Vector Analysis: Gradient, Divergence, Curl

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Divergence Theorem: Green Identities in R²

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

Electrostatics and Coulomb Force

Covers electrostatics, Coulomb force, and image charge method in electromagnetism.

Differential Operators: Vector Analysis

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

Curl in 2D: Rotation and Examples

Explores curl in 2D vector fields, demonstrating its rotation concept through examples and its application in physics.

Vector Fields and Lorentz Tensors: Representation Theory

Covers the transformation properties of vector fields and their representation in Lorentz tensors.

Tensor Transformations

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

Electric Potential & Gauss's Law

Explores electric potential, Gauss's law, and the relationship between field vectors and charges.

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, emphasizing energy considerations for motion against or with wind, and introduces unit tangent and unit normal vectors.

Second Maxwell's equation: Magnetic dipole

Covers Maxwell's equations, magnetic dipoles, vector potential, torque, and field patterns.