Differential Operators: Theorems and Proofs

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Differential Operators: Gradient and Divergence

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

Differential Operators: Vector Analysis

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

Divergence: Vector Calculus

Covers the concept of divergence in vector calculus and its computation with examples.

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.

Curve Integrals: Gauss/Green Theorem

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

Tensor Transformations

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

Divergence of Vector Fields

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

Divergence Theorem: Green Identities in R²

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

Vector Fields: Gradient and Divergence

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