Concept

Divergence

Related lectures (28)

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.

Neural networks under SGD

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

Nonlinear Equations: Bisection and Fixed-Point Methods

Explores nonlinear equations, bisection, fixed-point methods, error control, and graphical interpretations of fixed points.

Vector Calculus Review: Maxwell Equations

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

Gradient, divergence

Covers the definitions of gradient and divergence, including the Cartesian coordinate system and the divergence theorem.

Vector Analysis: Scalar Fields

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

Untitled

Divergence of Vector Fields

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

Navier-Stokes: Numerical Flow Simulation

Explores numerical simulation of fluid flow with Navier-Stokes equations, focusing on pressure role and divergence-free velocity fields.

Navier-Stokes: Equations and Simulation

Explores the challenges of Navier-Stokes equations, pressure checkerboard, staggered grid, and the SIMPLE algorithm.

Coordinate Systems: Polar, Cylindrical, Spherical

Covers position, velocity, and acceleration in polar, cylindrical, and spherical coordinate systems.

Curve Integrals: Gauss/Green Theorem

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

Differential Operators: Vector Analysis

Covers differential operators, vector analysis, Fourier analysis, and potential fields with applications to gravity.

Vector Calculus Theorems

Explores the Gauss and Green theorems in vector calculus, showcasing their applications through practical examples and geometric interpretations.

Symmetries and Conservation Laws

Covers symmetries and conservation laws in fluid dynamics, emphasizing the importance of maximizing symmetries in ideal fluid systems.

Linear Shell Theory: Equilibrium and Energy

Covers the expression of the Kirchhoff-Saint Venant energy in a covariant setting and explores equilibrium equations for spherical shells and linear shell theory.

Divergence Explained: Lightboard 2-4

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

Periodic Solutions in Planar Systems

Explores the absence and existence of periodic solutions in planar systems.

Green Theorems: Divergence Theorem and Identities of Green

Explores the application of Green theorems in 2D and 3D spaces.