Descriptive Geometry: Cones and Cylinders

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Covers linear pressure vessels, thin shells, and critical buckling pressure, emphasizing the dimensional reduction from 3D to 2D.

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Explores geometric surfaces, rules between shapes, and architectural applications.

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Covers the equations for curves and surfaces in space, including parametric and particular surfaces.

Differential Geometry: Parametric Curves & Surfaces

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

Developable Surfaces and Parametrization

Explores developable surfaces, parametrization, equations verification, and conformally flat surfaces.

Quadratic Surfaces in 3D Space

Explores quadratic surfaces in 3D space, discussing hyperboloids and their Cartesian equations, emphasizing the importance of reference frames.

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.

Real Surfaces: Defects and Reconstructions

Explores the difference between ideal and real surfaces, defects, and surface reconstructions.

Surfaces in Space

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

Descriptive Geometry: Cones and Cylinders

Explores tangent planes to cones and cylinders, parallel and perpendicular to given directions.