https://bit.ly/PG_Patreon - Help me make these videos by supporting me on Patreon!
https://lem.ma/LA - Linear Algebra on Lemma
https://lem.ma/prep - Complete SAT Math Prep
http://bit.ly/ITCYTNew - My Tensor Calculus Textbook

Views: 13334
MathTheBeautiful

https://bit.ly/PG_Patreon - Help me make these videos by supporting me on Patreon!
https://lem.ma/LA - Linear Algebra on Lemma
https://lem.ma/prep - Complete SAT Math Prep
http://bit.ly/ITCYTNew - My Tensor Calculus Textbook

Views: 5711
MathTheBeautiful

https://bit.ly/PG_Patreon - Help me make these videos by supporting me on Patreon!
https://lem.ma/LA - Linear Algebra on Lemma
https://lem.ma/prep - Complete SAT Math Prep
http://bit.ly/ITCYTNew - My Tensor Calculus Textbook

Views: 4340
MathTheBeautiful

Views: 7896
MathTheBeautiful

Complete playlist: http://bit.ly/PDEonYT Lemma http://lem.ma is the place to be!
These videos represent an entire course on Partial Differential Equations (PDEs). A strong emphasis is made on the Linear Algebra (http://lem.ma/LA) structure of the subject.
All questions asked in the comments will be promptly answered.
Pavel Grinfeld

Views: 3930
MathTheBeautiful

Views: 50371
MathTheBeautiful

This course will continue on Patreon at http://bit.ly/PavelPatreon
Textbook: http://bit.ly/ITCYTNew
Solutions: http://bit.ly/ITACMS_Sol_Set_YT Errata: http://bit.ly/ITAErrata
McConnell's classic: http://bit.ly/MCTensors
Weyl's masterpiece: http://bit.ly/SpaceTimeMatter Levi-Civita's classic: http://bit.ly/LCTensors Linear Algebra Videos: http://bit.ly/LAonYT
Table of Contents of http://bit.ly/ITCYTNew
Rules of the Game
Coordinate Systems and the Role of Tensor Calculus
Change of Coordinates
The Tensor Description of Euclidean Spaces
The Tensor Property
Elements of Linear Algebra in Tensor Notation
Covariant Differentiation
Determinants and the Levi-Civita Symbol
The Tensor Description of Embedded Surfaces
The Covariant Surface Derivative
Curvature
Embedded Curves
Integration and Gauss’s Theorem
The Foundations of the Calculus of Moving Surfaces
Extension to Arbitrary Tensors
Applications of the Calculus of Moving Surfaces
Index:
Absolute tensor
Affine coordinates
Arc length
Beltrami operator
Bianchi identities
Binormal of a curve
Cartesian coordinates
Christoffel symbol
Codazzi equation
Contraction theorem
Contravaraint metric tensor
Contravariant basis
Contravariant components
Contravariant metric tensor
Coordinate basis
Covariant basis
Covariant derivative
Metrinilic property
Covariant metric tensor
Covariant tensor
Curl
Curvature normal
Curvature tensor
Cuvature of a curve
Cylindrical axis
Cylindrical coordinates
Delta systems
Differentiation of vector fields
Directional derivative
Dirichlet boundary condition
Divergence
Divergence theorem
Dummy index
Einstein summation convention
Einstein tensor
Equation of a geodesic
Euclidean space
Extrinsic curvature tensor
First groundform
Fluid film equations
Frenet formulas
Gauss’s theorem
Gauss’s Theorema Egregium
Gauss–Bonnet theorem
Gauss–Codazzi equation
Gaussian curvature
Genus of a closed surface
Geodesic
Gradient
Index juggling
Inner product matrix
Intrinsic derivative
Invariant
Invariant time derivative
Jolt of a particle
Kronecker symbol
Levi-Civita symbol
Mean curvature
Metric tensor
Metrics
Minimal surface
Normal derivative
Normal velocity
Orientation of a coordinate system
Orientation preserving coordinate change
Relative invariant
Relative tensor
Repeated index
Ricci tensor
Riemann space
Riemann–Christoffel tensor
Scalar
Scalar curvature
Second groundform
Shift tensor
Stokes’ theorem
Surface divergence
Surface Laplacian
Surge of a particle
Tangential coordinate velocity
Tensor property
Theorema Egregium
Third groundform
Thomas formula
Time evolution of integrals
Torsion of a curve
Total curvature
Variant
Vector
Parallelism along a curve
Permutation symbol
Polar coordinates
Position vector
Principal curvatures
Principal normal
Quotient theorem
Radius vector
Rayleigh quotient
Rectilinear coordinates
Vector curvature normal
Vector curvature tensor
Velocity of an interface
Volume element
Voss–Weyl formula
Weingarten’s formula
Applications: Differenital Geometry, Relativity

