Lectures related to Divergence theorem

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

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

Nonlinear Equations: Bisection and Fixed-Point Methods

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

Divergence Theorem: Green Identities in R²

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

Green Theorems: Divergence Theorem and Identities of Green

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

Gradient, divergence

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

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.

Vector Fields: Gradient and Divergence

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

Green's Theorem: Understanding Rotations and Closed Paths

Explores Green's Theorem, rotations, closed paths, and integral signs.

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Green Theorems: Gauss Application

Covers the Green and Gauss theorems, focusing on their applications in vector calculus.

Understanding Surface Integrals

Explores surface integrals, emphasizing physical interpretation and mathematical calculations in vector fields and domains.

Surface Integrals, Divergence Theorem

Covers surface integrals, divergence theorem, and regular domains in 2D and 3D.

Understanding Positive and Negative Orientation in Curves

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

Tangent and Normal Vectors: Curves in R^2

Covers the parameterization of curves, tangent and normal vectors, simple closed curves, exterior normal, regular curves, and domains in R^2.

Neural networks under SGD

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

Conformal Ward Identities

Covers the stress tensor, Weyl invariance, and the integral form of conformal Ward identities.

Surface Integrals, Divergence Theorem and Stocks' Theorem

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

Surface Integrals: Change of Variables

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

Surface Integrals: Parameterization and Divergence Theorem

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