Covariance and Contravariance of Vectors

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Covers tensor analysis for arbitrary coordinate systems and introduces Christoffel symbols.

Covers tensor analysis, kinematics, and fluid mechanics in continuum mechanics.

Covers Lorentz transformations, Maxwell equations, and charge conservation in Lorentz invariant physics.

Explores mass conservation in continuum mechanics, covering stress, dynamics, constitutive laws, and solid deformation.

Covers the basics of tensors and indices, including contravariant vectors and tensor operations.

Explores the conservation of linear momentum and stress in a continuum, focusing on governing equations and constitutive laws.

Covers the covariant form of Maxwell equations and properties of the field strength tensor.

Covers the reminder of tensors, vectors, and Lorentz transformations, and the formulation of theory.

Covers the fundamentals of differential geometry of surfaces, including the equilibrium of shells, pressure vessels, and the curvature of surfaces.

Covers the basics of vectors in 3 dimensions, including representation, unit vectors, and basis transformations.

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