Vector Fields and Potentials

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Related lectures (31)

Page 3 of 4

Differentiating Vector Fields: How Not to Do It

Discusses the challenges in differentiating vector fields on submanifolds and the importance of choosing the right method.

Gradient: Scalar Field

Explores gradient in scalar fields, directional derivatives, and level sets.

Gauss Theorem in R^n+1

Explores the Gauss theorem in R^n+1, covering regular domains, vector fields, surface integrals, and volume calculations.

Divergence Theorem: Green Identities in R²

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

Divergence Explained: Lightboard 2-4

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

Connections: Axiomatic Definition

Explores connections on manifolds, emphasizing the axiomatic definition and properties of derivatives in differentiating vector fields.

Linear Systems in 2D: Stability

Explores stability in linear 2D systems, covering fixed points, vector fields, and phase portraits.

Differentiating Vector Fields: Definition

Introduces differentiating vector fields along curves on manifolds with connections and the unique operator satisfying specific properties.

Vector Fields: Gradient and Divergence

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

Curve Integrals of Vector Fields

Explores curve integrals of vector fields, energy calculations, potential functions, and tangential vectors, with a focus on line integrals and domains.