Surface Normals: Vector Analysis

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Differential Geometry: Parametric Curves & Surfaces

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

Regular Surfaces: Painting with Normal Vectors

Explores regular surfaces and painting with normal vectors, integral calculations, symmetries, and surface orientation.

Linear Algebra: Linear Dependence and Independence

Explores linear dependence and independence of vectors in geometric spaces.

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Covers differentiability in multivariable functions and the existence of tangent planes, emphasizing geometric interpretations and practical applications.

Analytical Geometry: Mixed Product and Determinant

Covers the analytical expression of the mixed product and its applications.

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Explores surfaces in space, including paraboloids, spheres, and hyperboloids, and their equations and intersections.

Surface Integrals: Change of Variables

Explores surface integrals, change of variables, and properties of regular surfaces.

Calculus Applications: Lengths and Surfaces of Revolution

Discusses the applications of calculus in calculating lengths and surfaces of revolution, emphasizing integral calculus and geometric interpretations.