Channel Title: Faculty of Khan Channel Description: Greetings students! I'm the Faculty of Khan. The name comes from my last name (Khan) and the university-level focus of my channel (since universities are often divided into separate 'Faculties' e.g. Faculty of Science). My post-secondary training has included a broad array of subjects, including Mathematics, Physics, Physiology, Medicine, and Chemical Engineering, which reflects the broad focus of my channel! If you think this is all worth your while, then go ahead and subscribe! <video> Lorentz Scalars and Proper Time | Special Relativity Description: Introduction to Lorentz scalars as invariants with Lorentz transformations and a deeper dive into the idea of proper time, and its use as a surrogate for arc length in Relativity. Questions/requests? Let me know in the comments! Pre-reqs: previous videos in this playlist - https://www.youtube.com/playlist?list=PLdgVBOaXkb9CkdpdSWT9oPDSvQ8BjjNTq Lecture Notes: https://drive.google.com/file/d/1Mlrm8c3kIhYQ_CTjl9JO810-qSfJVoKC/view?usp=drive_link Special thanks to my Patrons: Matthew Patapom Eugene Bulkin Andy Johnston Lina Stritt Patrick Gibson Joseph Dubeau </video> <video> The Geodesic Equation: Introduction and Derivation Description: One of my most important videos in Tensor Calculus...and in Calculus of Variations...and in Differential Geometry...and in General Relativity: the geodesic equation derived from first principles! This powerful equation will let you solve for the geodesic between two points on any Riemannian manifold as long as you have the metric tensor in handy. Questions/requests? Let me know in the comments! Pre-reqs: The previous videos in these playlists - https://www.youtube.com/playlist?list=PLdgVBOaXkb9D6zw47gsrtE5XqLeRPh27_ https://www.youtube.com/playlist?list=PLdgVBOaXkb9CD8igcUr9Fmn5WXLpE8ZE_ This Differential Geometry video on arc length reparametrization might also come in handy: https://www.youtube.com/watch?v=QXRsgPw5wmc&list=PLdgVBOaXkb9DJjk8V0-RkXTnD4ZXUOFsc&index=3 Lecture Notes: https://drive.google.com/file/d/115NG6FqLx-3isq-sgeIT61tk_moDwGeN/view?usp=drive_link Special thanks to my Patrons: Matthew Patapom Eugene Bulkin Andy Johnston Lina Stritt Patrick Gibson EDIT: there should be a factor of 1/2 on the right-hand side at 10:45. </video> <video> Dual Vector Properties and Raising/Lowering Indices Description: My second video on dual vectors discusses their properties and how they can be converted to their vector counterparts via the all-important Metric Tensor, which is introduced once again! Questions/requests? Let me know in the comments! Pre-reqs: Previous videos in this playlist - https://www.youtube.com/playlist?list=PLdgVBOaXkb9D6zw47gsrtE5XqLeRPh27_ Lecture Notes: https://drive.google.com/file/d/1iF4cAkClQaN6pZmoexxr7kx_XodmAUPh/view?usp=drive_link Special thanks to my Patrons: Matthew Patapom Eugene Bulkin Andy Johnston Lina Stritt Patrick Gibson Joseph Dubeau </video> <video> Harmonic Functions and Harmonic Conjugates | Complex Variables Description: An introduction to harmonic functions and harmonic conjugates in Complex Analysis, by relating these functions to the all-important Cauchy-Riemann relations. I prove in this video that a complex function is analytic if it is composed of two harmonic functions with the imaginary part of the function being a harmonic conjugate of the real part. I also work through an example involving a harmonic function. Questions/requests? Let me know in the comments! Pre-reqs: My basic #ComplexVariables playlist: https://www.youtube.com/playlist?list=PLdgVBOaXkb9CNMqbsL9GTWwU542DiRrPB Lecture Notes: https://drive.google.com/file/d/1nD30g1YTGNBKDivzltVaL_m-8KnszMb_/view?usp=drive_link Special thanks to my Patrons: Matthew Patapom Eugene Bulkin Andy Johnston Lina Stritt Patrick Gibson </video> <video> Wave Equation Solution for a Finite Domain: Standing Waves | Part 