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Lecture
Vector Analysis: Scalar Fields
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Related lectures (29)
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Geometrical Aspects of Differential Operators
Explores differential operators, regular curves, norms, and injective functions, addressing questions on curves' properties, norms, simplicity, and injectivity.
Differential Operators: Gradient and Divergence
Introduces differential operators, gradient, and divergence in vector fields.
Differential Operators: Vector Analysis
Covers differential operators, vector analysis, Fourier analysis, and potential fields with applications to gravity.
Curl in 2D: Rotation and Examples
Explores curl in 2D vector fields, demonstrating its rotation concept through examples and its application in physics.
Curve Integrals of Vector Fields
Explores curve integrals of vector fields, emphasizing energy considerations for motion against or with wind, and introduces unit tangent and unit normal vectors.
Continuity Equations: Internal Entropy Production
Explores continuity equations and internal entropy production in various coordinate systems, emphasizing scalar functions and vector quantities.
Divergence Theorem: Green Identities in R²
Explores the divergence theorem and corollaries related to Green identities in the plane, demonstrating their application through examples.
Vector Analysis: Second Class
Covers the mathematical operations in vector fields and their applications.
Divergence of Vector Fields
Explores divergence of vector fields, rotational definitions, and integral derivation applications.
Vector Analysis Review
Covers unit vectors, coordinate system conversion, divergence, and rotational concepts in vector analysis.
Fourier Analysis: Series and Divergence Theorem
Covers Fourier analysis, series convergence, divergence theorem, and vector analysis.
Tensor Transformations
Introduces tensor transformations, rotation matrices, and differential operators in mechanics.
Curve Integrals: Gauss/Green Theorem
Explores the application of the Gauss/Green theorem to calculate curve integrals along simple closed curves.
Vector Calculus Review: Maxwell Equations
Covers a review of vector calculus and the Maxwell equations in electromagnetism.
Neural networks under SGD
Explores the optimization of neural networks using Stochastic Gradient Descent (SGD) and the concept of dual risk versus empirical risk.
Vector Analysis: Gradient, Divergence, Curl
Covers the fundamental concepts of vector analysis, including the gradient, divergence, and curl operators.
Differential Operators: Theorems and Proofs
Covers the concept of differential operators and presents theorems and proofs related to scalar and vector fields.
Vector Calculus: Divergence and Notation
Explores divergence in vector fields, Laplacian notation, and proof for scalar and vector Laplacians.
Vector Fields: Gradient and Divergence
Covers vector fields, gradient, divergence, heat flux, and stress tensors.
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