h8lSfBkVrpjsqvUGTCx&index=6&t=389s 0:00 Intro to Jacobian 2:45 Multivariable Chain Rule 7:20 Basis vectors as Partial Derivatives 14:23 Change to Rindler Basis (Jacobian) 18:42 Change back to Inertial Basis (Inverse Jacobian) 22:28 All change-of-basis matrices are Jacobians 25:05 Change-of-components to Rindler coordinates 31:21 Change-of-components to Inertial coordinates 33:23 Summary