2/2 Description: In this video, I finish solving the wave equation for a finite domain, using good ol' separation of variables. Questions/requests? Let me know in the comments! Prereqs: Previous videos in this playlist: https://www.youtube.com/playlist?list=PLdgVBOaXkb9Ab7UM8sCfQWgdbzxkXTNVD Lecture Notes: https://drive.google.com/file/d/1fygY0e5MQfYUCZVNmR68ofjtM4AJQXF4/view?usp=drive_link Special thanks to my Patrons: Matthew Patapom Eugene Bulkin Andy Johnston Lina Stritt Patrick Gibson Joseph Dubeau </video> <video> The Covariant Derivative of a Tensor Description: In this video on #TensorCalculus, I develop the covariant derivative for both a contravariant tensor and a covariant tensor (the formulas are different in either case). Questions/requests? Let me know in the comments! Pre-reqs: The previous videos in the playlist (especially the one on transforming Christoffel symbols) - https://www.youtube.com/playlist?list=PLdgVBOaXkb9D6zw47gsrtE5XqLeRPh27_ Lecture Notes: https://drive.google.com/file/d/1CKmpoq2AAYiTAB5tZETqPoIfF5_3mIgB/view?usp=drive_link Special thanks to my Patrons: Matthew Patapom Eugene Bulkin Andy Johnston Lina Stritt Patrick Gibson </video> <video> Introducing 4-vectors in Special Relativity Description: Introduction to 4-vectors in Special Relativity, including their definition and key properties. The key example discussed in this video is the 4-vector for displacement/4-displacement. Questions/requests? Let me know in the comments! Pre-reqs: previous videos in this playlist - https://www.youtube.com/playlist?list=PLdgVBOaXkb9CkdpdSWT9oPDSvQ8BjjNTq Lecture Notes: https://drive.google.com/file/d/1dtwGcVwTDs9AxNr8HOrUK96-8jCmzYma/view?usp=drive_link Special thanks to my Patrons: Matthew Patapom Eugene Bulkin Andy Johnston Lina Stritt Patrick Gibson Joseph Dubeau </video> <video> The Metric of Flat Spacetime: Introducing the Minkowski Metric Description: Introduction and development of the Minkowski metric, using basic principles of dot products and the definition of the spacetime interval that we've discussed in previous videos on Special Relativity. Questions/requests? Let me know in the comments! Pre-reqs: basic Linear Algebra (matrix multiplication, what a dot product is) and previous videos in this playlist - https://www.youtube.com/playlist?list=PLdgVBOaXkb9CkdpdSWT9oPDSvQ8BjjNTq Lecture Notes: https://drive.google.com/file/d/1HOIkYBfJWDj-9nVDO1INLVDcii-Cv4gN/view?usp=drive_link Special thanks to my Patrons: Matthew Patapom Eugene Bulkin Andy Johnston Lina Stritt Patrick Gibson Joseph Dubeau </video> <video> How to Solve the Wave Equation for a Finite Domain | Part 1/2 | Partial Differential Equations Description: In this video, I begin solving the wave equation for a finite domain, using good ol' separation of variables. Questions/requests? Let me know in the comments! Prereqs: Previous videos in this playlist: https://www.youtube.com/playlist?list=PLdgVBOaXkb9Ab7UM8sCfQWgdbzxkXTNVD Lecture Notes: https://drive.google.com/file/d/1fygY0e5MQfYUCZVNmR68ofjtM4AJQXF4/view?usp=drive_link Special thanks to my Patrons: Matthew Patapom Eugene Bulkin Andy Johnston Lina Stritt Patrick Gibson Joseph Dubeau </video> <video> 4-Momentum and Mass-Energy Equivalence | Special Relativity Description: Development of the 4-momentum and demonstration of Einstein's famous mass-energy relation, E_o = mc^2 and how that arises from the 4-momentum. Questions/requests? Let me know in the comments! Pre-reqs: previous videos in this playlist - https://www.youtube.com/playlist?list=PLdgVBOaXkb9CkdpdSWT9oPDSvQ8BjjNTq Lecture Notes: https://drive.google.com/file/d/1tRe1ddrdWOJhV7qlqy3u_ZWJlg2sh1k8/view?usp=drive_link Special thanks to my Patrons: Matthew Patapom Eugene Bulkin Andy Johnston Lina Stritt Patrick Gibson Joseph Dubeau </video> <video> How to Transform Spacetime Diagrams | Special Relativity Description: A brief introduction, intuition, and