Curve Integrals of Vector Fields

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Curvilinear Integrals: Interpretation and Convexity

Explores the interpretation of curvilinear integrals in vector fields and the proof of potential fields.

Geometric Meaning of Line Integrals

Explores the geometric interpretation of line integrals in altimetric profiles of cycling stages.

Vectorial Fields: Parametrization and Stokes' Theorem

Covers the parametrization of vectorial fields and the application of Stokes' theorem.

Surface Integrals, Divergence Theorem and Stocks' Theorem

Covers surface integrals, the divergence theorem, and Stocks' theorem through examples and analogies.

Divergence of Vector Fields

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

Surface Integrals: Vector Fields

Explains the surface integral for vector fields and demonstrates its calculation process through examples.

Curve Integrals: Properties and Applications

Explores curve integrals, demonstrating properties and real-life applications, including tunnel excavation and safety assessment based on crime density.

Turbulence: Numerical Flow Simulation

Explores turbulence characteristics, simulation methods, and modeling challenges, providing guidelines for choosing and validating turbulence models.

Electric Fields: Curl and Path Integrals, Spherical Coordinates Supplement

Explores the integration of electric fields along paths and solutions for constant and radial fields.

Vector Calculus: Green's Theorem

Explores Green's theorem, vector field curl, Ampère's law, and magnetic field modeling.