Contravariant and Covariant Vectors | 2/2
In this video, I define contravariant and covariant vector components. Here, we define contravariant and covariant vector components according to their transformation definitions. I also define invariants, which are quantities with intrinsic significance.
I describe two examples of contravariant and covariant tensors. For contravariant tensors, I use the tangent vector of a parametric curve. For a covariant tensor, I use the example of a gradient vector of a scalar field.
Questions/requests? Let me know in the comments!
Pre-reqs: The previous videos in the playlist - https://www.youtube.com/playlist?list=PLdgVBOaXkb9D6zw47gsrtE5XqLeRPh27_
Lecture Notes: https://drive.google.com/open?id=1E2I-LpQcKV-ERMUXqYMOtIH2dZs5EM5E
Patreon: https://www.patreon.com/user?u=4354534
Twitter: https://twitter.com/FacultyOfKhan
Special thanks to my Patrons for supporting me at the $5 level or higher:
- Anonymous
- Cesar Garza
- Odissei
- Alvin Barnabas
- Jacob Soares
- Yenyo Pal
- Lisa Bouchard
- Bernardo Marques
- Connor Mooneyhan
- Richard McNair
- Guillaume Chereau
- Patapom
- Vitor Ciaramella
- McKay Oyler
- Dieter Walter Reule
Видео Contravariant and Covariant Vectors | 2/2 канала Faculty of Khan
I describe two examples of contravariant and covariant tensors. For contravariant tensors, I use the tangent vector of a parametric curve. For a covariant tensor, I use the example of a gradient vector of a scalar field.
Questions/requests? Let me know in the comments!
Pre-reqs: The previous videos in the playlist - https://www.youtube.com/playlist?list=PLdgVBOaXkb9D6zw47gsrtE5XqLeRPh27_
Lecture Notes: https://drive.google.com/open?id=1E2I-LpQcKV-ERMUXqYMOtIH2dZs5EM5E
Patreon: https://www.patreon.com/user?u=4354534
Twitter: https://twitter.com/FacultyOfKhan
Special thanks to my Patrons for supporting me at the $5 level or higher:
- Anonymous
- Cesar Garza
- Odissei
- Alvin Barnabas
- Jacob Soares
- Yenyo Pal
- Lisa Bouchard
- Bernardo Marques
- Connor Mooneyhan
- Richard McNair
- Guillaume Chereau
- Patapom
- Vitor Ciaramella
- McKay Oyler
- Dieter Walter Reule
Видео Contravariant and Covariant Vectors | 2/2 канала Faculty of Khan
Показать
Комментарии отсутствуют
Информация о видео
Другие видео канала
![Mathematical model of epidemics: Development and Analysis (2/2)](https://i.ytimg.com/vi/lHQrlwtPtbg/default.jpg)
![Length Contraction in Special Relativity](https://i.ytimg.com/vi/DJKDF86Ebnw/default.jpg)
![Problem 3: Thresholds, Inactivation, and Dendrite Length Constants](https://i.ytimg.com/vi/1V-EXrc8A3g/default.jpg)
![Dynamical Systems on a Circle | Nonlinear Dynamics](https://i.ytimg.com/vi/M4-L8h-gHHE/default.jpg)
![Real Analysis: The Natural Numbers and Mathematical Induction](https://i.ytimg.com/vi/368PoXE2Zjo/default.jpg)
![Old Channel Introduction](https://i.ytimg.com/vi/sYfe40UlOaE/default.jpg)
![Potentials and Impossibility of Oscillations | Nonlinear Dynamics](https://i.ytimg.com/vi/xlP-WLorYsQ/default.jpg)
![Problem 2: Action Potentials, Channel Inactivation and Refractory Period](https://i.ytimg.com/vi/tQSWknGyG8o/default.jpg)
![The Vertebrobasilar Circulation | Neurology](https://i.ytimg.com/vi/SppLmkAhMm4/default.jpg)
![The Faculty of Khan's 10,000 subscriber Q and A!](https://i.ytimg.com/vi/dn7esLIOqe8/default.jpg)
![Real Analysis: Introduction to Functions](https://i.ytimg.com/vi/opCtwhwXeBk/default.jpg)
![Introducing Weird Differential Equations: Delay, Fractional, Integro, Stochastic!](https://i.ytimg.com/vi/eJaHCZ3ITIc/default.jpg)
![Transcritical Bifurcations | Nonlinear Dynamics and Chaos](https://i.ytimg.com/vi/laHspBUscio/default.jpg)
![Closed Curves and Periodic Curves | Differential Geometry 4](https://i.ytimg.com/vi/0RjjNePffsI/default.jpg)
![Basic Linear Algebra Concepts for Tensors](https://i.ytimg.com/vi/KyBVNZRXgSU/default.jpg)
![Lagrange Equations: Multiple Particles and Constraints](https://i.ytimg.com/vi/Ku3y0nPMr_A/default.jpg)
![The Material Derivative | Fluid Mechanics](https://i.ytimg.com/vi/xlxK0VuY9yY/default.jpg)
![Supercritical and Subcritical Pitchfork Bifurcations | Nonlinear Dynamics and Chaos](https://i.ytimg.com/vi/RdnDqGfhV64/default.jpg)
![Dynamical Systems: Definitions, Terminology, and Analysis](https://i.ytimg.com/vi/5oPSHfKRKvI/default.jpg)
![Laplace's Method and the Stirling Approximation](https://i.ytimg.com/vi/7PuZQhqkWxk/default.jpg)
![Introduction to Operators in Quantum Mechanics](https://i.ytimg.com/vi/KvS7Z0rEutE/default.jpg)