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This course is on Lemma: http://lem.ma Lemma looking for developers: http://lem.ma/jobs
Other than http://lem.ma, I recommend Strang http://bit.ly/StrangYT, Gelfand http://bit.ly/GelfandYT, and my short book of essays http://bit.ly/HALAYT
Questions and comments below will be promptly addressed.
Linear Algebra is one of the most important subjects in mathematics. It is a subject with boundless practical and conceptual applications.
Linear Algebra is the fabric by which the worlds of geometry and algebra are united at the most profound level and through which these two mathematical worlds make each other far more powerful than they ever were individually.
Virtually all subsequent subjects, including applied mathematics, physics, and all forms of engineering, are deeply rooted in Linear Algebra and cannot be understood without a thorough understanding of Linear Algebra. Linear Algebra provides the framework and the language for expressing the most fundamental relationships in virtually all subjects.
This collection of videos is meant as a stand along self-contained course. There are no prerequisites. Our focus is on depth, understanding and applications. Our innovative approach emphasizes the geometric and algorithmic perspective and was designed to be fun and accessible for learners of all levels.
Numerous exercises will be provided via the Lemma system (under development)
We will cover the following topics:
Vectors
Linear combinations
Decomposition
Linear independence
Null space
Span
Linear systems
Gaussian elimination
Matrix multiplication and matrix algebra
The inverse of a matrix
Elementary matrices
LU decomposition
LDU decomposition
Linear transformations
Determinants
Cofactors
Eigenvalues
Eigenvectors
Eigenvalue decomposition (also known as the spectral decomposition)
Inner product (also known as the scalar product and dot product)
Self-adjoint matrices
Symmetric matrices
Positive definite matrices
Cholesky decomposition
Gram-Schmidt orthogonalization
QR decomposition
Elements of numerical linear algebra
I’m Pavel Grinfeld. I’m an applied mathematician. I study problems in differential geometry, particularly with moving surfaces.

Views: 3704
MathTheBeautiful

This course is on Lemma: http://lem.ma Lemma looking for developers: http://lem.ma/jobs
Other than http://lem.ma, I recommend Strang http://bit.ly/StrangYT, Gelfand http://bit.ly/GelfandYT, and my short book of essays http://bit.ly/HALAYT
Questions and comments below will be promptly addressed.
Linear Algebra is one of the most important subjects in mathematics. It is a subject with boundless practical and conceptual applications.
Linear Algebra is the fabric by which the worlds of geometry and algebra are united at the most profound level and through which these two mathematical worlds make each other far more powerful than they ever were individually.
Virtually all subsequent subjects, including applied mathematics, physics, and all forms of engineering, are deeply rooted in Linear Algebra and cannot be understood without a thorough understanding of Linear Algebra. Linear Algebra provides the framework and the language for expressing the most fundamental relationships in virtually all subjects.
This collection of videos is meant as a stand along self-contained course. There are no prerequisites. Our focus is on depth, understanding and applications. Our innovative approach emphasizes the geometric and algorithmic perspective and was designed to be fun and accessible for learners of all levels.
Numerous exercises will be provided via the Lemma system (under development)
We will cover the following topics:
Vectors
Linear combinations
Decomposition
Linear independence
Null space
Span
Linear systems
Gaussian elimination
Matrix multiplication and matrix algebra
The inverse of a matrix
Elementary matrices
LU decomposition
LDU decomposition
Linear transformations
Determinants
Cofactors
Eigenvalues
Eigenvectors
Eigenvalue decomposition (also known as the spectral decomposition)
Inner product (also known as the scalar product and dot product)
Self-adjoint matrices
Symmetric matrices
Positive definite matrices
Cholesky decomposition
Gram-Schmidt orthogonalization
QR decomposition
Elements of numerical linear algebra
I’m Pavel Grinfeld. I’m an applied mathematician. I study problems in differential geometry, particularly with moving surfaces.

Views: 3246
MathTheBeautiful

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MathTheBeautiful

Complete playlist: http://bit.ly/PDEonYT Lemma http://lem.ma is the place to be!
These videos represent an entire course on Partial Differential Equations (PDEs). A strong emphasis is made on the Linear Algebra (http://lem.ma/LA) structure of the subject.
All questions asked in the comments will be promptly answered.
Pavel Grinfeld

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This course is on Lemma: http://lem.ma Lemma looking for developers: http://lem.ma/jobs
Other than http://lem.ma, I recommend Strang http://bit.ly/StrangYT, Gelfand http://bit.ly/GelfandYT, and my short book of essays http://bit.ly/HALAYT
Questions and comments below will be promptly addressed.
Linear Algebra is one of the most important subjects in mathematics. It is a subject with boundless practical and conceptual applications.
Linear Algebra is the fabric by which the worlds of geometry and algebra are united at the most profound level and through which these two mathematical worlds make each other far more powerful than they ever were individually.
Virtually all subsequent subjects, including applied mathematics, physics, and all forms of engineering, are deeply rooted in Linear Algebra and cannot be understood without a thorough understanding of Linear Algebra. Linear Algebra provides the framework and the language for expressing the most fundamental relationships in virtually all subjects.
This collection of videos is meant as a stand along self-contained course. There are no prerequisites. Our focus is on depth, understanding and applications. Our innovative approach emphasizes the geometric and algorithmic perspective and was designed to be fun and accessible for learners of all levels.
Numerous exercises will be provided via the Lemma system (under development)
We will cover the following topics:
Vectors
Linear combinations
Decomposition
Linear independence
Null space
Span
Linear systems
Gaussian elimination
Matrix multiplication and matrix algebra
The inverse of a matrix
Elementary matrices
LU decomposition
LDU decomposition
Linear transformations
Determinants
Cofactors
Eigenvalues
Eigenvectors
Eigenvalue decomposition (also known as the spectral decomposition)
Inner product (also known as the scalar product and dot product)
Self-adjoint matrices
Symmetric matrices
Positive definite matrices
Cholesky decomposition
Gram-Schmidt orthogonalization
QR decomposition
Elements of numerical linear algebra
I’m Pavel Grinfeld. I’m an applied mathematician. I study problems in differential geometry, particularly with moving surfaces.

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Complete playlist: http://bit.ly/PDEonYT Lemma http://lem.ma is the place to be!
These videos represent an entire course on Partial Differential Equations (PDEs). A strong emphasis is made on the Linear Algebra (http://lem.ma/LA) structure of the subject.
All questions asked in the comments will be promptly answered.
Pavel Grinfeld

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