Vector Fields and Frenet Frame

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Geometrical Aspects of Differential Operators

Explores differential operators, regular curves, norms, and injective functions, addressing questions on curves' properties, norms, simplicity, and injectivity.

Mechanics of Kirchhoff Rods I

Covers the mechanics of slender structures, focusing on exact kinematics and equilibrium equations of rods.

Vector Fields Analysis

Explores vector fields analysis, covering curvilinear integrals, potential fields, and field connectivity conditions.

Vector Calculus: Line Integrals

Covers the concept of line integrals and their application in vector fields.

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.

Differentiating Vector Fields: Definition

Introduces differentiating vector fields along curves on manifolds with connections and the unique operator satisfying specific properties.

Surface Integrals, Divergence Theorem and Stocks' Theorem

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

Curvilinear Coordinates: Calculations and Examples

Covers curvilinear coordinates and area calculations using double integrals with examples of different curves.

Coordinate Systems: Polar and Spherical

Covers polar and spherical coordinate systems, position vectors, equations of motion, and Frenet frame concepts.

Covariant derivatives along curves

Explores covariant derivatives along curves and second-order optimality conditions in vector fields and manifolds.