overview of basic concepts regarding transformation of spacetime diagrams, and how this process leads to the relativity of simultaneity! Questions/requests? Let me know in the comments! Pre-reqs: Previous videos in this playlist - https://www.youtube.com/playlist?list=PLdgVBOaXkb9CkdpdSWT9oPDSvQ8BjjNTq Lecture Notes: https://drive.google.com/file/d/1tTvtKq0YLcJNzuHODrCzyjwqw614gMme/view?usp=drive_link Special thanks to my Patrons: Matthew Patapom Eugene Bulkin Andy Johnston Lina Stritt Patrick Gibson </video> <video> Deriving Time Dilation and Length Contraction from the Invariant interval | Special Relativity Description: A derivation of time dilation and length contraction using the invariance of the spacetime interval and a bunch of manipulation of spacetime diagrams. Questions/requests? Let me know in the comments! Pre-reqs: Previous videos in this playlist - https://www.youtube.com/playlist?list=PLdgVBOaXkb9CkdpdSWT9oPDSvQ8BjjNTq Lecture Notes: https://drive.google.com/file/d/1z05aU3FDZdHpaIexwZuggIZFld2slce4/view?usp=drive_link Special thanks to my Patrons: Matthew Patapom Eugene Bulkin Andy Johnston Lina Stritt Patrick Gibson Joseph Dubeau </video> <video> The Spacetime Interval and Causality | Special Relativity Description: An overview of the spacetime interval, its invariance, and how the nature of the spacetime interval between two events can be used to infer whether those events can be causally related. Questions/requests? Let me know in the comments! Pre-reqs: Previous videos in this playlist - https://www.youtube.com/playlist?list=PLdgVBOaXkb9CkdpdSWT9oPDSvQ8BjjNTq Lecture Notes: https://drive.google.com/file/d/1daCN2msQFGm1cMBstZv2tg69agZ4-zT5/view?usp=drive_link Special thanks to my Patrons: Matthew Patapom Eugene Bulkin Andy Johnston Lina Stritt Patrick Gibson </video> <video> Introducing Dual Vectors: Intuition and Definition Description: The foil to regular vectors in Tensor Analysis: dual vectors (a.k.a. covectors, one-forms) are best thought of as functions that operate on regular vectors. This video defines dual vectors (starting with the more general abstract definition followed by the tensor algebra definition) and then gives some intuition behind what dual vectors represent. Questions/requests? Let me know in the comments! Pre-reqs: Previous videos in this playlist - https://www.youtube.com/playlist?list=PLdgVBOaXkb9D6zw47gsrtE5XqLeRPh27_ Lecture Notes: https://drive.google.com/file/d/1Y-2hpP6RkOfX7najQkXx45B-_jEOhkyC/view?usp=drive_link Special thanks to my Patrons: Matthew Patapom Eugene Bulkin Andy Johnston Lina Stritt Patrick Gibson Joseph Dubeau </video> <video> 4-Velocity and 4-Acceleration in Special Relativity Description: A continuation of the previous video on 4-vectors, this video goes into more detail by defining and discussing the 4-velocity and 4-acceleration vectors. Some important properties are also highlighted. Questions/requests? Let me know in the comments! Pre-reqs: previous videos in this playlist - https://www.youtube.com/playlist?list=PLdgVBOaXkb9CkdpdSWT9oPDSvQ8BjjNTq Lecture Notes: https://drive.google.com/file/d/1cVJeRNre3-IHvWi06GaFMgS0wYBk8zXt/view?usp=drive_link Special thanks to my Patrons: Matthew Patapom Eugene Bulkin Andy Johnston Lina Stritt Patrick Gibson Joseph Dubeau </video>

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Description

Greetings students!

I'm the Faculty of Khan. The name comes from my last name (Khan) and the university-level focus of my channel (since universities are often divided into separate 'Faculties' e.g. Faculty of Science).

My post-secondary training has included a broad array of subjects, including Mathematics, Physics, Physiology, Medicine, and Chemical Engineering, which reflects the broad focus of my channel!

If you think this is all worth your while, then go ahead and subscribe!

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