Regular Surfaces: Painting with Normal Vectors

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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.

Surface Normals: Vector Analysis

Explains surface normals for parametric and implicit surfaces, focusing on vector analysis and examples with spheres.

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Closed Surfaces and Integrals

Explains closed surfaces like spheres, cubes, and cones without covers, and their traversal and removal of edges.

Vector Calculus: Line Integrals

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

Surface of Revolution

Explains the parametric equations of surfaces of revolution generated by curves in space.

Total Differential: Definition and Integrals

Explores the definition of total differential and its applications in integral calculus.

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.

Differential Geometry: Parametric Curves & Surfaces

Introduces the basics of differential geometry for parametric curves and surfaces, covering curvature, tangent vectors, and surface optimization.

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