How to Transform a Contravariant and Covariant Tensor under a change of coordinates @FacultyofKhan
How to Transform a Contravariant and Covariant Tensor under a change of coordinates  @FacultyofKhan
Uploaded May 2025 | Updated September 2026, 2 weeks ago
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Video covering examples of how to transform a contravariant tensor and covariant tensor (of rank 1, so a vector) when there is a coordinate transformation. For the covariant tensor, we even use that coordinate transformation to find the general solution of a 1st-order PDE!

Questions/requests? Let me know in the comments!

Pre-requisites: Previous videos in this playlist: youtube.com/playlist?list=PLdgVBOaXkb9D6zw47gsrtE5XqLeRPh27_

Special thanks to my Patrons:
Patapom
Eugene Bulkin
Andy Johnston
Patrick Gibson
Joseph Dubeau
David Johnston

#Tensors #TensorMath #TensorIntro

This video was sponsored by Brilliant.
How to Transform a Contravariant and Covariant Tensor under a change of coordinatesIntroducing Special Relativity and the Relativity of SimultaneityThe Lorentz Transformation | Special RelativitySupercritical and Subcritical Pitchfork Bifurcations | Nonlinear Dynamics and ChaosDeriving the Second Variation | Calculus of VariationsThe Spacetime Interval and Causality | Special RelativityDAlembert Solution to the Wave EquationThe Vertebrobasilar Circulation | NeurologyBessel Function of the 2nd Kind | 2nd solution of Bessels EquationTheorems on Stationary States | Quantum MechanicsCurvature: Intuition and Derivation | Differential GeometryIntroducing Torsion and Special Planes | Differential Geometry
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How to Transform a Contravariant and Covariant Tensor under a change of coordinates

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