Vector Fields: Gradient and Divergence

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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.

Tensor Transformations

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

Gradient, divergence

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

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 Calculus Review: Maxwell Equations

Covers a review of vector calculus and the Maxwell equations in electromagnetism.

Differential Operators: Gradient and Divergence

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

Differential Operators: Theorems and Proofs

Covers the concept of differential operators and presents theorems and proofs related to scalar and vector fields.

Divergence of Vector Fields

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

Continuum Mechanics: Theory and Applications

Covers the basics of continuum mechanics, including constitutive laws, stress, dynamics, and fluid motion.