Gradient, divergence

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Related lectures (31)

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Vector Analysis: Scalar Fields

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

Tensor Transformations

Introduces tensor transformations, rotation matrices, and differential operators in mechanics.

Continuity Equations: Internal Entropy Production

Explores continuity equations and internal entropy production in various coordinate systems, emphasizing scalar functions and vector quantities.

Deformable Bodies: Stress Tensors and Divergence Theorem

Explores stress tensors and the divergence theorem in deformable bodies through examples and demonstrations.

Spherical Coordinates: Conversion and Applications

Covers the conversion and applications of spherical coordinates in mathematical and physical contexts.

Introduction: Mathematical background

Covers basics of modeling for micro/nano devices and emphasizes the importance of computational thinking in understanding and improving device design.

Vector Fields: Gradient and Divergence Log in to Mediaspace to watch this video

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

Divergence Theorem: Green Identities in R² Log in to Mediaspace to watch this video

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

Curve Integrals of Vector Fields Log in to Mediaspace to watch this video

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 Log in to Mediaspace to watch this video

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

Divergence of Vector Fields Log in to Mediaspace to watch this video

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

Vector Calculus Review: Maxwell Equations Log in to Mediaspace to watch this video

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

Differential Operators: Gradient and Divergence Log in to Mediaspace to watch this video

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

Curve Integrals: Gauss/Green Theorem Log in to Mediaspace to watch this video

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

Understanding Positive and Negative Orientation in Curves Log in to Mediaspace to watch this video

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

Neural networks under SGD Log in to Mediaspace to watch this video

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 Log in to Mediaspace to watch this video

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

Surface Integrals: Parameterization and Divergence Theorem Log in to Mediaspace to watch this video

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

Divergence Explained: Lightboard 2-4 Log in to Mediaspace to watch this video

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

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