Lectures related to Gradient, divergence

Covers vector fields, gradient, divergence, heat flux, and stress tensors.

Divergence Theorem: Green Identities in R²

Explores the divergence theorem and corollaries related to Green identities in the plane, demonstrating their application through examples.

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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.

Differential Operators: Theorems and Proofs

Covers the concept of differential operators and presents theorems and proofs related to scalar and vector fields.

Divergence of Vector Fields

Explores divergence of vector fields, rotational definitions, and integral derivation applications.

Vector Calculus Review: Maxwell Equations

Covers a review of vector calculus and the Maxwell equations in electromagnetism.

Differential Operators: Gradient and Divergence

Introduces differential operators, gradient, and divergence in vector fields.

Curve Integrals: Gauss/Green Theorem

Explores the application of the Gauss/Green theorem to calculate curve integrals along simple closed curves.

Understanding Positive and Negative Orientation in Curves

Explores positive and negative orientation in curves, emphasizing their impact on tangent and normal vectors.

Neural networks under SGD

Explores the optimization of neural networks using Stochastic Gradient Descent (SGD) and the concept of dual risk versus empirical risk.

Surface Integrals, Divergence Theorem and Stocks' Theorem

Covers surface integrals, the divergence theorem, and Stocks' theorem through examples and analogies.

Vector Analysis: Scalar Fields

Covers the analysis of scalar fields, including divergence, gradient, and Laplacian.

Surface Integrals: Parameterization and Divergence Theorem

Explores surface integrals using parameterization and the divergence theorem, with practical examples included.

Divergence Explained: Lightboard 2-4

Explores how sources and sinks affect the divergence of vector fields.

Surface Integrals: Change of Variables

Explores surface integrals, change of variables, and properties of regular surfaces.

Vector Analysis Review

Covers unit vectors, coordinate system conversion, divergence, and rotational concepts in vector analysis.

Fluids and Electromagnetism

Explores closed and non-closed surfaces, divergence theorem, Stokes theorem, and fluid properties in fluid dynamics and electromagnetism.

Vector Calculus: Gradient, Divergence, Curl

Covers vector calculus concepts like gradient, divergence, and curl with applications in physics and engineering.

Vectors and Tensors: Derivatives and Transformations

Explores gradient, divergence, and integral theorems in vector calculus.